Chapter 19
ASSET PRICES, CONSUMPTION, AND THE BUSINESS
CYCLE *
JOHN Y. CAMPBELL
Harvard University and NBER. Department of Economics, Littauer Center, Harvard University,
Cambridge, MA 02138, USA
Contents
Abstract 1232
Keywords 1232
1. Introduction 1233
2. International asset market data 1238
3. The equity premium puzzle 1245
3.1. The stochastic discount factor 1245
3.2. Consumption-based asset pricing with power utility 1249
3.3. The riskfree rate puzzle 1252
3.4. Bond returns and the equity premium and riskfrce rate puzzles 1255
3.5. Separating risk aversion and intertemporal substitution 1256
4. The dynamics of asset returns and consumption 1260
4.1. Time-variation in conditional expectations 1260
4.2. A loglinear asset pricing framework 1264
4.3. The stock market volatility puzzle 1268
4.4. Implications for the equity premium puzzle 1272
4.5. What does the stock market forecast? 1275
4.6. Changing volatility in stock returns 1277
4.7. What does the bond market forecast? 1280
5. Cyclical variation in the price of risk 1284
5.1. Habit formation 1284
5.2. Models with heterogeneous agents 1290
* This chapter draws heavily on John Y. Campbell, "Consumption and the Stock Market: Interpreting
International Experience", Swedish Economic Policy Review 3:251-299, Autumn 1996. I am grateful
to the National Science Foundation for financial support, to Tim Chue, Vassil Konstantinov, and Luis
Viceira for able research assistance, to Andrew Abel, Olivier Blanchard, Ricardo Caballero, Robert
Shiller, Andrei Shleifer, John Taylor, and Michael Woodford for helpful comments, and to Barclays
de Zoete Wedd Securities Limited, Morgan Stanley Capital International, David Barr, Bjorn Hansson,
and Paul S6derlind for providing data.
Handbook of Mactveconomics, Volume 1, Edited by J.B. lhylor and M. WoodJbrd
© 1999 Elsevier Science B.V. All tqghts reserved
1231
1232 J..Y Campbell
5.3. Irrationalexpectations
6. Some implications for macroeconomics
References
1293
1296
1298
Abstract
This chapter reviews the behavior of financial asset prices in relation to consumption.
The chapter lists some important stylized facts that characterize US data, and relates
them to recent developments in equilibrium asset pricing theory. Data from other
countries are examined to see which features of the US experience apply more
generally. The chapter argues that to make sense of asset market behavior one needs
a model in which the market price of risk is high, time-varying, and correlated with
the state of the economy. Models that have this feature, including models with habitformation
in utility, heterogeneous investors, and irrational expectations, are discussed.
The main focus is on stock returns and short-term real interest rates, but bond returns
are also considered.
Keywords
JEL classification: G12
Ch. 19." Asset Prices, Consumption, and the Business Cycle 1233
1. Introduction
The behavior of aggregate stock prices is a subject of enduring fascination to investors,
policymakers, and economists. In recent years stock markets have continued to show
some familiar patterns, including high average returns and volatile and procyclical
price movements. Economists have struggled to understand these patterns. If stock
prices are determined by fundamentals, then what exactly are these fundamentals and
what is the mechanism by which they move prices? Researchers, working primarily
with US data, have documented a host of interesting stylized facts about the stock
market and its relation to short-term interest rates and aggregate consumption:
(1) The average real return on stock is high. In quarterly US data over the period
1947.2 to 1996.4, a standard data set that is used throughout this chapter, the
average real stock return has been 7.6% at an annual rate. (Here and throughout
the chapter, the word return is used to mean a log or continuously compounded
return unless otherwise stated.)
(2) The average riskless real interest rate is low. 3-month Treasury bills deliver a
return that is riskless in nominal terms and close to riskless in real terms because
there is only modest uncertainty about inflation at a 3-month horizon. In the
postwar quarterly US data, the average real return on 3-month Treasury bills
has been 0.8% per year.
(3) Real stock returns are volatile, with an annualized standard deviation of 15.5%
in the US data.
(4) The real interest rate is much less volatile. The annualized standard deviation
of the ex post real return on US Treasury bills is 1.8%, and much of this is
due to short-run inflation risk. Less than half the variance of the real bill return
is forecastable, so the standard deviation of the ex ante real interest rate is
considerably smaller than 1.8%.
(5) Real consumption growth is very smooth. The annualized standard deviation
of the growth rate of seasonally adjusted real consumption of nondurables and
services is 1.1% in the US data.
(6) Real dividend growth is extremely volatile at short horizons because dividend
data are not adjusted to remove seasonality in dividend payments. The annualized
quarterly standard deviation of real dividend growth is 28.8% in the US data.
At longer horizons, however, the volatility of dividend growth is intermediate
between the volatility of stock returns and the volatility of consumption growth.
At an annual frequency, for example, the volatility of real dividend growth is
only 6% in the US data.
(7) Quarterly real consumption growth and real dividend growth have a very weak
correlation of 0.06 in the US data, but the correlation increases at lower
frequencies to just over 0.25 at a 4-year horizon.
(8) Real consumption growth and real stock returns have a quarterly correlation of
0.22 in the US data. The correlation increases to 0.33 at a 1-year horizon, and
declines at longer horizons.
1234 J.Y. Campbell
(9) Quarterly real dividend growth and real stock returns have a very weak correlation
of 0.04 in the US data, but the correlation increases dramatically at lower
frequencies to reach 0.51 at a 4-year horizon.
(10) Real US consumption growth is not well forecast by its own history or by
the stock market. The first-order autocorrelation of the quarterly growth rate of
real nondurables and services consumption is a modest 0.2, and the log pricedividend
ratio forecasts less than 5% of the variation of real consumption growth
at horizons of 1 to 4 years.
(11) Real US dividend growth has some short-run forecastability arising from the
seasonality of dividend payments. But it is not well forecast by the stock market.
The log price-dividend ratio forecasts no more than about 8% of the variation
of real dividend growth at horizons of 1 to 4 years.
(12) The real interest rate has some positive serial correlation; its first-order autocorrelation
in postwar quarterly US data is 0.5. However the real interest rate is not
well forecast by the stock market, since the log price-dividend ratio forecasts less
than 1% of the variation of the real interest rate at horizons of 1 to 4 years.
(13) Excess returns on US stock over Treasury bills are highly forecastable. The log
price-dividend ratio forecasts 18% of the variance of the excess return at a 1-year
horizon, 34% at a 2-year horizon, and 51% at a 4-year horizon.
These facts raise two important questions for students of macroeconomics and
finance:
• Why is the average real stock return so high in relation to the average short-term
real interest rate?
• Why is the volatility of real stock returns so high in relation to the volatility of the
short-term real interest rate?
Mehra and Prescott (1985) call the first question the "equity premium puzzle". 1
Finance theory explains the expected excess return on any risky asset over the riskless
interest rate as the quantity of risk times the price of risk. In a standard consumptionbased
asset pricing model of the type studied by Hansen and Singleton (1983), the
quantity of stock market risk is measured by the covariance of the excess stock return
with consumption growth, while the price of risk is the coefficient of relative risk
aversion of a representative investor. The high average stock return and low riskless
interest rate (stylized facts 1 and 2) imply that the expected excess return on stock, the
equity premium, is high. But the smoothness of consumption (stylized fact 5) makes
the covariance of stock returns with consumption low; hence the equity premium can
only be explained by a very high coefficient of risk aversion.
Shiller (1982), Hansen and Jagannathan (1991), and Cochrane and Hansen (1992)
have related the equity premium puzzle to the volatility of the stochastic discount
factor, or equivalently the volatility of the intertemporal marginal rate of substitution
of a representative investor. Expressed in these terms, the equity premium puzzle is
I For excellentrecent surveys,see Cochraneand l-lansen(1992) or Kocherlakota(1996).
Ch. 19: Asset Prices, Consumption, and the Business Cycle 1235
that an extremely volatile stochastic discount factor is required to match the ratio of
the equity premium to the standard deviation of stock returns (the Sharpe ratio of the
stock market).
Some authors, such as Kandel and Stambaugh (1991), have responded to the equity
premium puzzle by arguing that risk aversion is indeed much higher than traditionally
thought. However this can lead to the "riskfree rate puzzle" of Weil (1989). If investors
are very risk averse, then they have a strong desire to transfer wealth from periods with
high consumption to periods with low consumption. Since consumption has tended to
grow steadily over time, high risk aversion makes investors want to borrow to reduce
the discrepancy between future consumption and present consumption. To reconcile
this with the low real interest rate we observe, we must postulate that investors are
extremely patient; their preferences give future consumption almost as much weight
as current consumption, or even greater weight than current consumption. In other
words they have a low or even negative rate of time preference.
I will call the second question the "stock market volatility puzzle". To understand
the puzzle, it is helpful to classify the possible sources of stock market volatility.
Recall first that prices, dividends, and returns are not independent but are linked by an
accounting identity. If an asset's price is high today, then either its dividend must be
high tomorrow, or its return must be low between today and tomorrow, or its price must
be even higher tomorrow. If one excludes the possibility that an asset price can grow
explosively forever in a "rational bubble", then it follows that an asset with a high price
today must have some combination of high dividends over tile indefinite future and low
returns over the indefinite future. Investors must recognize this fact in forming their
expectations, so when an asset price is high investors expect some combination of high
future dividends and low future returns. Movements in prices must then be associated
with some combination of changing expectations ("news") about future dividends and
changing expectations about future returns; the latter can in turn be broken into news
about future riskless real interest rates and news about future excess returns on stocks
over short-term debt.
Until the early 1980s, most financial economists believed that there was very little
predictable variation in stock returns and that dividend news was by far the most
important factor driving stock market fluctuations. LeRoy and Porter (1981) and Shiller
(1981) challenged this orthodoxy by pointing out that plausible measures of expected
future dividends are far less volatile than real stock prices. Their work is related to
stylized facts 6, 9, and 11.
Later in the 1980s Campbell and Shiller (1988), Fama and French (1988a,b, 1989),
Poterba and Summers (1988) and others showed that real stock returns are highly
forecastable at long horizons. The variables that predict returns are ratios of stock
prices to scale factors such as dividends, earnings, moving averages of earnings, or
the book value of equity. When stock prices are high relative to these scale factors,
subsequent long-horizon real stock returns tend to be low. This predictable variation
in stock returns is not matched by any equivalent variation in long-term real interest
rates, which are comparatively stable and do not seem to move with the stock market.
1236 J.Y. Campbell
in the late 1970s, for example, real interest rates were unusually low yet stock prices
were depressed, implying high forecast stock returns; the 1980s saw much higher real
interest rates along with buoyant stock prices, implying low forecast stock returns. Thus
excess returns on stock over Treasury bills are just as forecastable as real returns on
stock. This work is related to stylized facts 12 and 13. Campbell (1991) uses this
evidence to show that the great bulk of stock market volatility is associated with
changing forecasts of excess stock returns. Changing forecasts of dividend growth and
real interest rates are much less important empirically.
The stock market volatility puzzle is closely related to the equity premium puzzle. A
complete model of stock market behavior must explain both the average level of stock
prices and their movements over time. One strand of work on the equity premium
puzzle makes this explicit by studying not the consumption covariance of measured
stock returns, but the consumption covariance of returns on hypothetical assets whose
dividends are determined by consumption. The same model is used to generate both
the volatility of stock prices and the implied equity premium. This was the approach of
Mehra and Prescott (1985), and many subsequent authors have followed their lead.
Unfortunately, it is not easy to construct a general equilibrium model that fits all
the stylized facts given above. The standard model of Mehra and Prescott (1985) gets
variation in stock price-dividend ratios only from predictable variation in consumption
growth which moves the expected dividend growth rate and the riskless real interest
rate. The model is not consistent with the empirical evidence for predictable variation
in excess stock returns. Bond market data pose a further challenge to this standard
model of stock returns. In the model, stocks behave very much like long-term real
bonds; both assets are driven by long-term movements in the riskless real interest rate.
Thus parameter values that produce a large equity premium tend also to produce a large
term premium on real bonds. While there is no direct evidence on real bond premia,
nominal bond premia have historically been much smaller than equity premia.
Since the data suggest that predictable variation in excess returns is an important
source of stock market volatility, researchers have begun to develop models in which
the quantity of stock market risk or the price of risk change through time. ARCH
models and other econometric methods show that the conditional variance of stock
returns is highly variable. If this conditional variance is an adequate proxy for
the quantity of stock market risk, then perhaps it can explain the predictability of
excess stock returns. There are several problems with this approach. First, changes in
conditional variance are most dramatic in daily or monthly data and are much weaker
at lower frequencies. There is some business-cycle variation in volatility, but it does not
seem strong enough to explain large movements in aggregate stock prices [Bollerslev,
Chou and Kroner (1992), Schwert (1989)]. Second, forecasts of excess stock returns do
not move proportionally with estimates of conditional variance [Harvey (1989, 1991),
Chou, Engle and Kane (1992)]. Finally, one would like to derive stock market volatility
endogenously within a model rather than treating it as an exogenous variable. There
is little evidence of cyclical variation in consumption or dividend volatility that could
explain the variation in stock market volatility.
Ch. 19: Asset Prices, Consumption, and the Business Cycle 1237
A more promising possibility is that the price of risk varies over time. Time-variation
in the price of risk arises naturally in a model with a representative agent whose utility
displays habit-formation. Campbell and Cochrane (1999), building on the work of Abel
(1990), Constantinides (1990), and others, have proposed a simple asset pricing model
of this sort. Campbell and Cochrane suggest that assets are priced as if there were
a representative agent whose utility is a power function of the difference between
consumption and "habit", where habit is a slow-moving nonlinear average of past
aggregate consumption. This utility fi.mction makes the agent more risk-averse in bad
times, when consumption is low relative to its past history, than in good times, when
consumption is high relative to its past history. Stock market volatility is explained
by a small amount of underlying consumption (dividend) risk, amplified by variable
risk aversion; the equity premium is explained by high stock market volatility, together
with a high average level of risk aversion.
Time-variation in the price of risk can also arise from the interaction of heterogeneous
agents. Constantinides and Duffle (l 996) develop a simple framework with many
agents who have identical utility functions but heterogeneous streams of labor income;
they show how changes in the cross-sectional distribution of income can generate any
desired behavior of the market price of risk. Grossman and Zhou (1996) and Wang
(1996) move in a somewhat different direction by exploring the interactions of agents
who have different levels of risk aversion.
Some aspects of asset market behavior could also be explained by irrational
expectations of investors. If investors are excessively pessimistic about economic
growth, for example, they will overprice short-term bills and underprice stocks; this
would help to explain the equity premium and riskfree rate puzzles. If investors
overestimate the persistence of variations in economic growth, they will overprice
stocks when growth has been high and underprice them when growth has been low,
producing time-variation in the price of risk [Barsky and DeLong (1993)].
This chapter has three objectives. First, it tries to summarize recent work on stock
price behavior, much of which is highly technical, in a way that is accessible to a
broader professional audience. Second, the chapter summarizes stock market data from
other countries and asks which of the US stylized facts hold true more generally.
The recent theoretical literature is used to guide the exploration of the international
data. Third, the chapter systematically compares stock market data with bond market
data. This is an important discipline because some popular models of stock prices are
difficult to reconcile with the behavior of bond prices.
The organization of the chapter is as follows. Section 2 introduces the international
data and reviews stylized facts 1-9 to see which of them apply outside the USA.
(Additional details are given in a Data Appendix available on the author's web page
or by request from the author.) Section 3 discusses the equity premium puzzle, taking
the volatility of stock returns as given. Section 4 discusses the stock market volatility
puzzle; this section also reviews stylized facts 10-13 in the international data.
Sections 3 and 4 drive one towards the conclusion that the price of risk is both
high and time-varying. It must be high to explain the equity premium puzzle, and it
1238 J. Y Campbell
must be time-varying to explain the predictable variation in stock returns that seems
to be responsible for the volatility of stock returns. Section 5 discusses models which
produce this result, including models with habit-formation in utility, heterogeneous
investors, and irrational expectations. Section 6 draws some implications for other
topics in macroeconomics, including the modelling of investment, labor supply, and
the welfare costs of economic fluctuations.
2. International asset market data
The stylized facts described in the previous section apply to postwar quarterly US data.
Most empirical work on stock prices uses this data set, or a longer annual US time
series originally put together by Shiller (1981). But data on stock prices, interest rates,
and consumption are also available for many other countries.
In this chapter I use an updated version of the international developed-country data
set in Campbell (1996a). The data set includes Morgan Stanley Capital International
(MSCI) stock market data covering the period since 1970. ! combine the MSCI data
with macroeconomic data on consumption, short- and long-term interest rates, and
the price level from the International Financial Statistics (IFS) of the International
Monetary Fund. For some countries the IFS data are only available quarterly over a
shorter sample period, so I use the longest available sample for each country. Sample
start dates range from 1970.1 to 1982.2, and sample end dates range from 1995.1 to
1996.4. I work with data from 11 countries: Australia, Canada, France, Germany, Italy,
Japan, the Netherlands, Sweden, Switzerland, the United Kingdom, and the United
States 2.
For some purposes it is useful to have data over a much longer span of calendar
time. I have been able to obtain annual data for Sweden over the period 1920-1994 and
the UK over the period 1919-1994 to complement the US annual data for the period
1891-1995. The Swedish data come from Frennberg and Hansson (1992) and Hassler,
Lundvik, Persson and S6derlind (1994), while the UK data come from Barclays de
Zoete Wedd Securities (1995) and The Economist (1987) 3.
In working with international stock market data, it is important to keep in mind
that different national stock markets are of very different sizes, both absolutely and in
2 The first version of this paper, following Campbell (1996a), also presented data for Spain. However
Spain, unlike the other countries in the sample, underwent a major political change to democratic
governmentduringthe sampleperiod, and both asset returns and inflationshow dramatic shifts fi'omthe
1970s to the 1980s. It seems more conservativeto consider Spain as an emerging market and exclude
it from the developed-countrydata set.
3 1acknowledgethe invaluableassistance of Bjorn Hansson and Paul S6derlindwith the Swedishdata,
and David Barr with the UK data. Full details about the construction of the quarterly and annual data
are givenin a Data Appendixavailable on the attthor's web page or by request fi'omthe author.
Ch. 19." Asset Prices, Consumption, and the Business Cycle
Table 1
MSCI market capitalization, 1993a
1239
vl v, vi
Country V/ -- (%) - - (%)
(Bill. of US$) GDPi VusMxcl ~f';4Vi
- - (%)
AUL 117.9 41.55 4.65 1.85
CAN 167.3 30.62 6.60 2.63
FR 272.5 22.49 10.75 4.29
GER 280.7 16.83 11.07 4.41
ITA 86.8 9.45 3.42 1.37
JAP 1651.9 39.74 65.16 25.98
NTH 136.7 45.91 5.39 2.15
SWD 62.9 36.22 2.48 0.99
SWT 205.6 87.46 8.12 3.23
UK 758.4 79.52 29.91 11.93
USA MSCI 2535.3 37.25 100.00 39.88
USA CRSP 4875.6 71.64 192.30
a vi is the stock indexmarket capitalizationin billions of 1993 US dollars. All stock index data are
from Morgan StanleyCapital International(MSCI),exceptfor USA-CRSPwhich is from the Center for
Research in SecurityPrices. Vi/GDPi is the indexmarket capitalization as a percentageof 1993 GDP,
Vi/VtjsMscI is the indexmarket capitalizationas a percentage of the market capitalizationof the US
MSCI index, and Vi/(~ i Vi) is the percentage share of the index market capitalizationin the total
market capitalizationof all the MSCI indexes.
Abbreviations:AUL, Australia; CAN, Canada; FR, France; GER, Germany; 1TA,Italy; JPN, Japan;
NTH, Netherlands; SWD, Sweden; SWT, Switzerland;UK, United Kingdom; USA, United States of
America.
proportion to national GDP's. Table 1 illustrates this by reporting several measures of
stock market capitalization for the quarterly MSCI data. Column 1 gives the market
capitalization for each country's MSCI index at the end of 1993, in billions of $US.
Column 2 gives the market capitalization for each country as a fraction of its GDP.
Column 3 gives the market capitalization for each country as a fraction of the US MSCI
index capitalization. Column 4 gives the market capitalization for each country as a
fraction of the value-weighted world MSCI index capitalization. Since the MSCI index
for the United States is only a subset of the US market, the last row of the table
gives the same statistics for the value-weighted index of New York Stock Exchange
and American Stock Exchange stocks reported by the Center for Research in Security
Prices (CRSP) at the University of Chicago.
Table 1 shows that most countries' stock markets are dwarfed by the US market.
Column 3, for example, shows that the Japanese MSCI index is worth only 65% of
the US MSCI index, the UK MSCI index is worth only 30% of the US index, the
French and German MSCI indexes are worth only 11% of the US index, and all
1240 J.Y. Campbell
other countries' indexes are worth less than 10% of the US index. Column 4 shows
that the USA and Japan together account for 66% of the world market capitalization,
while the USA, Japan, the UK, France, and Germany together account for 86%. In
interpreting these numbers one must keep in mind that the MSCI indexes do not cover
the whole market in each country (the US MSCI index, for example, is worth about
half the US CRSP index), but they do give a guide to relative magnitudes across
countries.
Table 1 also shows that different countries' stock market values are very different
as a fraction of GDP. If one thinks that total wealth-output ratios are likely to be
fairly constant across countries, then this indicates that national stock markets are
very different fractions of total wealth in different countries. In highly capitalized
countries such as the UK and Switzerland, the MSCI index accounts for about 80%
of GDP, whereas in Germany and Italy it accounts for less than 20% of GDR The
theoretical convention of treating the stock market as a claim to total consumption, or
as a proxy for the aggregate wealth of an economy, makes much more sense in the
highly capitalized countries 4.
Table 2 reports summary statistics for international asset returns. For each country
the table reports the mean, standard deviation, and first-order autocorrelation of the
real stock return and the real return on a short-term debt instrument 5.
The first line of Table 2 gives numbers for the standard postwar quarterly US data
set summarized in the introduction. The next panel gives numbers for the 11-country
quarterly MSCI data, and the bottom panel gives numbers for the long-term annual
data sets. The table shows that the first four stylized facts given in the introduction are
fairly robust across countries.
(1) Stock markets have delivered average real returns of 5% or better in almost every
country and time period. The exceptions to this occur in short-term quarterly
data, and are concentrated in markets that are particularly small relative to GDP
(Italy), or that predominantly represent claims on natural resources (Australia and
Canada).
(2) Short-term debt has rarely delivered an average real return above 3%. The
exceptions to this occur in two countries, Germany and the Netherlands, whose
sample periods begin in the late 1970s and thus exclude much of the surprise
inflation of the oil-shock period.
4 Stock ownership also tends to be much more concentrated in the countries with low capitalization.
La Porta, Lopez-de-Silanes, Shleifer and Vishny (1997) have related these international patterns to
differences in the protections afforded outside investors by different legal systems.
5 As explained in the Data Appendix, the best available short-term interest rate is sometimes a Treasury
bill rate and sometimes another money market interest rate. Both means and standard deviations are
given in almualizedpercentage points. To annualize the raw quarterly numbers, means are multiplied by
400 while standard deviations are multiplied by 200 (since standard deviations increase with the square
root of the time interval in serially uncorrelated data).
Ch. 19." Asset Prices, Consumption, and the Business Cycle 1241
Table 2
International stock and bill returns a
Country Sample period re o(r~) p(rc) rj-~ a(rf ) p(rj )
USA 1947.2-1996.4 7.569 15.453 0.104 0.794 1.761 0.501
AUL 1970.1 1996.3 2.633 23.459 0.008 1.820 2,604 0.636
CAN 1970.1-1996.3 4,518 16,721 0.119 2.738 1.932 0.674
FR 1973.2-1996.3 7.207 22.877 0,088 2.736 1.917 0.714
GER 1978.4-1996.3 8.135 20.326 0,066 3.338 1.161 0.322
ITA 1971.2-1995.3 0.514 27.244 0.071 2.064 2.957 0.681
JPN 1970.2--1996.3 5.831 21,881 0,017 1.538 2.347 0.493
NTH 1977.2-1996.2 12.721 15.719 0.027 3.705 1.542 -0.099
SWD 1970.1-1995.1 7.948 23.867 0.053 1.520 2.966 0.218
SWT 1982.~1996,3 11.548 20.431 0.112 1.466 1.603 0.255
UK 1970.1-1996,3 7,236 21,555 0,103 1,081 3.067 0,474
USA 1970.1-1996.4 5.893 17.355 0.076 1.350 1,722 0.568
SWD 1920-1994 6.219 18.654 0.064 2.073 5.918 0,708
UK 1919-1994 7.314 22.675 -0.024 1.198 5.446 0.591
USA 1891 1995 6.697 18.634 0.025 1.955 8.919 0.338
a ~ is the mean log real return on the stock market index, multiplied by 400 in quarterly data or 100 in
annual data to express in annualized percentage points, tY(re) is the standard deviation of the log real
return on the market index, multiplied by 200 in quarterly data or 100 in annual data to express in
annualized percentage points, p(re) is the first-order autocorrelation of the log real return on the market
index, rT, o(rf), and p(t).) are defined in the same way for the real return on a 3-month money market
instrument. The money market instruments vary across countries and are described in detail in the Data
Appendix.
Abbreviations: AUL, Australia; CAN, Canada; FR, France; GER, Germany; ITA, Italy; JPN, Japan;
NTH, Netherlands; SWD, Sweden; SWT, Switzerland; UK, United Kingdom; USA, United States of
America.
(3) The annualized standard deviation of stock returns ranges from 15% to 27%. It
is striking that the market with the highest volatility, Italy, is the smallest market
relative to GDP and the one with the lowest average return,
(4) In quarterly data the annualized volatility of real returns on short debt is around
3% for the UK, Italy, and Sweden, around 2.5% for Australia and Japan, and below
2% for all other countries. Volatility is higher in long-term annual data because
of large swings in inflation in the interwar period, particularly in t919-21. Much
of the volatility in these real returns is probably due to unanticipated inflation and
does not reflect volatility in the ex ante real interest rate.
1242 J Y. Campbell
These numbers show that high average stock returns, relative to the returns on shortterm
debt, are not unique to the United States but characterize many other countries as
well. Recently a number of authors have suggested that average excess returns in the
USA may be overstated by sample selection or survivorship bias. if economists study
the USA because it has had an unusually successful economy, then sample average US
stock returns may overstate the true mean US stock return. Brown, Goetzmann and
Ross (1995) present a formal model of this effect. While survivorship bias may affect
data from all the countries included in Table 2, it is reassuring that the stylized facts
are so consistent across these countries 6.
Table 3 turns to data on aggregate consumption and stock market dividends. The
table is organized in the same way as Table 2. It illustrates the robustness of two more
of the stylized facts given in the introduction.
(5) In the postwar period the annualized standard deviation of real consumption
growth is never above 3%. This is true even though data are used on total
consumption, rather than nondurables and services consumption, for all countries
other than the USA. Even in the longer annual data, which include the turbulent
interwar period, consumption volatility slightly exceeds 3% only in the USA.
(6) The volatility of dividend growth is much greater than the volatility of consumption
growth, but generally less than the volatility of stock returns. The exceptions
to this occur in countries with highly seasonal dividend payments; these countries
have large negative autocorrelations for quarterly dividend growth and much
smaller volatility when dividend growth is measured over a full year rather than
over a quarter.
Table 4 reports the contemporaneous correlations among real consumption growth,
real dividend growth, and stock returns. It turns out that these correlations are
somewhat sensitive to the timing convention used for consumption. A timing
convention is needed because the level of consumption is a flow during a quarter
rather than a point-in-time observation; that is, the consumption data are timeaveraged
7. If we think of a given quarter's consumption data as measuring consumption
at the beginning of the quarter, then consumption growth for the quarter is next
quarter's consumption divided by this quarter's consumption. If on the other hand
6 Goetzmalm and Jorion (1997) consider imernational stock-price data from earlier in the 20th Century
and argue that the long-term average real growth rate of stock prices has been higher in the US than
elsewhere. However they do not have data on dividend yields, which are an important component of
total return and are likely to have been particularly important in Europe dtmng the troubled intei~ar
period.
7 Tilne-averaging is one of a number of interrelated issues that arise in relating measured consumption
data to the theoretical concept of consumption. Other issues include measurement error, seasonal
adjustment, and the possibilitythat some goods classified as nondurable in the national income accounts
are in fact durable. Grossman, Melino and Shiller (1987), Wheatley (1988), Miron (1986), and Heaton
(1995) handle time-averaging, measurement error, seasonality, and dinability, respectively, in a much
more careful way than is possible here, while Wilcox (1992) provides a detailed account of the sampling
procedures used to constxuct US consumption data.
Ch. 19." Asset Prices, Consumption, and the Business Cycle 1243
Table 3
International consumption and dividends a
Country Sample period Ac o(Ac) p(Ac) Ad ~r(Ad) p(Ad)
USA 1947.2-1996.4 1.921 1.085 0.221 2.225 28.794 -0.544
AUL 1970.1-1996.3 1.886 2.138 0.351 0.883 36.134 -0.451
CAN 1970.1 1996.3 1.853 2.083 0.113 -0.741 5.783 0.540
FR 1973.2 1996.3 1.600 2.121 --0.093 1.214 13.383 -0.159
GER 1978.4 1996.3 1.592 2.478 -0.328 1.079 8.528 0.018
ITA 1971.2-1995.3 2.341 1.724 0.253 -4.919 19.635 0.294
JPN 1970.2-1996.3 3.384 2.347 -0.225 2.489 4.504 0.363
NTH 1977.2 1996.2 1.661 2.772 -0.265 4.007 4.958 0.277
SWD 1970.1-1995.1 0.705 1.920 0.305 1.861 13.595 0.335
SWT 1982.2-1996.3 0.376 2.246 -0.4t9 4.143 6.156 0.165
UK 1970.1-1996.3 1.991 2.583 -0.017 0.681 7.125 0.335
USA 1970.1 1996.4 1.722 0.917 0.390 0.619 17.229 0.581
SWD 1920 1994 1.790 2.866 0.159 0.423 12.215 0.214
UK 1919-1994 1.443 2.898 0.281 1.844 7.966 0.225
USA 1891-1995 1.773 3.256 -0.117 1.485 14.207 -0.087
a Ac is the mean log real consumption growth rate, multiplied by 400 in quarterly data or 100 in
annual data to express in annualized percentage points, cr(Ac) is the standard deviation of the log
real consumption growth rate, multiplied by 200 in quarterly data or 100 in annual data to express in
annualized percentage points, p(Ac) is the first-order autocorrelation of the log real consumption growth
rate. Ad, a(Ad), and p(Ad) are defined in the same way for the real dividend growth rate. Consumption
is nondurables and selwices consumption in the USA, and total consumption elsewhere.
Abbreviations: AUL, Australia; CAN, Canada; FR, France; GER, Germany; ITA, Italy; JPN, Japan;
NTH, Netherlands; SWD, Sweden; SWT, Switzerland; UK, United Kingdom; USA, United States of
America.
we think of the consumption data as measuring consumption at the end of the
quarter, then consumption growth is this quarter's consumption divided by last quarter's
consumption. Table 4 uses the former, "beginning-of-quarter" timing convention
because this produces a higher contemporaneous correlation between consumption
growth and stock returns.
The timing convention has less effect on correlations when the data are measured
at longer horizons. Table 4 also shows how the correlations among real consumption
growth, real dividend growth, and real stock returns vary with the horizon. Each
pairwise correlation among these series is calculated for horizons of 1, 4, 8, and 16
quarters in the quarterly data and for horizons of 1, 2, 4, and 8 years in the long-term
annual data. The table illustrates three more stylized facts from the introduction.
1244 J.Y. Campbell
%
o
m
0
0
I l l II
II [I
I I I I
II I
I I I I I
I I I I I
;a4zaaza;a a
~ d e m ~ : d ~ d ~ d o NN~
', ~
'~ o "~, . ~ b ~
fa,
>~
N ~
ca
Ch. 19: AssetPrices',Consumption,and the BusinessCycle 1245
(7) Real consumption growth and dividend growth are generally weakly positively
correlated in the quarterly data. In many countries the correlation increases
strongly with the measurement horizon. However long-horizon correlations remain
close to zero for Australia and Switzerland, and are substantially negative for Italy
(with a very small stock market) and Japan (with anomalous dividend behavior).
The correlations of consumption and dividend growth are positive and often quite
large in the longer-term annual data sets.
(8) The correlations between real consumption growth rates and stock returns are quite
variable across countries. They tend to be somewhat higher in high-capitalization
countries (with the notable exception of Switzerland), which is consistent with the
view that stock returns proxy more accurately for wealth returns in these countries.
Correlations typically increase with the measurement horizon out to 1 or 2 years,
and are moderately positive in the longer-term annual data sets.
(9) The correlations between real dividend growth rates and stock returns are small at
a quarterly horizon but increase dramatically with the horizon. This pattern holds
in every country. The correlations also increase strongly with the horizon in the
longer-term annual data.
After this preliminary look at the data, I now use some simple finance theory to
interpret the stylized facts.
3. The equity premium puzzle
3.1. The stochastic discount factor
To understand the equity premium puzzle, consider the intertemporal choice problem
of an investor, indexed by k, who can trade freely in some asset i and can obtain a
gross simple rate of return (1 +Ri,t+l) on the asset held from time t to time t + 1. If
the investor consumes Ck~ at time t and has time-separable utility with discount factor
6 and period utility U(Ckt), then her first-order condition is
g'((~t) = 6E~ [(1 +Ri, l+l)Ut(Ck,t+l)]. (1)
The left-hand side of Eqnation (1) is the marginal utility cost of consuming one real
dollar less at time t; the right-hand side is the expected marginal utility benefit from
investing the dollar in asset i at time t, selling it at time t + 1, and consuming the
proceeds. The investor equates marginal cost and marginal benefit, so Equation (1)
must describe the optimum.
Dividing Equation (1) by U'(C~) yields
v'(G,,+,)]1 = Et (1 +Ri,,~,)6 ~ j --E, [(1 +Ri,,+,)Ma,,+lJ, (2)
where Mk,t.~l = 6U'(Ck, t+l)/U/(Ct) is the intertemporal marginal rate of substitution
of the investor, also known as the stochastic discountjdctor. This way of writing the
1246 J..Y Campbell
model in discrete time is due originally to Grossman and Shiller (1981), while the
continuous-time version of the model is due to Breeden (1979). Cochrane and Hansen
(1992) and Hansen and Jagannathan (1991) have developed the implications of the
discrete-time model in detail.
The derivation just given for Equation (2) assumes the existence of an investor
maximizing a time-separable utility function, but in fact the equation holds more
generally. The existence of a positive stochastic discount factor is guaranteed by the
absence of arbitrage in markets in which non-satiated investors can trade freely without
transactions costs. In general there can be many such stochastic discount factors for
example, different investors k whose marginal utilities follow different stochastic
processes will have different M~,t+l - but each stochastic discount factor must satisfy
Equation (2). It is common practice to drop the subscript k from this equation and
simply write
1 = E, [(1 +&t+,lMi+~]. (3)
In complete markets the stochastic discount factor Mt+l is unique because investors
can trade with one another to eliminate any idiosyncratic variation in their marginal
utilities.
To understand the implications of Equation (3) it is helpful to write the expectation
of the product as the product of expectations plus the covariance,
E1[(1 +Ri,,~l)m~+l] = Et[(l + Ri,,+I)]E~[M,+I] + Covt[R~,l.~,M,+~]. (4)
Substituting into Equation (3) and rearranging gives
1 - Covt[Ri, ¢+1,Mr+l]
1 + E,[R~,,+I] - (5)
Et[Mt+l]
An asset with a high expected simple return must have a low covariance with the
stochastic discount factor. Such an asset tends to have low retunas when investors have
high marginal utility. It is risky in that it fails to deliver wealth precisely when wealth
is most valuable to investors. Investors therefore demand a large risk premium to hold
it.
Equation (5) must hold for any asset, including a riskless asset whose gross simple
return is 1 + Ry;t~1. Since the simple riskless return has zero covariance with the
stochastic discount factor (or any other random variable), it is just the reciprocal of
the expectation of the stochastic discount factor:
1
1 +R/;,+t - Et[M,+I]" (6)
This can be used to rewrite Equation (5) as
1 +Et[Ri,,+t] = (1 +RLt+I)(1 -Cov,[Ri,~+L,Mi+l]). (7)
For simplicity I now follow Hansen and Singleton (1983) and assume that the joint
conditional distribution of asset returns and the stochastic discount factor is lognormal
Ch. 19." Asset Prices, Consumption, and the Business Cycle 1247
and homoskedastic. While these assumptions are not literally realistic - stock returns
in particular have fat-tailed distributions with variances that change over time - they do
make it easier to discuss the main forces that should determine the equity premium.
When a random variable X is conditionally lognormally distributed, it has the
convenient property that
log EtX E~ logX + ½Vart logX, (8)
where VartlogX = G[(logX -EtlogX)2]. If in addition X is conditionally
homoskedastic, then Var, logX = E[(logX - E, logX) 2] = Var(logX - Et logX).
Thus with joint conditional lognormality and homoskedasticity of asset returns and
consumption, I can take logs of Equation (3) and obtain
2
0 = Etri, t+l + Etmt+l + (1) [02 + O£,+ 20,m]. (9)
Here rnt - log(Mr) and r, -- log(1 + Ri,), while 02 denotes the unconditional variance
of log return innovations Var(r/, t+t -Gri, t+l), a2 denotes the unconditional variance
of innovations to the stochastic discount factor Var(mt~l Etmt+l), and G,, denotes the
unconditional covariance of innovations Cov(ri, t+l - Elri, tvl, rntel - Etmt+l).
Equation (9) has both time-series and cross-sectional implications. Consider first an
asset with a riskless real return rt; ¢)1. For this asset the return innovation variance c~2
and the covariance aim are both zero, so the riskless real interest rate obeys
rj;l+l =-Etmt+l 02
2 (10)
This equation is the log counterpart of Equation (6).
Subtracting Equation (10) from Equation (9) yields an expression for the expected
excess return on risky assets over the riskless rate:
o.2
Et[ri,/+1 - 9; tM] + ~- - -oi ....
2
(ll)
The variance term on the left-hand side of Equation (11) is a Jensen's Inequality
adjustment arising from the fact that we are describing expectations of log returns.
This term would disappear if we rewrote the equation in terms of the log expectation
of the ratio of gross simple returns: log G [(1 + Ri, t +I)/(1 + Rf, ~+1)] = -aim. The righthand
side of Equation (11) says that the log risk premium is determined by the negative
of the covariance of the asset with the stochastic discount factor. This equation is the
log counterpart of Equation (7).
The covariance O,m can be written as the product of the standard deviation of the
asset return a,., the standard deviation of the stochastic discount factor (7,,,, and the
1248 J Y. Campbell
~P
f~
L)
q,
3
o
o
o
V~=7
>,~° ~
•~ ,.=
03 r.~
'~ :~ Z
~ ~'"
•~ o=° ~o ~
,.~ II
rm ~.
o,~o <z~
2~=~ .~#
.- .o~ <
&S
Ch. 19: Asset Prices, Consumption, and the Business Cycle 1249
correlation between the asset return and the stochastic discount factor Pim. Since
Pim ~ -1, -~m <, ~YiOrn.Substituting into Equation (11),
Et[ri, t+l - rl;t-, 1] + 0,2/2
Om >1 (12)
This inequality was first derived by Shiller (1982); a multi-asset version was derived
by Hansen and Jagannathan (1991) and developed further by Cochrane and Hansen
(1992). The right-hand side of Equation (12) is the excess return on an asset, adjusted
for Jensen's Inequality, divided by the standard deviation of the asset's return - a
logarithmic Sharpe ratio for the asset. Equation (12) says that the standard deviation of
the log stochastic discount factor must be greater than this Sharpe ratio for all assets i,
that is, it must be greater than the maximum possible Sharpe ratio obtainable in asset
markets.
Table 5 uses Equation (12) to illustrate the equity premium puzzle. For each data
set the first column of the table reports the average excess return on stock over shortterm
debt, adjusted for Jensen's inequality by adding one-half the sample variance
of the excess log return to get a sample estimate of the numerator in Equation (12).
This adjusted average excess return is multiplied by 400 to express it in annualized
percentage points. The second column of the table gives the aunualized standard
deviation of the excess log stock return, a sample estimate of the denominator in
Equation (12). This standard deviation was reported earlier in Table 2. The third
column gives the ratio of the first two columns, multiplied by 100; this is a sample
estimate of the lower bound on the standard deviation of the log stochastic discount
factor, expressed in annualized percentage points. In the postwar US data the estimated
lower bound is a standard deviation greater than 50% a year; in the other quarterly data
sets it is below 10% for Italy, between 15% and 20% for Australia and Canada, and
above 30% for all the other countries, in the long-run annual data sets the lower bound
on the standard deviation exceeds 30% for all three countries.
3.2. Consumption-based asset pricing with power utility
To understand why these numbers are disturbing, I now follow Mehra and Prescott
(1985) and other classic papers on the equity premium puzzle and assume that there
is a representative agent who maximizes a time-separable power utility function defined
over aggregate consumption G:
C¢-Y-1
u(G) - - - , (13)
1-7
where y is the coefficient of relative risk aversion. This utility function has several
important properties. First, it is scale-invariant; with constant return distributions,
risk premia do not change over time as aggregate wealth and the scale of the
1250 Jg CampbeH
economy increase. Related to this, if different investors in the econonW have different
wealth levels but the same power utility function, then they can be aggregated
into a single representative investor with the same utility function as the individual
investors. A possibly less desirable property of power utility is that the elasticity of
intertemporal substitution, which I write as ~p, is the reciprocal of the coefficient
of relative risk aversion y. Epstein and Zin (1989, 1991) and Weil (1989) have
proposed a more general utility specification that preserves the scale-invariance of
power utility but breaks the tight link between the coefficient of relative risk aversion
and the elasticity of intertemporal substitution. I discuss this form of utility in
section 3.4 below.
Power utility implies that marginal utility UI(C,) = Ct r, and the stochastic discount
factor Mt+l = CS(Ct+t/CI)-r. The assumption made previously that the stochastic
discount factor is conditionally lognormal will be implied by the assumption that
aggregate consumption is conditionally lognormal [Hansen and Singleton (1983)].
Making this assumption for expositional convenience, the log stochastic discount factor
is mt+l = log(cS)- 7Ac,+1, where c, --- log(Q), and Equation (9) becomes
0 = Etri,,+l +log (5- yE, Act~l + (½) [a,.2+ y20~2- 2ro,c]. (14)
Here a2 denotes Var(ct+l -Etct+l), the unconditional variance of log consumption
innovations, and eric denotes Cov(ri, t+l- Etri, t Fl, ct+l - EtCt+l), the unconditional
covariance of innovations.
Equation (10) now becomes
~,2at2
tj/;,+t = log C5+ ]/EtAct+l 2 (15)
This equation says that the riskless real rate is linear in expected consumption growth,
with slope coefficient equal to the coefficient of relative risk aversion. The conditional
variance of consumption growth has a negative effect on the riskless rate which can
be interpreted as a precautionary savings effect.
Equation (11) becomes
Et[ri, t+~ --rj;t+l] + ~- = 7oic. (16)
The log risk premium on any asset is the coefficient of relative risk aversion times
the covariance of the asset return with consumption growth. Intuitively, an asset with
a high consumption covariance tends to have low returns when consumption is low,
that is, when the marginal utility of consumption is high. Such an asset is risky and
commands a large risk premium.
Table 5 uses Equation (16) to illustrate the equity premium puzzle. As already
discussed, the first column of the table reports a sample estimate of the left-hand
Ch. 19." Asset Prices, Consumption, and the Business Cycle 1251
side of Equation (16), multiplied by 400 to express it in annualized percentage points.
The second column reports the annualized standard deviation of the excess log stock
return (given earlier in Table 2), the fourth column reports the annualized standard
deviation of consumption growth (given earlier in Table 3), the fifth column reports the
correlation between the excess log stock return and consumption growth, and the sixth
column gives the product of these three variables which is the annualized covariance
a,~.between the log stock return and consumption growth.
Finally, the table gives two columns with implied risk aversion coefficients. The
column headed RRA(1) uses Equation (16) directly, dividing the adjusted average
excess return by the estimated covariance to get estimated risk aversion 8. The column
headed RRA(2) sets the correlation of stock returns and consumption growth equal to
one before calculating risk aversion. While this is of course a counterfactual exercise,
it is a valuable diagnostic because it indicates the extent to which the equity premium
puzzle arises from the smoothness of consumption rather than the low correlation
between consumption and stock returns. The correlation is hard to measure accurately
because it is easily distorted by short-term measurement errors in consumption, and
Table 4 indicates that the sample correlation is quite sensitive to the measurement
horizon. By setting the correlation to one, the RRA(2) column indicates the extent
to which the equity premium puzzle is robust to such issues. A correlation of one
is also implicitly assumed in the volatility bound for the stochastic discount factor,
Equation (12), and in many calibration exercises such as Mehra and Prescott (1985),
Campbell and Cochrane (1999), or Abel (1999).
Table 5 shows that the equity premium puzzle is a robust phenomenon in
international data. The coefficients of relative risk aversion in the RRA(1) column are
generally extremely large. They are usually many times greater than 10, the maximum
level considered plausible by Mehra and Prescott (1985). In a few cases the risk
aversion coefficients are negative because the estimated covariance of stock returns
with consumption growth is negative, but in these cases the covariance is extremely
close to zero. Even when one ignores the low correlation between stock returns and
consumption growth and gives the model its best chance by setting the correlation to
one, the RRA(2) column still has risk aversion coefficients above 10 in most cases.
Thus the fact shown in Table 4, that for some countries the correlation of stock returns
and consumption increases with the horizon, is unable by itself to resolve the equity
premium puzzle.
The risk aversion estimates in Table 5 are of course point estimates and are subject
to sampling error. No standard errors are reported for these estimates. However authors
such as Cecchetti, Lam and Mark (1993) and Kocherlakota (1996), studying the long-
8 The calculationis donecorrectly,in naturalunits,eventhoughthe tablereportsaverageexcessreturns
and covafiancesin percentagepoint units. Equivalently,the ratio of the quantities givenin the table is
multipliedby 100.
1252 J E Campbell
run annual US data, have found small enough standard errors that they can reject risk
aversion coefficients below about 8 at conventional significance levels.
Of course, the validity of these tests depends on the characteristics of the data set in
which they are used. Rietz (1988) has argued that there may be a peso problem in these
data. A peso problem arises when there is a small positive probability of an important
event, and investors take this probability into account when setting market prices. If
the event does not occur in a particular sample period, investors will appear irrational
in the sample and economists will mis-estimate their preferences. While it may seem
unlikely that this could be an important problem in 100 years of annual data, Rietz
(1988) argues that an economic catastrophe that destroys almost all stock-market value
can be extremely unlikely and yet have a major depressing effect on stock prices.
One difficulty with this argument is that it requires not only a potential catastrophe,
but one which affects stock market investors more seriously than investors in short-term
debt instruments. Many countries that have experienced catastrophes, such as Russia
or Germany, have seen very low returns on short-term government debt as well as
on equity. A peso problem that affects both asset returns equally will affect estimates
of the average levels of returns but not estimates of the equity premium 9. The major
example of a disaster for stockholders that did not negatively affect bondholders is
the Great Depression of the early 1930s, but of course this is included in the long-run
annual data for Sweden, the UK, and the USA, all of which display an equity premium
puzzle.
Also, the consistency of the results across countries requires investors in all countries
to be concerned about catastrophes. If the potential catastrophes are uncorrelated across
countries, then it becomes less likely that the data set includes no catastrophes; thus the
argument seems to require a potential international catastrophe that affects all countries
simultaneously.
3.3. The riskf?ee rate puzzle
One response to the equity premium puzzle is to consider larger values for the
coefficient of relative risk aversion ~/. Kandel and Stambaugh (1991) have advocated
9 Thispoint is relevant for the studyof Goetzmann and Jorion (1997). These authors measure average
growth rates &real stock prices, as a proxy for real stock returns, bnt they do not look at real returns on
short-term debt. Theyfind low real stock-pricegrowth rates in many countriesin the early 20th Century;
in somecases these may havebeen accompaniedby low returns to holders of short-term debt. Note also
that stock-price growth rates are a poor proxy for total stock returns in periods where investors expect
low growth rates, since dividend yields will tend to be higher in such periods.
Ch. 19: Asset Prices, Consumption, and the Business Cycle 1253
this l°. However this leads to a second puzzle. Equation (15) implies that the
unconditional mean riskless interest rate is
y2~ (17)Er];t+l =-log6+gg- 2 '
where g is the mean growth rate of consumption. Since g is positive, as shown in
Table 3, high values of 7 imply high values of 7g. Ignoring the term -y2o~2/2 for
the moment, this can be reconciled with low average short-term real interest rates,
shown in Table 2, only if the discount factor 6 is close to or even greater than one,
corresponding to a low or even negative rate of time preference. This is the riskfree
rate puzzle emphasized by Weil (1989).
Intuitively, the riskfree rate puzzle is that if investors are risk-averse then with
power utility they must also be extremely unwilling to substitute intertemporally. Given
positive average consumption growth, a low riskless interest rate and a high rate of
time preference, such investors would have a strong desire to borrow from the future to
reduce their average consumption growth rate. A low riskless interest rate is possible
in equilibrium only if investors have a low or negative rate of time preference that
reduces their desire to borrow 11
Of course, if the risk aversion coefficient g is high enough then the negative
quadratic term -V2a~/2 in Equation (17) dominates the linear term and pushes the
riskless interest rate down again. The quadratic term reflects precautionary savings;
risk-averse agents with uncertain consumption streams have a precautionary desire to
save, which can work against their desire to borrow. But a reasonable rate of time
preference is obtained only as a knife-edge case.
Table 6 illustrates the riskfree rate puzzle in international data. The table first shows
the average riskfree rate from Table 2 and the mean consumption growth rate and
standard deviation of consumption growth from Table 3. These moments and the risk
aversion coefficients calculated in Table 5 are substituted into Equation (17), and the
equation is solved for an implied time preference rate. The time preference rate is
reported in percentage points per year; it can be interpreted as the riskless real interest
rate that would prevail if consumption were known to be constant forever at its current
level, with no growth and no volatility. Risk aversion coefficients in the RRA(2) range
imply negative time preference rates in every country except Switzerland, whereas
larger risk aversion coefficients in the RRA(I) range imply time preference rates that
are often positive but always implausible and vary wildly across countries.
J0 One might think that introspectionwould be sufficientto rule out very largevalues of V,but Kandel
and Stambaugh (1991) point out that introspection can deliver very different estimatesof risk aversion
depending on the size of the gamble considered. This suggests that introspection can be misleading or
that some more general model of utility is needed.
I~ As Abel (1999) and Kocherlakota(1996) point out,negative time preference is consistentwith finite
utility in a time-separable model provided that consumption is growing, and marginal utility shrinking,
sufficientlyrapidly.The question is whether negative thne preference is plausible.
1254 J.Y. Campbell
Table 6
The riskfree rate puzzlea
Country Sample period r~ Ac o(Ae) RRA(1) TPR(1) RRA(2) TPR(2)
USA 1947.2-1996.3 0.794 1.908 1.084 246.556 112.474 47.600 -76.710
AUL 1970.1 1996.2 1.820 1.854 2.142 45.704 -34.995 7.107 -10.196
CAN 1970.1-1996.2 2.738 1.948 2.034 56.434 41.346 8.965 -13.066
FR 1973.~1996.2 2.736 1.581 2.130 < 0 N/A 14.634 -15.536
GER 1978.4-1996.2 3.338 1.576 2.495 343.133 >1000 13.327 12.142
ITA 1971.2 1995.2 2.064 2.424 1.684 >1000 >1000 4.703 -9.021
JPN 1970.2-1996.2 1.538 3.416 2.353 134.118 41.222 13.440 -39.375
NTH 1977.2-1996.1 3.705 1.466 2.654 >1000 >1000 23.970 -11.201
SWD 1970.1 1994.4 1.520 0.750 1.917 >1000 >1000 20.705 -6.126
SWT 1982.2-1996.2 1.466 0.414 2.261 < 0 N/A 26.785 8.698
UK 1970.1 1996.2 1.08i 2.025 2.589 156.308 503.692 14.858 -21.600
USA 1970.1-1996.3 1.350 1.710 0.919 150.136 -160.275 37.255 -56.505
SWD 1920 1993 2.073 1.748 2.862 65.642 63.778 11.091 -12.274
UK 1919-1993 1.198 1.358 2.820 39.914 10.364 14.174 -10.057
USA 1891-1994 1.955 1.742 3.257 20.861 11.305 10.366 10.406
a ~: is the mean money market return from Table 2, in annualized percentage points. Ae and cr(Ae)
are the mean and standard deviation of consmnption growth from Table 3, in annualized percentage
points. RRA(1) and RRA(2) are the risk aversion coefficients from Table 5. TPR(1)=7- RRA(1)Ac +
RRA(1)2g2(Ac)/200, and TPR(2)= ~- RRA(2)Ac + RRA(2)2oZ(Ac)/200.From Equation (17), these
time preference rates give the real interest rate, in annualized percentage points, that would prevail
if consumption growth had zero mean and zero standard deviation and risk aversion were RRA(1) or
RRA(2), respectively.
Abbreviations: AUL, Australia; CAN, Canada; FR, France; GER, Germany; ITA, Italy; JPN, Japan;
NTH, Netherlands; SWD, Sweden; SWT, Switzerland; UK, United Kingdom; USA, United States of
America.
An interesting issue is how mismeasurement of average inflation might affect these
calculations. There is a growing consensus that in recent years conventional price
indices have overstated true inflation by failing to fully capture the effects of quality
improvements, consumer substitution to cheaper retail outlets, and price declines in
newly introduced goods. If inflation is overstated by, say, 1%, the real interest rate
is understated by 1%, which by itself might help to explain the riskfree rate puzzle.
Unfortunately the real growth rate of consumption is also understated by 1%, which
worsens the riskfree rate puzzle. When y > 1, this second effect dominates and
understated inflation makes the riskfree rate puzzle even harder to explain.
Ch. 19." Asset Prices, Consumption, and the Business Cycle 1255
Table 7
International yield spreads and bond excess returns a
Country Sample period ~ a(s) p(s) er~ a(erb) p(erb)
USA 1947.2-1996.4 1.199 0.999 0.783 0.011 8.923 0.070
AUL 1970.1-1996.3 0.938 1.669 0.750 0.156 8.602 0.162
CAN 1970.1 1996.3 1.057 1.651 0.819 0.950 9.334 -0.009
FR 1973.2 1996.3 0.917 1.547 0.733 1.440 8.158 0.298
GER 1978.4-1996.3 0.99l 1.502 0.869 0.899 7.434 0.117
ITA 197t.~1995.3 0.200 2.025 0.759 1.386 9.493 0.335
JPN 1970.2-1996.3 0.593 1.488 0.843 1.687 9.165 -0.058
NTH 1977.2-1996.2 1.212 1.789 0.574 1549 7.996 0.032
SWD 1970.1-1995.1 0.930 2.046 0.724 0.212 7.575 0.244
SWT 1982.2 1996.3 0.471 1.655 0.755 1.071 6.572 0.268
UK 1970.1 1996.3 1.202 2.106 0.893 0.959 11.611 0.057
USA 1970.1-1996.4 1.562 1.190 0.737 1.504 10.703 0.033
SWD 1920-1994 0.284 1.140 0.280 -0.075 6.974 0.185
UK 1919-1994 1.272 1.505 0.694 0.318 8.812 -0.098
USA 1891 1995 0.720 1.550 0.592 0.172 6.499 0.153
a Sis the mean of the log yield spread, the difference between the log yield on long-term bonds and the log
3-month money market return, expressed in annualized percentage points. ~7(s)is the standard deviation
of the log yield spread and p(s) is its first-order autocorrelation, erh, a(ert,), and p(erb) are defined in
the same way for the excess 3-month return on long-term bonds over money market instruments, where
the bond return is calculated from the bond yield using the par-bond approximation given in Campbell,
Lo and MacKinlay (1997), Chapter 10, equation (10.1.I9). Full details of this calculation are given in
thc Data Appendix.
Abbreviations: AUL, Australia; CAN, Canada; FR, France; GER, Germany; ITA, Italy; JPN, Japan;
NTH, Netherlands; SWD, Sweden; SWT, Switzerland; UK, United Kingdom; USA, United States of
America.
3.4. Bond returns and the equity premium and riskfree rate puzzles
Some authors have argued that the riskfree interest rate is low because short-term
government debt is more liquid than long-term financial assets. Short-term debt is
"moneylike" in that it facilitates transactions and can be traded at minimal cost. The
liquidity advantage of debt reduces its equilibrium return and increases the equity
premium [Bansal and Coleman (1996), Heaton and Lucas (1996)].
The difficulty with this argument is that it implies that all long-term assets should
have large excess returns over short-term debt. Long-term government bonds, for
example, are not moneylike and so the liquidity argument implies that they should
offer a large term premium. But historically, the term premium has been many times
smaller than the equity premium. This point is illustrated in Table 7, which reports two
1256 Jg Campbell
alternative measures of the term premium. The first measure is the average log yield
spread on long-term bonds over the short-term interest rate, while the second is the
average quarterly excess log return on long bonds. In a long enough sample these two
averages should coincide if there is no upward or downward drift in interest rates.
The average yield spread is typically between 0.5% and 1.5%. A notable outlier
is Italy, which has a negative average yield spread in this period. Average long
bond returns are quite variable across countries, reflecting differences in inflationary
experiences; however in no country does the average excess bond return exceed 1.7%
per year. Thus both measures suggest that term premia are far smaller than equity
premia.
Table 8 develops this point further by repeating the calculations of Table 5, using
bond returns rather than equity returns. The average excess log return on bonds over
short debt, adjusted for Jensen's Inequality, is divided by the standard deviation of
the excess bond return to calculate a bond Sharpe ratio which is a lower bound on
the standard deviation of the stochastic discount factor. The Sharpe ratio for bonds is
several times smaller than the Sharpe ratio for equities, indicating that term premia
are small even after taking account of the lower volatility of bond returns.
This finding is not consistent with a strong liquidity effect at the short end of the term
structure, but it is consistent with a consumption-based asset pricing model if bond
returns have a low correlation with consumption growth. Table 8 shows that sample
consumption correlations often are lower for bonds, so that RRA(1) risk aversion
estimates for bonds, which use these correlations, are often comparable to those for
equities.
A direct test of the liquidity story is to measure excess returns on stocks over long
bonds, rather than over short debt. If the equity premium is due to a liquidity effect
on short-term interest rates, then there should be no "equity-bond premium" puzzle.
Table 9 carries out this exercise and finds that the equity-bond premium puzzle is just
as severe as the standard equity premium puzzle 12.
3.5. Separating risk aversion and intertemporal substitution
Epstein and Zin (1989, 1991) and Weil (1989) use the theoretical framework of Kreps
and Porteus (1978) to develop a more flexible version of the basic power utility model.
That model is restrictive in that it makes the elasticity of intertemporal substitution,
% the reciprocal of the coefficient of relative risk aversion, 7. Yet it is not clear that
these two concepts should be linked so tightly. Risk aversion describes the consumer's
reluctance to substitute consumption across states of the world and is meaningful even
12 The excess return of equities over bonds must be measured with the appropriatecorrection for
Jensen's Inequality.From Equation (16), the appropriatemeasure is the log excessreturn on equities
overshort-termdebt,lessthe log excessreturn on bondsovershort-termdebt,plus one-halfthe variance
of the log equityreturn, less one-halfthe varianceof the log bond return.
Ch, 19.• Asset Prices, Consumption, and the Business Cycle
%
0
V
~,, ~ . , ~ ,.n ~ ~ ~. ~..
I
• " ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
2
~, r¢3
o ~ t'4
V
V
t-'q ~ t"~
~ ~ rz
t'-q
,,6 ~6 ,,6
1257
•~ z
,.~ Z
t
r~
1258 JK Campbell
%
~o
<~
~2
o
o
~ V V ~
oo ~
. . ~ ~ . ~ . .
¢S"~ ~
o
O9
~ , ~
~~ ~ L~
.~q i~~
_ ~
°<% ~
~ J ~.~
"~'" I!~ ~
"~ <
-~ ~.~
~ o ~ ,~ ~.~
Ch. 19: Asset Prices, Consumption, and the Business Cycle 1259
in an atemporal setting, whereas the elasticity of intertemporal substitution describes
the consumer's willingness to substitute consumption over time and is meaningful even
in a deterministic setting. The Epstein-Zin--Weil model retains many of the attractive
features of power utility but breaks the link between the parameters y and ~p.
The Epstein-Zin-Weil objective function is defined recursively by
0
U,= (1-6)C 7+6 G_.f\ , (18)
where 0 = (1 -y)/(l - l/W). When y - I/W, 0 = 1 and Equation (18) becomes
linear; it can then be solved forward to yield the familiar time-separable power utility
model.
The integemporal budget constraint for a represemative agent can be written as
V/t+1 - (1 + Rw,t+l) (J4zt- - CI), (19)
where Wt+l is the representative agent's wealth, and (1 + Rw,t+l) is the gross simple
return on the portfolio of all invested wealth 13. This form of the budget constraint is
appropriate for a complete-markets model in which wealth includes human capital as
well as financial assets. Epstein and Zin use dynamic programming arguments to show
that Equations (18) and (19) together imply an Euler equation of the form
1I=G \CT-t / (1 +Rw, t<) (1 +R,,,+I) . (20)
If I assume that asset returns and consumption are homoskedastic and jointly
lognormal, then this implies that the riskless real interest rate is
0-1 2 0 2
rj;t+l = -log6+ E,[Act+l] + ~2-- cG - ~2 o~. (21)
The riskless interest rate is a constant, plus 1/~p times expected consumption growth.
In the power utility model, 1/ip = y and 0 = 1, so Equation (21) reduces to
Equation (15).
The premium on risky assets, including the wealth portfolio itself, is
62 o,,
E,[ri,,+l] - rj;,+l + " - 0 +(1 - O)oiw. (22)
2 ~0
The risk premium on asset i is a weighted combination of asset i's covariance with
consumption growth (divided by the elasticity of intertemporal substitution W) and
13 This is often called the "market" return and written Rm,t~i, but l have already used m to denote the
stochastic discount factor so I write R,,,t~l to avoid confusion.
1260 J.Y. Campbell
asset i's covariance with the return on wealth. The weights are 0 and 1 - 0 respectively.
The Epstein-Zin-Weil model thus nests the consumption CAPM with power utility
(0 = 1) and the traditional static CAPM (0 = 0).
Equations (21) and (22) seem to indicate that Epstein-Zin-Weil utility might
be helpful in resolving the equity premium and riskfree rate puzzles. First, in
Equation (21) a high risk aversion coefficient does not necessarily imply a low average
riskfree rate, because
0--1 2 0
Erj;t+l =-log6+ g + ~rw- or2. (23)
The average consumption growth rate is divided by ~p here, and in the Epstein-ZinWell
framework ~pneed not be small even if ~ is large.
Second, Equation (22) suggests that it might not even be necessary to have a high
risk aversion coefficient to explain the equity premium. If 0 ~ 1, then the risk premium
on an asset is determined in part by its covariance with the wealth portfolio, a/w. If the
return on wealth is more volatile than consumption growth, as implied by the common
use of a stock index return as a proxy for the return on wealth, then Oiw may be much
larger than oic, and this may help to explain the equity premium.
Unfortunately, there are serious difficulties with both these potential escape routes
from the equity premium and riskfree rate puzzles. The difficulty with the first is that
there is direct empirical evidence for a low elasticity of intertemporal substitution in
consumption. The difficulty with the second is that consumption and wealth are linked
through the intertemporal budget constraint; if consumption is smooth and wealth is
volatile, this itself is a puzzle that must be explained, not an exogenous fact that can
be used to resolve other puzzles. I now develop these points in detail by analyzing
the dynamic behavior of stock returns and short-term interest rates in relation to
consumption.
4. The dynamics of asset returns and consumption
4.1. Time-variation in conditional expectations
Equations (21) and (22) imply a tight link between rational expectations of asset
returns and of consumption growth. Expected asset returns are perfectly correlated
with expected consumption growth, with a standard deviation 1/~p times as large.
Equivalently, the standard deviation of expected consumption growth is ~p times as
large as the standard deviation of expected asset returns.
Ch. 19: Asset Prices', Consumption, and the Business Cycle 1261
This suggests a way to estimate % Hansen and Singleton (1983), followed by
Campbell and Mankiw (1989), Hall (1988), and others, have proposed an instrumental
variables (IV) regression approach. If we define an error term
t/i,t+l ~ ri, t+l - - Et[ri, t+l] - 7(Act+t - Et[ACt+l]),
then we can rewrite Equations (21) and (22) as a regression equation,
(24)
In general the error term t/i,t+l will be correlated with realized consumption growth
so OLS is not an appropriate estimation method. However t/i,t+l is uncorrelated with
any variables in the information set at time t. Hence any lagged variables correlated
with asset returns can be used as instruments in an IV regression to estimate 1/%
Table 10 illustrates two-stage least squares estimation of Equation (24). In each panel
the first set of results uses the short-term real interest rate, while the second set uses the
real stock return. The instruments are the asset return, the consumption growth rate,
and the log price-dividend ratio. The instruments are lagged twice to avoid difficulties
caused by time-aggregation of the consumption data ]Campbell and Mankiw (1989,
1991), Wheatley (1988)].
For each asset and set of instruments, the table first reports the R2 statistics and
significance levels for first-stage regressions of the asset return and consumption
growth rate onto the instruments. The table then shows the IV estimate of 1/~p with its
standard error, and (in the column headed "Test (1)") the R2 statistic for a regression
of the residual on the instruments together with the associated significance level of a
test of the over-identifying restrictions of the model.
The quarterly results in Table 10 show that the short-term real interest rate is highly
forecastable in every country except Germany. The real stock return is also forecastable
in many countries, but there is weaker evidence for forecastability in consumption
growth. In fact the R2 statistic for forecasting consumption growth is lower than the
R2 statistic for stock returns in all but four of the quarterly data sets. The IV estimates
of 1/~p are very imprecise; they are sometimes large and positive, often negative, but
they are almost never significantly different from zero. The overidentifying restrictions
of the model are often strongly rejected, particularly when the short-term interest rate
is used in the model. Results are similar for the annual data sets in Table 10, except
that twice-lagged instruments have almost no ability to forecast real interest rates or
stock returns in the annual US data 14
14 Campbell, Lo and MacKinlay (1997), Table 8.2, showsmuch greater fbrecastabilityof returns using
once-laggedinstruments in a similarannual US data set. Even with twice-laggedhlstruments, US annual
returns become forecastableonce one increasesthe return horizon beyond one year,as shownin Table12
below.
1262
Table 10
Predictable variation in returns and consumption growth a
J Y. Campbell
Count~2¢ Sample period Asset First-stage (1/~--~)
regressions (s.e.) (s.e.)
ri Ac
Testb
1 2
USA
AUL
CAN
FR
GER
ITA
JPN
NTH
SWD
1947.~1996.3 rf 0.160
0.000
re 0.065
0.003
1970.2 1996.2 rf 0.404
0.000
r,, 0.060
0.034
1970.2 1996.2 rf 0.292
0.000
r~ 0.040
0.269
1973.2-1996.2 r! 0.519
0.000
r~ 0.111
0.006
1978.4-1996.2 1)- 0.062
0.328
r~ 0.046
0.050
1971.2-1995.2 rj 0.405
0.000
re 0.048
0.278
1970.~1996.2 rf 0.203
0.002
r~ 0.115
0,001
1977.2-1996.1 rj 0.248
0.000
re 0.021
0.756
1970.2 1994.4 rj 0.262
0.000
r~, 0.110
0.039
0.037 0.260 0.025 0.165 0.037
0.077 0.740 0.114 0.000 0.027
0.037 -8.187 0.021 0.035 0.025
0.077 7.069 0.028 0.033 0.090
0.013 4.450 0.099 0.017 0,008
0.432 2.973 0.107 0.419 0,676
0.013 20.250 0.038 0.004 0.003
0.432 13.145 0.026 0.828 0.856
0.048 -0.970 -0.174 0.142 0.041
0.042 0.677 0.177 0.001 0.123
0.048 6.635 0.130 0.004 0.004
0,042 4.536 0.092 0.822 0.819
0.010 -2.189 -0.051 0.073 0.009
0.751 2.170 0.133 0.037 0,667
0.010 -27.662 -0.021 0.006 0.004
0.751 29.994 0.026 0,750 0.833
0.057 0.481 1.773 0.005 0.005
0.085 0.354 1.141 0.840 0.841
0.057 -6.117 0.079 0.017 0.018
0.085 4.992 0.066 0.569 0.547
0.010 -2.432 -0.019 0.171 0.010
0.877 3.353 0.113 0.000 0,624
0.010 19.919 0.016 0.013 0.007
0.877 26.244 0.034 0.540 0.734
0.044 -0.446 -0.093 0.162 0.04 l
0.081 0.464 0.266 0.000 0.121
0.044 11.028 0.047 0.026 0.019
0.081 5.458 0.027 0.260 0.376
0.024 0,167 0.052 0.218 0.023
0.373 0.385 0.428 0,000 0.428
0.024 -4.532 -0.138 0.005 0,005
0.373 6.571 0.162 0,835 0.832
0.005 -1.056 -0.007 0.197 0.005
0.806 2,949 0.085 0000 0,779
0.005 15.210 0.004 0.047 0.005
0.806 21.187 0.017 0.107 0.790
continued on next page
Ch. 19." Asset Prices, Consumption, and the Business Cycle 1263
Table 10, continued
Country Sample period Asset First-stage (1/~-~) ~ Test b
regressions (s.e.) (s.e.) 1 2
ri Ac
SWT 1982.2 1996.2 rf 0.194 0.007 0.731 0.065 0.074 0.006
0.000 0.887 1.273 0.397 0.136 0.844
re 0.033 0.007 20.084 0.048 0.000 0.000
0.270 0.887 31.100 0.070 0.996 0.996
UK 1970.~1996.2 rf 0.306 0.057 1.992 0.260 0.047 0.028
0.000 0.042 0.988 0.136 0.090 0.238
re 0.097 0.057 -4.493 0.038 0.056 0.040
0.094 0.042 3.793 0.034 0.058 0.132
USA 1970.2-1996.3 J) 0.307 0.071 1.573 0.t02 0.188 0.062
0.000 0.015 0.704 0.111 0.000 0.041
rC 0.069 0.071 4.977 0.016 0.069 0.071
0.095 0.015 7.677 0.023 0.029 0.025
SWD 1920-1993 rf 0.302 0.052 2.740 0.194 0.037 0.023
0.000 0.202 1.466 0.t61 0.266 0.437
r~ 0.041 0.052 -1.537 0.043 0.034 0.041
0.342 0.202 3.349 0.082 0.304 0.236
UK 1920-1993 r~/ 0.265 0.061 2.499 0.197 0.056 0.033
0.000 0.140 1.509 0.123 0.139 0.314
r~, 0.147 0.061 5.861 0.037 0.115 0.055
0.096 0.140 4.569 0.021 0.017 0.144
USA 1891-1994 ~/ 0.013 0.065 -0.293 -0.202 0.012 0.049
0.783 0.004 0.892 0.341 0.552 0.085
r,, 0.037 0.065 0.723 0.038 0.040 0.074
0.184 0.004 2.003 0.070 0.132 0.024
a This table reports two-stage least squares eshination results for Equations (24) and (25). The first set
of results for each country uses the short-term real interest rate, while the second set uses the real stock
return. The instruments are the asset return, the consumption growth rate, and the log price-dividend
ratio, lagged twice. For each asset and set of instruments, the first two colunms show the R2 statistics,
with significance levels below, lbr first-stage regressions of the asset return and consumption growth
rate onto the instruments. The third column shows the IV estimate of 1/~p from Equation (24) with its
standard error below, and the fourth column shows the IV estimate of ~p from Equation (25) with its
standard error below. The fifth column, headed "Test (1)", shows the R2 statistic for a regression of the
residual from Equation (24) on the instruments, with the associated significance level below of a test of
the over-identifying restrictions of the model. The sixth column, headed "Test (2)" is the equivalent of
the fifth column for Equation (25).
Abbreviations: AUL, Australia; CAN, Canada; FR, France; GER, Germany; ITA, Italy; JPN, Japan;
NTH, Netherlands; SWD, Sweden; SWT, Switzerland; UK, United Kingdom; USA, United States of
America.
b Tests: (1)ri,t~ j =t,ti-t-(1/~O)Act+t+rli,t+l; (2) Act+t - Ti + ~/)1~,1~1 +~z,t41.
1264 JE Campbell
Campbell and Mankiw (1989, 1991) have explored this regression in more detail,
using both US and international data, and have found that predictable variation in
consumption growth is often associated with predictable variation in income growth.
This suggests that some consumers keep their consumption close to their income,
either because they follow "rules of thumb", or because they are liquidity-constrained,
or because they are "buffer-stock" savers [Deaton (1991), Carroll (1992)]. After
controlling for the effect of predictable income growth, there is little remaining
predictable variation in consumption growth to be explained by consumers' response
to variation in real interest rates.
One problem with IV estimation of Equation (24) is that the instruments are only
very weakly correlated with the regressor because consumption growth is hard to
forecast in this data set. Nelson and Startz (1990) have shown that in this situation
asymptotic theory can be a poor guide to inference in finite samples; the asymptotic
standard error of the coefficient tends to be too small and the overidentifying
restrictions of the model may be rejected even when it is true. To circumvent this
problem, one can reverse the regression (24) and estimate
Act+ 1 = ~ -t- ~gri, t+ 1 + ~i,t+l. (25)
If the orthogonality conditions hold, then the estimate of 'qJ in Equation (25) will
asymptotically be the reciprocal of the estimate of 1/~p in Equation (24). In a finite
sample, however, if ~p is small then IV estimates of Equation (25) will be better
behaved than IV estimates of Equation (24).
In Table 7 ~p is almost always estimated to be close to zero. The estimates are
much more precise than those for 1/% The overidentifying restrictions of the model
are sometimes rejected, but less often and less strongly than when Equation (24) is
estimated. These results suggest that the elasticity of intertemporal substitution ~p is
small, so that the generality of the Epstein-Zin-Weil model, which allows ~p to be
large even if ~/is large, does not actually help one fit the data on consumption and
asset returns 15.
4.2. A loglinear asset pricing J?amework
in order to understand the second momems of stock returns, it is essential to have
a framework relating movements in stock prices to movements in expected future
dividends and discount rates. The present value model of stock prices is intractably
nonlinear when expected stock returns are time-varying, and this has forced researchers
to use one of several available simplifying assumptions. The most common approach
is to assume a discrete-state Markov process either for dividend growth [Mehra and
15 Attanasioand Weber(1993) and Beaudryand van Wincoop(1996)havearguedthatthis conclusion
depends on the use of aggregateconsumptiondata. Theywork with cohort-leveland state-leveldata,
respectively,and fred some evidencefor a larger elasticityof intertemporalsubstitution.
Ch. 19: Asset Prices', Consumption, and the Business Cycle 1265
Prescott (1985)] or, following Hamilton (1989), for conditionally expected dividend
growth [Abel (1994, 1999), Cecchetti, Lam and Mark (1990, 1993), Kandel and
Stambaugh (1991)]. The Markov structure makes it possible to solve the present value
model, but the derived expressions for returns tend to be extremely complicated and
so these papers usually emphasize numerical results derived under specific numerical
assumptions about parameter values 16.
An alternative framework, which produces simpler closed-form expressions and
hence is better suited for an overview of the literature, is the loglinear approximation
to the exact present value model suggested by Campbell and Shiller (1988). Campbell
and Shiller's loglinear relation between prices, dividends, and returns provides an
accounting framework: High prices must eventually be followed by high future
dividends or low future returns, and high prices must be associated with high expected
future dividends or low expected future returns. Similarly, high returns must be
associated with upward revisions in expected future dividends or downward revisions
in expected future returns. The loglinear approximation starts with the definition of
the log return on some asset i, ri, t+l ~ log(Pi, t+l + Di, t+l) - log(Pit). The timing
convention here is that prices are measured at the end of each period so that they
represent claims to next period's dividends. The log return is a nonlinear function of
log prices Pit and pi, t+l and log dividends di, t+l, but it can be approximated around
the mean log dividend-price ratio, (dit -Pa), using a first-order Taylor expansion. The
resulting approximation is
ri, t+l ~ k +/)Pi, t tl +(1 -/))di, t+l-Pit, (26)
where/) and k are parameters of linearization defined by/) = 1/(1 + exp(~))
and k - log(/)) - (1 -/))log(l//) - 1). When the dividend-price ratio is constant,
then p = Pi/(Pi + Di), the ratio of the ex-dividend to the cum-dividend stock price.
In the postwar quarterly US data shown in Table 3, the average price-dividend ratio
has been 26.4 on an annual basis, implying that/) should be about 0.964 in annual
data 17 The Taylor approximation (26) replaces the log of the sum of the stock price
and the dividend in the exact relation with a weighted average of the log stock price
and the log dividend. The log stock price gets a weight/) close to one, while the log
dividend gets a weight 1 -p close to zero because the dividend is on average much
smaller than the stock price, so a given percentage change in the dividend has a much
smaller effect on the return than a given percentage change in the price.
Ic, A partial exceptionto thisstatementis that Abel (1994)derivesseveralanalyticalresultsfor the first
momentsof retarns in a Markovmodel for expecteddividendgrowth.
17 Strictly speakingbothp and k should have asset subscripts i, but 1 omit these for simplicity.The
assetpricingformulaslater in this chapterassumethat all assetshavethe samep, whichsimplifiessome
expressionsbut doesnot changeany of the qualitativeconclusions.
1266 JE Campbe#
Equation (26) is a linear difference equation for the log stock price. Solving forward,
imposing the terminal condition that limj~o~ PJPi, t+j = 0, taking expectations, and
subtracting the current dividend, one gets
0<3
pit-d#- k kE~Zp.i[Adi,~+l+j-ri,,+l+j]. (27)
1 -p .i=o
This equation says that the log price-dividend ratio is high when dividends are expected
to grow rapidly, or when stock returns are expected to be low. The equation should
be thought of as an accounting identity rather than a behavioral model; it has been
obtained merely by approximating an identity, solving forward subject to a terminal
condition, and taking expectations. Intuitively, if the stock price is high today, then
from the definition of the return and the terminal condition that the stock price is
non-explosive, there must either be high dividends or low stock returns in the future.
hwestors must then expect some combination of high dividends and low stock returns
if their expectations are to be consistent with the observed price.
The terminal condition used to obtain Equation (27) is perhaps controversial. Models
of "rational bubbles" do not impose this condition. Blanchard and Watson (1982)
and Froot and Obstfeld (1991) have proposed simple, explicit models of explosive
bubbles in asset prices. There are however several reasons to rule out such bubbles. The
theoretical circumstances under which bubbles can exist are quite restrictive; Tirole
(1985), for example, uses an overlapping generations framework and finds that bubbles
can only exist if the economy is dynamically inefficient, a condition which seems
unlikely on prior grounds and which is hard to reconcile with the empirical evidence
of Abel, Mankiw, Summers and Zeckhauser (1989). Santos and Woodford (1997) also
conclude that the conditions under which bubbles can exist are fragile. Empirically,
bubbles imply explosive behavior of prices in relation to dividends and other measures
of fundamentals; there is no evidence of this, although nonlinear bubble models are
hard to reject using standard linear econometric methods is
Equation (27) describes the log price-dividend ratio rather than the log price
itself. This is a useful way to write the model because in many data sets dividends
appear to follow a loglinear unit root process, so that log dividends and log prices
are nonstationary. In this case changes in log dividends are stationary, so from
Equation (27) the log price-dividend ratio is stationary provided that the expected
stock return is stationary. Thus log stock prices and dividends are cointegrated, and
the stationary linear combination of these variables involves no unknown parameters
since it is just the log ratio.
Table 11 reports some summary statistics for international stock prices in relation
to dividends. The table gives the average price-dividend ratio, the standard deviation
t8 Campbell,Lo and MacKinlay(1997),Chapter7, givesa somewhatmoredetailedtextbookdiscussion
of the literatureon rationalbubbles.
Ch. 19." Asset Prices, Consumption, and the Business Cycle 1267
Table 11
International stock prices and dividends a
Country Sample period P/D a(p-d) p(p d) ADF(1) Ap Ad Ap-d
USA 1947.~1996.4 27.121 0.265 0.941 -1.752 3.547 2.225 1.688
AUL 1970.1 1996.3 25.919 0.267 0.856 3.273 -1.410 0.883 -2.477
CAN 1970.1-1996.3 30.108 0.221 0.902 -1.900 0.754 -0.741 1.200
FR 1973.2-1996.3 22.718 0.541 0.971 -1.3t0 1.358 -1.214 2.538
GER 1978.4-1996.3 27.787 0.300 0.922 -1.660 4.186 1.079 3.853
ITA 1971.2-1995.3 41.345 0.318 0.882 -3.743 2.172 4.919 3.531
JPN 1970.2-1996.3 91.251 0.642 0.964 -1.574 4.192 2.489 6.974
NTH 1977.2 1996.2 21.139 0.272 0.932 -0.727 7.540 4.007 3.637
SP 1984.2 1996.2 22.509 0.319 0.823 -3.075 6.843 -3.086 10.078
SWD 1970.1-1995.1 35.021 0.439 0.941 -1.632 4.922 1.861 3.499
SWT 1982.2-1996.3 47.320 0.217 0.814 -1.588 9.291 4.143 6.074
UK 1970.1 1996.3 18.434 0.280 0.913 -1.657 1.464 0.681 0.579
USA 1970.1 1996.4 27.882 0.235 0.904 -1.372 2.034 0.619 1.582
SWD 1920-1994 26.706 0.333 0.746 0.768 2.129 0.423 2.054
UK 1919 1994 20.806 0.238 0.514 4.093 2.064 1.844 0.220
USA 1891-1995 22.733 0.279 0.778 -1.868 2.064 1.485 0.477
a P/D is the mean price-dividendratio, c~(p-d) is the standard deviation of the log price-dividendratio
in natural units (not annualizedpercentage points), p(p - d) is the first-order autocorrelation of the log
price-dividend ratio. ADF(1) is the augmented Dickey-Fuller t-ratio for the lagged log price--dividend
ratio when the change in the log price-dividend ratio is regressed on a constant, four lagged changes,
and the lagged log price dividend ratio. Ap, Ad, and Ap- d are the mean changes in log prices, log
dividends, and the log price-dividend ratio respectively, in annualizedpercentage points.
Abbreviations: AUL, Australia; CAN, Canada; FR, France; GER, Germany; ITA, Italy; JPN, Japan;
NTH, Netherlands; SWD, Sweden; SWT, Switzerland; UK, United Kingdom; USA, United States of
America.
of the log price-dividend ratio in natural units, the first-order autocorrelation of the
log price-dividend ratio, average growth rates of prices, dividends, and the log pricedividend
ratio in percentage points per year, and a test statistic for the null hypothesis
that the log price-dividend ratio has a unit root. Following standard practice, the pricedividend
ratio is measured as the ratio of the current stock price to the total of dividends
paid during the past year.
Average price-dividend ratios vary considerably across countries but generally lie
between 20 and 30. The extreme outlier is Japan, which has an average price-dividend
ratio of 91. The volatility and first-order autocorrelation of the log price-dividend ratio
are also unusually high for Japan, reflecting an upward trend in the Japanese log price-
1268 J.Y. Campbell
dividend ratio for much of the sample period which is also visible in the average growth
rates of prices and dividends at the right of the table.
Other countries in the quarterly data set, with the exception of France, have firstorder
autocorrelation coefficients for the log price-dividend ratio of between 0.85
and 0.95. Unit root tests do not reject the unit root null hypothesis for most of
these countries, but this may reflect low power of the tests in short data samples.
Equation (27) implies that the log price-dividend ratio must be stationary if real
dividend growth and stock returns are stationary, so this gives some reason to assume
stationarity for the series.
So far I have written asset prices as linear combinations of expected future dividends
and returns. Following Campbell (1991), I can also write asset returns as linear
combinations of revisions in expected future dividends and returns. Substituting
Equation (27) into Equation (26), I obtain
OO OO
ri, l+l -Et ri, t+l = (Et+l -Et) ~PJA~,t,1 i:j- (Et ~l -Et) ~ pJri, t+l+j.
.i- o j - 1
(28)
This equation says that unexpected stock returns must be associated with changes
in expectations of future dividends or real returns. An increase in expected future
dividends is associated with a capital gain today, while an increase in expected future
returns is associated with a capital loss today. The reason is that with a given dividend
stream, higher future returns can only be generated by future price appreciation from
a lower current price.
4.3. The stock market oolatility puzzle
I now use this accounting framework to illustrate the stock market volatility puzzle.
The intertemporal budget constraint for a representative agent, Equation (19), implies
that aggregate consumption is the dividend on the portfolio of all invested wealth,
denoted by subscript w:
dwt = ct. (29)
Many authors, including Grossman and Shiller (1981), Lucas (1978), and Mehra and
Prescott (1985), have assumed that the aggregate stock market, denoted by subscript
e for equity, is equivalent to the wealth portfolio and thus pays consumption as its
dividend. Here I follow Campbell (1986) and Abel (1999) and make the slightly more
general assumption that the dividend on equity equals aggregate consumption raised
to a power )~. In logs, we have
det - ,~ct. (30)
Abel (1999) shows that the coefficient )~ can be interpreted as a measure of leverage.
When )~ > 1, dividends and stock returns are more volatile than the returns on the
Ch. 19." AssetPrices, Consumption,and the BusinessCycle 1269
aggregate wealth portfolio. This framework has the additional advantage that a riskless
real bond with infinite maturity - an inflation-indexed consol, denoted by subscript b can
be priced merely by setting )~= 0.
The representative-agent asset pricing model with Epstein-Zin-Weil utility, conditional
lognormality, and homoskedasticity [Equations (21) and (22)] implies that
Etre,t+l=~e+(@)EtAct+l, (31)
where g~ is an asset-specific constant term. The expected log return on equity, like the
expected log return on any other asset, is just a constant plus expected consumption
growth divided by the elasticity of intertemporal substitution % Power utility is the
special case where the coefficient of relative risk aversion y is the reciprocal of ~p so
the effect of expected consumption growth on expected asset returns is proportional
to y; but this is not true in general.
Substituting Equations (30) and (31) into Equations (27) and (28), I find that
~-t- )~--~)) Et ZpJmct+l±f,
j=0
(32)
and
re,t+l-Et re,t+l = Z(Act+l -E/AG+I)+ Z - (Et+l -Et) Zp/Act+I+j.
j=[
(33)
Expected future consumption growth has offsetting effects on the log price-dividend
ratio. It has a direct positive effect by increasing expected future dividends X-forone,
but it has an indirect negative effect by increasing expected future real interest
rates (1/~0)-for-one. The unexpected log return on the stock market is X times contemporaneous
unexpected consumption growth (since contemporaneous consumption
growth increases the contemporaneous dividend X-for-one), plus (3,- 1/~p) times the
discounted sum of revisions in expected future consumption growth.
For future reference I note that Equation (33) can be inverted to express consumption
growth as a function of tile unexpected return on equity and revisions in expectations
about future returns on equity. Rearranging Equation (33) and using Equation (31),
ACt+l - Et Act+l = (re,t ~q- Efre,t+l) + -~P (Et~l-Et)ZpJr.,t+l+j.
j=l
(34)
An innovation in the equity return raises wealth by a factor (1/;~), and this raises
consumption by the same factor. Increases in expected future equity returns have
offsetting income and substitution effects on consumption; the positive income effect
is (t/)~), and the negative substitution effect is -%
1270 1 Y. Campbell
These equations can be simplified if I assume that expected aggregate consumption
growth, which I write as zt, follows an AR(1) process with mean g and positive
persistence O:
Act+l = zt + Cc, t+l, (35)
zt+l = (1 - O)g + ~zt + ez, t+l. (36)
This is a linear version of the model used by Cecchetti, Lam and Mark (1990, 1993)
and Kandel and Stambaugh (1991), in which expected consumption growth follows
a persistent discrete-state Markov process. The contemporaneous shocks to realized
consumption growth ~c,t+~ and expected future consumption growth c~,t+~ may be
positively or negatively correlated. The correlation between these contemporaneous
shocks controls the univariate autocovariances of consumption growth; the first-order
autocovariance is ~bVar(zt)+ Cov(ez, t ~1, co,t+l), and higher-order autocovariances die
out geometrically at rate ~b. Thus consumption growth inherits the positive serial
correlation of the zt process unless the contemporaneous shocks are sufficiently
negatively correlated. An important special case of the model sets Cz,t+l = ~ec, t+l
to make consumption growth itself an AR(1) process; this is a linear version of the
model of Mehra and Prescott (1985) 19
From Equation (21), the riskless interest rate is linear in expected consumption
growth zs, so this model implies a homoskedastic AR(1) process for the riskless interest
rate, with persistence 0. It is a discrete-time version of the Vasicek (1977) model of
the term structure of interest rates. Campbell, Lo and MacKinlay (1997), Chapter 11,
gives a detailed textbook exposition of this model following Backus (1993), Singleton
(1990), and Sun (1992).
Equations (35) and (36) allow me to rewrite Equations (32) and (33) as
- - + ,~- + (37)
_Pc, det 1-p ~ 1-p~bJ '
and
= - ez,~+l. (38)
Equation (38) shows why it is difficult to match the volatility of stock returns within
this standard framework. The most obvious way to generate volatile stock returns is
19 The empiricalevidenceonunivariateserial correlationin consumptiongrowthis mixed.Table4 shows
small negative autocorrelation in 8 out of 12 quarterly data sets, but only 1 out of 3 annual data sets.
Measurement problems may bias these autocorrelations in either direction. Durability of consumption
tends to bias autocorrelation downwards, but time-averaging and seasonal adjustment tend to bias it
upwards. Empirical estimates of discrete-state Markov models by Cecchetti, Lain and Mark (1990,
1993), Kandel and Stambaugh (1991), and Mehra and Prescott (1985) find some evidence for modest
but persistent predictable variation in consumption growth.
Ch. 19: Asset Prices',Consumption,and the Business Cycle 1271
to assume a large ,t, that is, a volatile dividend, increasing )~, however, has mixed
effects; it increases the volatility of the first term in Equation (38) proportionally,
but as long as '1 < 1/*p it diminishes the volatility of the second term because the
dividend and real interest rate effects of expected consumption growth offset each
other more exactly. The overall volatility of stock returns may actually fall, or grow
only slowly, with '1 until the point is reached where '1 > 1/~p. The empirical evidence
for small ~ppresented in Table 10 suggests that very high ,t will be needed to generate
volatile stock returns. A similar point has been made by Abel (1999), who emphasizes
that predictable variation in expected consumption growth can dampen stock market
volatility and exacerbate the equity premium puzzle.
This model also tends to produce highly volatile returns on real (inflation-indexed)
bonds. By setting '1 = 0 in Equations (37) and (38), the log yield and unexpected return
on a real consol bond, denoted by a subscript b, are
kl, ~ + (39)
Ybt = db~ Pbt - 1- p 1- p~ ] '
and
rb,t+l-Etrb, t+l---(;) (1 P_~)ez, t+l. (40)
When ~p is small, even modest variation in zt will tend to produce large variation in
the riskffee interest rate and in the yields and returns on long-term real bonds. The
correlation of stock and real bond returns is positive if )~ < 1/% but turns negative if
'1 is large enough so that ,~ > 1/~p.
Of course, all these calculations are dependent on the assumption made at the
beginning of this subsection, that the log dividend on stocks is a multiple )~ of log
aggregate consumption. More general models, allowing separate variation in dividends
and consumption, can in principle generate volatile stock returns without excessive
variation in real interest rates. For example, we might modify Equation (30) to allow
a second autonomous component of the dividend:
det -'1c~ ~ at, (41)
where Aat ~qhas a similar structure to consumption growth, being forecast by an AR(1)
state variable:
Aat~l - Yt + ~a,t+l,
Yt+l = (1 - 0)v + Oy, -~ey,~+l.
(42)
(43)
This modification of the basic model would add a term v/(1 ---p) + (Yt v)/(1 -pO) to
the formula for the log price-dividend ratio, Equation (37), and would add a term
1272 JY. Campbell
~a,t+l + p~y,t+l/(l -pO) to the formula for the unexpected log stock return, (38).
Cecchetti, Lain and Mark (1993) estimate a discrete-state Markov model allowing
for this sort of separate variability in consumption and dividends. While such a
model provides a more realistic description of dividends, it requires large predictable
movements in dividends to explain stock market volatility. Unfortunately, as section 4.5
shows, there is little evidence for this.
4.4. Implications Jbr the equity premium puzzle
I now return to the basic model in which the log dividend is a multiple of log aggregate
consumption, and use the formulas derived in the previous subsection to gain a deeper
understanding of the equity premium puzzle. The discussion of the puzzle in section 3
treated the covariance of stock returns with consumption as exogenous, but given a
tight link between stock dividends and consumption the covariance can be derived from
the stochastic properties of consumption itself. This is the approach of many papers
including Abel (1994, 1999), Kandel and Stambaugh (1991), Mehra and Prescott
(1985), and Rietz (1988).
An advantage of this approach is that it clarifies the implications of Epstein-ZinWeil
utility. The Epstein-Zin-Weil Euler equation is derived by imposing a budget
constraint that links consumption and wealth, and it explains risk premia by the
covariances of asset returns with both consumption growth and the return on the
wealth portfolio. The stochastic properties of consumption, together with the budget
constraint, can be used to substitute either consumption or wealth out of the EpsteinZin-Weil
model.
To understand this point, note that Equation (33) applies to the return on the wealth
portfolio when ,~= 1. Setting e = w and )~= 1, Equation (33) becomes
rw,t+~-Etrw, t+l Act+l-EtAct~l + 1 - (Et+~-Et)ZpJAc~+l~/, (44)
j=l
an equation derived by Restoy and Weil (1998) applying the approach of Campbell
(1993). It follows that the covariance of any asset return with the wealth portfolio
must satisfy
aiw- o~c+ (1-~) ai~, (45)
where agz denotes the covariance of asset return i with revisions in expectations of
future consumption growth:
oc
aig =~Coy(ri,t+~- E~ri,t+1,(Et+l - Et) Z pJAct+l+j). (46)
j-1
The letter g is used here as a mnemonic for consumption growth.
Ch. 19." Asset Prices, Consumption, and the Business Cycle 1273
Substituting this expression into the formula for risk premia in the Epstein-Zin-Weil
model, Equation (22), that formula simplifies to
Et[ri,t+l]-rj;t+l +~- = ]/(Yic-~ Y- Oig. (47)
The risk premium on any asset is the coefficient of risk aversion 3/times the covariance
of that asset with consumption growth, plus (7- 1/~p) times the covariance of the
asset with revisions in expected future consumption growth. The second term is zero
if X = 1/% the power utility case, or if there are no revisions in expected future
consumption growth 20.
I now return to the assumption made in the previous subsection that expected
consumption growth is an AR(1) process given by Equation (36). Under this
assumption,
(E,+I - Et) Z pJAct+L+j= ez,t+1. (48)
j=l
Equations (38), (47) and (48) imply that
E,[r~,,t+l]- rf,l+l+-~ y
(49)
This expression nests many of the leading cases explored in the literature on the
equity premium puzzle. To understand it, it is helpful to break the equity premium
into two components, the premium on real consol bonds over the riskless interest rate,
and the premium on equities over real consol bonds:
4E,[rt,,,+ll-rt,t+l+T=7[-~ (1 P--@)
_}_(~/_~) [_@{1_~)20z21" (50)
Et[re,,+l- r<,+I] + 022 ~-Y'~Ia~2+(<p~)aczJ2
(51)
20 Using a continuous-timemodel, Svensson(1989) also emphasizesthat risk premiain the Epstein
Zin Weil model are determined only by risk aversionwhen investment opportunities and expected
consumptiongrowthare constant.
1274 J.Z Campbell
Equations (50) and (51) add up to Equation (49). The first term in each of
these expressions represents the premium under power utility, while the second term
represents the effect on the premium of moving to Epstein-Zin utility and allowing the
coefficient of risk aversion to differ from the reciprocal of the intertemporal elasticity
of substitution. Given the evidence for small ~ppresented in section 4.1, the key issue
is whether Epstein-Zin utility allows y to be smaller than 1/lp and in this sense helps
resolve the equity premium puzzle.
Under power utility, the real bond premium in Equation (50) is determined by the
covariance oc., of realized consumption growth and innovations to expected future
consumption growth. If this covariance is positive, then an increase in consumption is
associated with higher expected future consumption growth, higher real interest rates,
and lower bond prices. Real bonds accordingly have hedge value and the real bond
premium is negative. If oc~is negative, then the real bond premium is positive 21. Under
Epstein-Zin utility with g < 1/% assets that covary negatively with expected future
consumption growth have higher risk premia. Since real bonds have this characteristic,
Epstein-Zin utility with ]/ < 1/~p tends to produce large term premia. This runs
counter to the empirical observation in Tables 7 and 8 that term premia are only
modest; while the term premia measured in the tables are on nominal rather than
real bonds, nominal term premia should if anything be larger than real term premia
because they include a reward for bearing inflation risk which is unlikely to be
negative.
The premium on equities over real bonds is proportional to the coefficient )~ that
governs the volatility of dividend growth. Under power utility the equity-bond premium
is just risk aversion y times 7~times terms in G2 and ocz. Since both G.2 and G.z must be
small to match the observed moments of consumption growth, it is hard to rationalize
the large equity-bond premium shown in Table 9. Epstein-Zin utility with g < 1/~p
adds a second term in oc~ and 62. Unfortunately the o~2 term is negative, which makes
it even harder to rationalize the equity-bond premium.
In conclusion, the consumption-based model with Epstein-Zin-Weil utility is no
more successful than the consumption-based model with power utility in fitting equity
and bond premia with a small coefficient of relative risk aversion. Given the time-series
evidence for a small intertemporal elasticity of substitution % relative risk aversion
y must be large - close to the reciprocal of ~p as implied by power utility - in order
to produce the large equity premia and small bond premia that are measured in the
data.
Campbell (1993) uses these relations in a different way. Instead of substituting the
wealth return out of the Epstein-Zin-Weil model, Campbell substitutes consumption
21 Calnpbetl(1986)developsthis intuitionin a univariatemodelfor consumptiongrowth.
Ch. 19." Asset Prices, Consumption,and the Business Cycle 1275
out of the model to get a discrete-time version of the intertemporal CAPM of Merton
(1973). Setting e = w and )~= 1 in Equation (34), the innovation in consumption is
O(3
Ac, ~- Et ACt+l = rw,t+l - Etr,~,/+1 + (1 - ~P)(E/+I - Et) ~ pJrw, t+l+j.
j=l
(52)
Thus the covariance of any asset return with consumption growth must satisfy
~c = ~w + (1 - ap)~.h, (53)
where oih denotes the covariance of asset return i with revisions in expected future
returns on wealth:
(X3
Oih = Cov(ri, t+l - - Elri, t+l, (Et+l - E~) ZpJrw,/+l+])-
j=l
(54)
The letter h here is used as a mnemonic for hedging demand [Merton (1973)], a term
commonly used in the finance literature to describe the component of asset demand
that is determined by investors' responses to changing investment opportunities.
@ can now be substituted out of Equation (22) to obtain
<
Et[ri, t+l] rj;t+l + ~- = y~riw+(y- 1)~h. (55)
The risk premium on any asset is the coefficient of risk aversion y times the covariance
of that asset with the return on the wealth portfolio, plus (y - 1) times the covariance of
the asset with revisions in expected future returns on wealth. The second term is zero
if y - 1; in this case it is well known that intertemporal asset demands are zero and
asset pricing is myopic. Campbell (1996b) uses this formula to study US stock price
data, assuming that the log return on wealth is a linear combination of the stock return
and the return on human capital (proxied by innovations to labor income). He argues
that mean-reversion in US stock prices implies a positive covariance O~wbetween US
stock returns and the current return on wealth, but a negative covariance a~h between
US stock returns and revisions in expected future returns on wealth. Equation (55)
then implies that increases in y above one have only a damped effect on the equity
premium, so high risk aversion is needed to explain the equity premium puzzle. This
conclusion is reached without any reference to measured aggregate consumption data.
4.5. What does the stock market Jorecast?
All the calculations in sections 4.3 and 4.4 rely heavily on the assumptions of
the representative-agent model with power utility, lognormal distributions, constant
variances, and a deterministic link between stock dividends and consumption. They
1276 J.Y. Campbell
leave open the possibility that the stock market volatility puzzle could be resolved by
relaxing these assumptions, for example to allow independent variation in dividends in
the manner discussed at the end of Section 4.3. A more direct way to understand the
stock market volatility puzzle is to use the loglinear asset pricing framework to study
the empirical relationships between log price-dividend ratios and future consumption
or dividend growth rates, real interest rates, and excess stock returns. According to
Equation (27), the log price-dividend ratio embodies rational forecasts of dividend
growth rates and stock returns, which in turn are the sum of real interest rates and
excess stock returns, discounted to an infinite horizon. One can compare the empirical
importance of these different forecasts by regressing long-horizon consumption and
dividend growth rates, real interest rates,and excess stock returns onto the log price
dividend ratio.
Table 12 (p. 1278) reports the results of this exercise. For comparative purposes
real output growth, realized stock market volatility, and the excess bond return are also
included as dependent variables. For each quarterly data set the dependent variables are
computed in natural units over 4, 8, and 16 quarters (1, 2, and 4years) and regressed
onto the log price-dividend ratio divided by its standard deviation. Thus the regression
coefficient gives the effect of a one standard deviation change in the log price-dividend
ratio on the cumulative growth rate or rate of return in natural units. The table reports
the regression coefficient, heteroskedasticity- and autocorrelation-consistent t statistic,
and R2 statistic.
In the benchmark postwar quarterly US data, the log price-dividend ratio has no
clear ability to forecast consumption growth, output growth, dividend growth, or the
real interest rate at any horizon. What it does forecast is the excess return on stocks,
with t statistics that start above 4 and increase, and with R2 statistics that start at
0.20 and increase to 0.55 at a 4-year horizon. In the introduction these results were
summarized as stylized facts 10, 11, 12, and 13. Table 12 extends them to international
data.
(10) Regressions of consumption growth on the log price-dividend ratio give
very mixed results across countries. There are statistically significant positive
coefficients in Germany and the Netherlands, but statistically significant negative
coefficients in Australia, Canada, Italy, Japan, and Switzerland. The other
countries resemble the USA in that they have no statistically significant
consumption growth forecasts. The regressions with output growth as the
dependent variable show a similar pattern across countries.
(11) Results are somewhat more promising for real dividend growth in many countries.
Positive and statistically significant coefficients are fotmd in Canada, France,
Germany, Italy, Japan, the Netherlands, Sweden, and the UK. It seems clear that
changing forecasts of real dividend growth have some role to play in explaining
stock market movements.
(12) The short-term real interest rate does not seem to be a promising candidate for
the driving force behind stock market fluctuations. One would expect to find
high price-dividend ratios forecasting low real interest rates, but the regression
Ch. 19: Asset Prices, Consumption,and the Business Cycle 1277
coefficients are significantly positive in France, Italy, Japan, the Netherlands,
Sweden, Switzerland, and the UK. This presumably reflects the fact that stock
markets in most countries were depressed in the 1970s, when real interest rates
were low, and buoyant during the 1980s, when real interest rates were high.
(13) Finally, the log price-dividend ratio is a powerful forecaster of excess stock
returns in almost every country. The regression coefficients are uniformly
negative and statistically significant.
In the long-term annual data for Sweden, the UK, and the USA, I use horizons of
1 year, 4 years, and 8 years. In the US data the log price-dividend ratio fails to forecast
real dividend growth, suggesting that authors such as Barsky and DeLong (t993)
overemphasize the role of dividend forecasts in interpreting long-run US experience.
Consistent with the quarterly results, the log price-dividend ratio also fails to forecast
consumption growth, output growth, or the real interest rate, but does forecast excess
stock returns.
The UK data are similar, although here the 8-year regression coefficients for
consumption growth and dividend growth are even statistically significant with the
wrong (negative) sign. The 8-year regression coefficient for the real interest rate is
also significantly negative, consistent with the idea that the UK stock market is related
to the real interest rate. But much the strongest relation is between the log pricedividend
ratio and future excess returns on the UK stock market. The Swedish data are
quite different; here the log price-dividend ratio forecasts short-run dividend growth
positively but has no predictive power for consumption growth, output growth, the real
interest rate, or the excess log stock return.
The rightmost column of Table 12 considers one more dependent variable, the excess
bond return. The predictive power of the stock market for excess stock returns does not
generally carry over to excess bond returns; there are significant negative coefficients
only in Australia and the UK (and in Germany and Switzerland at long horizons).
Overall, these results suggest that a new model of stock market volatility is needed.
The standard model of section 4.3 drives all stock market fluctuations from changing
forecasts of long-run consumption growth, dividend growth, and real interest rates;
forecasts of excess stock returns are constant. The data for many countries suggest
instead that forecasts of consumption growth, dividend growth, and real interest rates
are variable only in the short run, so that long-run forecasts of these variables are
almost constant; stock market fluctuations seem to be driven largely by changing
forecasts of excess stock returns.
4.6. Changing volatility in stock returns
One reason why excess stock returns might be predictable is that the risk of stock
market investment, as measured for example by the volatility of stock returns, might
vary over time. With a constant price of risk, shifts in the quantity of risk will lead to
changes in the equity risk premium.
1278
%
6
eq "~
g
o
g
N
g
"v
J.Y Campbell
~ l l l l l l l l l I I I t I I I
RR RR R R R R~ o R o R R o R R RR R R R R R R R R ~
g ~ g g g ~ g g g g ~ g ~ g ~ g ~ g ~ g g g g g g
R R R @RR R R ~ RR RR RR RR R R R o o R R R R R
I I I I I I I I I I I I I I I I I I I I I I 1 [ [ 1 1
dd d 5 5 d d d d 5 d 5 5 5 d d 5 d d S o S d d 5 5 d
,~ o o ~ 2 ~ . . . . 0002 . . . . . . . . . . . . .
? o~-2 . . . . . . . . . . . . . . . 2<-oII
w . . . . . . . . . . . . . . . . . . . . . . . . . . .
R o R R R R R R R R R R R RR RR R R R R R R ~R R R
,~ ~ o o ~ o ~ o ~ o o o . . . . . . . . . . . . . . .
II l ] l l I I I ] 1 1
,~ 22o oo~ 2 I 2 . . . . . . tt ? ? t? . . . . 22
c~ O O Q O O ~ O O O O Q Q Q O ~ O O ~ ¢ ~ r ~ Q Q Q
I I I ] 1 1
. q @ @ q ~ R ~ R .q . q q ~ q q ~ q ~qq ~ q q .q
Ch. 19." Asset Prices, Consumption, and the Business Cycle
o
=o
I l J l l l l I [ [ l l [i
d d d d d d d d d d d d d d d d d d
I [ 1 1 1 1 1 I I 1 [ I II
[ I I I I l l
I I I I I I I
d d d d d d d & & d d d d d d d d d
I l l l l l l l l l l l l l l l l l
M d & ~ 2 d 2 2 ~ d d d d 2 ~ d d &
I I I I I I l l l I
O q O q q O q O q q q q q O ~ q O q
o o - = o ~o - - ~ o o - ~ o o
d d M M ~ d £ d £ d M ~ £ £ d £ d d
11 I I I I [
d d d d d d d o d d d d & o d & d d
II I ] I I I
d d d d d d d d d d d d d d d d d d
4 ~ -' " o ~ o o ~ ~ ~ ~o o o ~ o o
i i i ii I l l l l l ii
i i i Ii I I I I I i ii
= o o o o o o ~ o o o o E o o ~
oo oo ~ o o o oo
II 1 1 1 1 1 1 1 I I I I
"~ '~ 0
E ~ ~ :~
~ ~..
o= .~z
0a
o
1279
t280 J.g Campbell
There is a vast literature documenting the fact that stock market volatility does
change with time. However, the variation in volatility is concentrated at high
frequencies; it is most dramatic in daily or monthly data and is much less striking at
lower frequencies. There is some business-cycle variation in volatility, but it does not
seem strong enough to explain large movements in aggregate stock prices [Bollerslev,
Chou and Kroner (1992), Schwert (1989)].
A second difficulty is that there is only weak evidence that periods of high
stock market volatility coincide with periods of predictably high stock returns.
Some papers do find a positive relationship between conditional first and second
moments of returns [Bollerslev, Engle and Wooldridge (1988), French, Schwert and
Stambaugh (1987), Harvey (1989)], but other papers find that when short-term nominal
interest rates are high, the conditional volatility of stock returns is high while the
conditional mean stock return is low [Campbell (1987), Glosten, Jagannathan and
Runkle (1993)].
French, Schwert and Stambaugh (1987) emphasize that innovations in volatility
are strongly negatively correlated with innovations in returns. This could be indirect
evidence for a positive relationship between volatility and expected returns, but it could
also indicate that negative shocks to stock prices raise volatility, perhaps by raising
financial or operating leverage of companies [Black (1976)].
Some researchers have built models that allow for independent variation in the
quantity and price of risk. Harvey (1989, 1991) uses "the Generalized Method of
Moments to estimate such a system, and finds that the price of risk appears to vary
countercyclically. Chou, Engle and Kane (1992) find similar results using a GARCH
framework.
Within the confines of this chapter it is not possible to do justice to the sophistication
of the econometrics used in this literature. Instead i illustrate the empirical findings
of the literature by constructing a crude measure of ex post volatility for excess
stock returns - the average over 4, 8, or 16 quarters of the squared quarterly excess
stock return - and regressing it onto the log price-dividend ratio. The results of this
regression are reported in the sixth data column of Table 12. There are nmnerous
significant coefficients in these regressions, but they are all positive, indicating that
high price-dividend ratios predict high, not tow volatility in these data.
These results reinforce the conclusion of the literature that the price of risk seems to
vary over time in relation to the level of aggregate consumption. Section 5 discusses
economic models that have this property.
4.7. What does the bond market forecast?
I conclude this section by briefly comparing the results of Table 12 with those that
carl be obtained using bond market data. Table 13 repeats the regressions of Table 12
using the yield spread between long-term and short-term bonds as the regressor. Many
authors have found that in US data, yield spreads have some ability to forecast excess
bond returns [Campbell (1987), Campbell and Shiller (199l), Fama and Bliss (1987)].
Ch. 19: Asset Prices', Consumption, and the Business Cycle 1281
This contradicts the expectations hypothesis of the term structure, the hypothesis that
excess bond returns are unforecastable. Other authors have found that yield spreads are
powerful forecasters of macroeconomic conditions, particularly output growth [Chen
(1991), Estrella and Hardouvelis (1991)]. Fama and French (1989) have argued that
both price-dividend ratios and yield spreads capture short-term cyclical conditions,
although yield spreads are more highly correlated with conventional measures of the
US business cycle.
The results of Table 13 are strikingly different from those of Table 12. In the
quarterly data, yield spreads forecast positive output growth in almost every country,
and positive consumption growth in many countries. Outside the USA, there is also a
strong tendency for yield spreads to forecast low real interest rates. Thus the findings
of Chen (1991) and Estrella and Hardouvelis (1991) carry over to international data.
Yield spreads are much less successful as forecasters of excess stock returns, stock
market volatility, or even excess bond returns; the ability of the yield spread to
forecast excess bond returns appears to be primarily a US rather than an international
phenomenon 2~. Similar conclusions are reported by Hardouvelis (1994) and Bekaert,
Hodrick and Marshall (1997). While these authors do report some evidence for
predictability of excess bond returns in international data, the evidence is much weaker
than in US data.
These results are consistent with the view that there is some procyclical variation
in tile short-term real interest rate which is not matched by the long-term real interest
rate. Thus yield spreads tend to rise at business cycle troughs when real interest rates
are predictably low and future output and consumption growth are predictably high.
This interpretation is complicated by the fact that yields are measured on nominal
bonds rather than real bonds. Inflationary expectations and monetary policy therefore
have a large impact on yield spreads. The particular characteristics of US monetary
policy may help to explain why previously reported US results do not carry over
to other countries in Table 13. US monetary policy has tended to smooth real and
nominal interest rates, which reduces the forecastability of real interest rates and
increases the sensitivity of the yield spread to changes in bond-market risk premia.
Mankiw and Miron (1986) have found that the yield spread was a better forecaster
of US interest rates in the period before the founding of the Federal Reserve, while
Kugler (1988) has found that the yield spread is a better forecaster of interest
rates in Germany and Switzerland and has related this to the characteristics of
German and Swiss monetary policy. The findings in Table 13 are consistent with this
literature.
22 Resultsat a one-quarterhorizon,not reportedin the table, are qualitativelyconsistentwith the longhorizon
results.
1282
"¢3
e,~'~-,
em
©
v
~g
v
g
~g
~g
g
N
.g
2
2
dE Campbell
II I II }{ {I [I I ~
II I II II II II I ~
g ~ m g ~ g g m g g ~ g g ~ g g ~ g ~ g ~ $
6 6 ~ 6 ~ 6 ~ d 6 6 6 6 ~ 6 ~ 6 6 ~ 6 ~ 6 ~
~ X % 2 q ~ q ~ Q q ~ X q q 2 q ~ 2 q q ~ q
77 ~ ~ 7 ~ 7 7 5 . . . . . . 7 o ~ 77 o ~ ~ ~
~ E g ~ g N ~ g g ~ ¢ g E g g g ~ g g g g
Q Q ~ Q Q Q Q Q Q Q Q Q Q Q Q Q . Q Q Q Q
~ q q q q q q q ~ q . ~ Q q Q Q q q Q q Q q q
I I I I [
q q q q q q q q q q q ~ q q q q q q q q q V q q
~ N ~ ~ ¢ N ~ g ~ ~ g N ~ g g~g ~ ~ g g g N
~ ~ ~ ~ ~ ~ ~ ~ ~ • • • # ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
i i i i i l l l l l l l { l l l l i i i
q q q ~ q q ~ q q ~ V q q q ~ q q q q q q q q
e ~ g g e g ~ ¢ ~ g g g ~ z ~ g g m ~ g g
g g ~ g g g ~ g D g g ~ g ~ g ~ g g g g ~ g
] I l l
R R R R R R R R R R R R R R R R R R R R R R R ~
R R R R R R ~ R ~ R R R R R R R R R R R R R R R
I
[ I I I I
Q Q ~ Q ~ ~ Q Q Q Q Q Q Q Q Q Q Q Q Q
Ch. 19." Asset Prices, Consumption, and the Business Cycle
o
o ~
g
N
N ~
~K
I I I II II
0 0 o o 0 0 o o o o 0 0 0 0 0 0 o o o 0 0
I l l ] l I I I I I
d d d d d d o d d d d d d d d e d d d d d
M M ~ d d d d £ £ M M o d d d £ ~ d & & d
I I I 1 [ I I I I I I I I ~s
ad
5 d d d d 5 d d d 5 ,5 d d ,5 d d d 5 5 5 ,5 ~ g
I I I I I I ~
I I I I I I I I I I I I I ] I I I I I ~ ;~
I I I
cR q q q q o. ~R q q q q c~ q q c: o q cR q q q
I I I I I I I
c~ ~ ~ <
~. c..)
o., c~
1283
1284 J E Campbell
5. Cyclical variation in the price of risk
In previous sections I have documented a challenging array of stylized facts and have
discussed the problems they pose for standard asset pricing theory. Briefly, the equity
premium puzzle suggests that risk aversion must be high on average to explain high
average excess stock returns, while the stock market volatility puzzle suggests that risk
aversion must vary over time to explain predictable variation in excess returns and the
associated volatility of stock prices. This section describes some models that display
these features.
5.1. Habit formation
Constantinides (1990), Ryder and Heal (1973), and Sundaresan (1989) have argued
for the importance of habit formation, a positive effect of today's consumption on
tomorrow's marginal utility of consumption.
Several modeling issues arise at the outset. Writing the period utility function as
U(Ct,Xt), where Xt is the time-varying habit or subsistence level, the first issue is the
functional form for U(.). Abel (1990, 1999) has proposed that U(.) should be a power
function of the ratio CJX~,while Boldrin, Christiano and Fisher (1995), Campbell and
Cochrane (1999), Constantinides (1990), and Sundaresan (1989) have used a power
function of the difference Ct-Xt. The second issue is the effect of an agent's own
decisions on future levels of habit. In standard "internal habit" models such as those
in Constantinides (1990) and Sundaresan (1989), habit depends on an agent's own
consumption and the agent takes account of this when choosing how much to consume.
In "external habit" models such as those in Abel (1990, 1999) and Campbell and
Cochrane (1999), habit depends on aggregate consumption which is unaffected by
any one agent's decisions. Abel calls this "catching up with the Joneses". The third
issue is the speed with which habit reacts to individual or aggregate consumption.
Abel (1990, 1999), Durra and Singleton (1986), and Ferson and Constantinides (1991)
make habit depend on one lag of consumption, whereas Boldrin, Christiano and Fisher
(1995), Constantinides (1990), Sundaresan (1989), Campbell and Cochrane (1999),
and Heaton (1995) assume that habit reacts only gradually to changes in consumption.
The choice between ratio models and difference models of habit is important because
ratio models have constant risk aversion whereas difference models have time-varying
risk aversion. To see this, consider Abel's (1990, 1996) specification in which an agent's
utility can be written as a power function of the ratio CSXt,
C~
(Ct+/X,~I) 1 Y 1
U~ = Z 6t - (56)
1-y
j-O
where Xt summarizes the influence of past consumption levels on today's utility. For
simplicity, specify X~ as an external habit depending on only one lag of aggregate
consumption:
Xt = C,~-t, (57)
Ch. 19: Asset Prices, Consumption, and the Business Cycle 1285
where Ct i is aggregate past consumption and the parameter t¢ governs the degree of
time-nonseparability. Since there is a representative agent, in equilibrium aggregate
consumption equals the agent's own consumption, so in equilibrium
x,=c5_1. (58)
With this specification of utility, in equilibrium the first-order condition is
1 = OEt [(1 +Ri,t+I)(Ct/Ct_I)~V(Y-1)(CI_I/Ct)Y]. (59)
Assuming homoskedasticity and joint lognonnality of asset returns and consumption
growth, this implies the following restrictions on risk premia and the riskless real
interest rate:
rJ;t+l = - - log 6 - 720"~2/2 + 7EtAct+l tc(y - 1)Ac.
Et [ri,, +1 - rj; t +1] -k 0,2/2 = 7oi~.
(60)
(61)
Equation (60) says that the riskless real interest rate equals its value under power
utility, less tc(y- 1)Act. Holding consumption today and expected consumption
tomorrow constant, an increase in consumption yesterday increases the marginal utility
of consumption today. This makes the representative agent want to borrow from the
future, driving up the real interest rate. Equation (61) describing the risk premium
is exactly the same as Equation (16), the risk premium formula for the power utility
model. The external habit simply adds a term to the Euler equation (59) which is
known at time t, and this does not affect the risk premium.
Abel (1990, 1999) nevertheless argues that catching up with the Joneses can help
to explain the equity premium puzzle. This argument is based on two considerations.
First, the average level of the riskless rate in Equation (60) is -log 6- y2o~.2/2+
(y - tc(y - 1))g, where g is the average consumption growth rate. When risk aversion
y is very large, a positive t¢ reduces the average riskless rate. Thus catching up
with the Joneses enables one to increase risk aversion to solve the equity premium
puzzle without encountering the riskless rate puzzle. Second, a positive t¢ is likely to
make the riskless real interest rate more variable because of the term -tc(y-1)Ac, in
Equation (60). If one solves for the stock returns implied by the assumption that stock
dividends equal consumption, a more variable real interest rate increases the covariance
of stock returns and consumption oic and drives up the equity premium.
The second of these points can be regarded as a weakness rather than a strength
of the model. The puzzle illustrated in Table 5 is that the ratio of the measured
equity premium to the measured covariance oic is large; increasing the consumption
covariance oic does not by itself help to explain the size of this ratio. Also, Table 2
shows that the real interest rate is fairly stable ex post, while Table 7 shows that at
most half of its variance is forecastable. Thus the standard deviation of the expected
1286 J. Y Campbell
real interest rate is quite small, and this is not consistent with large values of t¢ and
y in Equation (60).
This difficulty with the riskless real interest rate is a fundamental problem for habit
formation models. Time-nonseparable preferences make marginal utility volatile even
when consumption is smooth, because consumers derive utility from consumption
relative to its recent history rather than from the absolute level of consumption. But
unless the consumption and habit processes take particular forms, time-nonseparability
also creates large swings in expected marginal utility at successive dates, and this
implies large movements in the real interest rate. I now present an alternative
specification in which it is possible to solve this problem, and in which risk aversion
varies over time.
Campbell and Cochrane (1999) build a model with external habit formation in which
a representative agent derives utility from the difference between consumption and a
time-varying subsistence or habit level. They assume that log consumption follows
a random walk. This fits the observation that most countries do not have highly
predictable consumption or dividend growth rates (Tables 7 and 9). The consumption
growth process is
Act+l = g + ~c,t+l, (62)
where co,t+1 is a normal homoskedastic innovation with variance ao2. This is just the
ARMA(1,1) model (35) of the previous section, with constant expected consumption
growth.
The utility function of the representative agent takes the form
oc [ C X~ ,~1 .y
V' 6J ~ t+j- t+jj -1
Et (63)
1-y
j-0
Here Xt is the level of habit, 6 is the subjective discount factor, and 7 is the utility
curvature parameter. Utility depends on a power function of the difference between
consumption and habit; it is only defined when consumption exceeds habit.
It is convenient to capture the relation between consumption and habit by the surplus
consumption ratio St, defined by
G-X,
St =- (64)
C,
The surplus consumption ratio is the fraction of consumption that exceeds habit and
is therefore available to generate utility in Equation (63). If habit Xt is held fixed as
consumption Ct varies, the local coefficient of relative risk aversion is
-Cute_ 7
uc St' (65)
where uc and ucc are the first and second derivatives of utility with respect to
consumption. Risk aversion rises as the surplus consumption ratio St declines, that
Ch. 19." Asset Prices, Consumption, and the Business Cycle 1287
is, as consumption approaches the habit level. Note that y, the curvature parameter in
utility, is no longer the coefficient of relative risk aversion in this model.
To complete the description of preferences, one must specify how the habit Xt
evolves over time in response to aggregate consumption. Campbell and Cochrane
suggest an AR(1) model for the log surplus consumption ratio, st -= log(St):
s~+l = (1 - q0)~+ q)st + Z (st) ~c,t+l. (66)
The parameter q0governs the persistence of the log surplus consumption ratio, while
the "sensitivity function" Z(st) controls the sensitivity of st~-i and thus of log habit xt+l
to innovations in consumption growth ce,t+l.
Equation (66) specifies that today's habit is a complex nonlinear function of current
and past consumption. A linear approximation may help to understand it. If I substitute
the definition st =- log(1 - exp(xt - ct)) into Equation (66) and linearize around the
steady state, I find that Equation (66) is approximately a traditional habit-formation
model in which log habit responds slowly and linearly to log consumption,
CxD
xM ,-~ (1-q0)a+qvxt+(1 q0)ct= a+(l q))~cpJct=i. (67)
j-0
The linear model (67) has two serious problems. First, when consumption follows an
exogenous process such as Equation (62) there is nothing to stop consumption falling
below habit, in which case utility is undefined. This problem does not arise when one
specifies a process for st, since any real value for st corresponds to positive S~ and
hence Ct > Xt. Second, the linear model typically implies a highly volatile riskless
real interest rate. The process (66) with a non-constant sensitivity function Z(st) allows
one to control or even eliminate variation in the riskless interest rate.
To derive the real interest rate implied by this model, one first calculates the marginal
utility of consumption as
d(Ct) = (G-X,) 7 = S rCr. (68)
The gross simple risktess rate is then
(i +RIll) = (0E, Ut(G'l)~ '= (OEt (~tiJ 7 \-GI.,/(C'4'~-Y)'U'(Q) ) . (69)
Taking logs, and using Equations (62) and (66), the log riskless real interest rate is
2 2
' - 7Gr/) 1 = - log(0) + yg - y(1 - cp)(s, - s) - -~- [Z(s,) + 1]2 . (70)
The first two terms on the right-hand side of Equation (70) are familiar from the
power utility model (17), while the last two terms are new. The third term (linear in
1288 JY. Campbell
(st -~)) reflects intertemporal substitution. If the surplus consumption ratio is low, the
marginal utility of consumption is high. However, the surplus consumption ratio is
expected to revert to its mean, so marginal utility is expected to fall in the future.
Therefore, the consumer would like to borrow and this drives up the equilibrium
riskfree interest rate. Note that what determines intertemporal substitution is meanreversion
in marginal utility, not mean-reversion in consumption itself. In this model
consumption follows a random walk so there is no mean-reversion in consumption; but
habit formation causes the consumer to adjust gradually to a new level of consunlption,
creating mean-reversion in marginal utility.
The fourth term (linear in D~(s~)+ l]2) reflects precautionary savings. As uncertainty
increases, consumers become more willing to save and this drives down the
equilibrium riskless interest rate. Note that what determines precautionary savings
is uncertainty about marginal utility, not uncertainty about consumption itself. In
this model the consumption process is homoskedastic so there is no time-variation
in uncertainty about consumption; but habit formation makes a given level of
consumption uncertainty more serious for marginal utility ,when consumption is low
relative to habit.
Equation (70) can be made to match the observed stability of real interest rates in two
ways. First, it is helpful if the habit persistence parameter q~is close to one, since this
limits the strength of the intertemporal substitution effect. Second, the precautionary
savings effect offsets the intertemporal substitution effect if A(s~)declines with st. In
fact, Campbell and Cochrane parametrize the ,~(st) function so that these two effects
exactly offset each other everywhere, implying a constant riskless interest rate. With
a constant riskless rate, real bonds of all maturities are also riskless and there are no
real term premia. Thus in the Campbell-Cochrane model the equity premium is also
an equity-bond premium.
The sensitivity function ,~(st) is not fully determined by the requirement of a constant
riskless interest rate. Campbell and Cochrane choose the function to satisfy three
conditions: (1) The riskless real interest rate is constant. (2) Habit is predetermined
at the steady state s~ = 3. (3) Habit is predetermined near the steady state, or,
equivalently, positive shocks to consumption may increase habit but never reduce it. To
understand conditions (2) and (3), recall that the traditional notion of habit makes it a
predetermined variable. On the other hand habit cannot be predetermined everywhere,
or a sufficiently low realization of consumption growth would leave consumption
below habit. To make habit "as predetermined as possible", Campbell and Cochrane
assume that habit is predetermined at and near the steady state. This also eliminates
the counterintuitive possibility that positive shocks to consumption cause declines in
habit.
Using these three conditions, Campbell and Cochrane show that the steady-state
surplus consumption ratio must be a function of the other parameters of the model, and
that the sensitivity function )~(st) must take a particular form. Campbell and Cochrane
pick parameters for the model by calibrating it to fit postwar quarterly US data. They
choose the mean consumption growth rate g = 1.89% per year and the standard
Ch. 19: Asset Prices, Consumption, and the Business Cycle 1289
deviation of consumption growth oc = 1.50% per year to match the moments of the
US consumption data.
Campbell and Cochrane follow Mehra and Prescott (1985) by assuming that the
stock market pays a dividend equal to consumption. They also consider a more realistic
model in which the dividend is a random walk whose innovations are correlated with
consumption growth. They show that results in this model are very similar because
the implied regression coefficient of dividend growth on consumption growth is close
to one, which produces similar asset price behavior. They use numerical methods to
find the price-dividend ratio for the stock market as a function of the state variable st.
They set the persistence of the state variable, ~, equal to 0.87 per year to match the
persistence of the log price-dividend ratio. They choose y = 2.00 to match the ratio of
unconditional mean to unconditional standard deviation of return in US stock returns.
These parameter values imply that at the steady state, the surplus consumption ratio
= 0.057 so habit is about 94% of consumption. Finally, Campbell and Cochrane
choose the discount factor 6 = 0.89 to give a riskless real interest rate of just under
1% per year.
It is important to understand that with these parameter values the model uses high
average risk aversion to fit the high unconditional equity premium. Steady-state risk
aversion is y/S = 2.00/0.057 = 35. In this respect the model resembles a power utility
model with a very high risk aversion coefficient.
There are however two important differences between the model with habit
formation and the power utility model with high risk aversion. First, the model with
habit formation avoids the riskfree rate puzzle. Evaluating Equation (70) at the steadystate
surplus consumption ratio and using the restrictions on the sensitivity function
)~(&), the constant riskless interest rate in the Campbell-Cochrane model is
r/+j - log(6) + yg- ~-. (71)
In the power utility model the same large coefficient y would appear in the consumption
growth term and the consumption volatility term [Equation (17)]; in the CampbellCochrane
model the curvature parameter ]e appears in the consumption growth term,
and this is much lower than the steady-state risk aversion coefficient y/5: which appears
in the consumption volatility term. Thus a much lower value of the discount factor 6
is consistent with the average level of the risk free interest rate, and the model implies
a less sensitive relationship between mean consumption growth and interest rates.
Second, the model with habit formation has risk aversion that varies with the level
of consumption, whereas a power utility model has constant risk aversion. The time.variation
in risk aversion generates predictable movements in excess stock returns like
those documented in Table 12, enabling the Campbell-Cochrane model to match the
volatility of stock prices even with a smooth consumption series and a constant riskless
interest rate.
1290 J Y.Campbell
5.2. Models' with heterogeneous agents
All the models considered so far assume that assets can be priced as if there is a
representative agent who consumes aggregate consumption. An alternative view is that
aggregate consumption is not an adequate proxy for the consumption of stock market
investors.
One simple explanation for a discrepancy between these two measures of consumption
is that there are two types of agents in the economy: constrained agents
who are prevented from trading in asset markets and simply consume their labor
income each period, and unconstrained agents. The consumption of the constrained
agents is irrelevant to the determination of equilibrium asset prices, but it may be
a large fraction of aggregate consumption. Campbell and Mankiw (1989) argue that
predictable variation in consumption growth, correlated with predictable variation in
income growth, suggests an important role for constrained agents, while Mankiw
and Zeldes (1991) and Brav and Geczy (1996) use US panel data to show that the
consumption of stockholders is more volatile and more highly correlated with the stock
market than the consumption of non-stockholders. Such effects are likely to be even
more important in countries with low stock market capitalization and concentrated
equity ownership.
The constrained agents in the above model do not directly influence asset prices,
because they are assumed not to hold or trade financial assets. Another strand of
the literature argues that there may be some investors who buy and sell stocks for
exogenous, perhaps psychological reasons. These "noise traders" can influence stock
prices because other investors, who are rational utility-maximizers, must be induced
to accommodate their shifts in demand. If utility-maximizing investors are risk-averse,
then they will only buy stocks from noise traders who wish to sell if stock prices fall
and expected stock returns rise; conversely they will only sell stocks to noise traders
who wish to buy if stock prices rise and expected stock returns fall. Campbell and
Kyle (1993), Cutler, Poterba and Summers (1991), DeLong, Shleifer, Summers and
Waldmalm (1990), and Shiller (1984) develop this model in some detail. The model
implies that rational investors do. not hold the market portfolio - instead they shift in
and out of the stock market in response to changing demand from noise traders - and
do not consume aggregate consumption since some consumption is accounted for by
noise traders. This makes the model hard to test without having detailed information
on the investment strategies of different market participants 23.
It is also possible that utility-maximizing stock market investors are heterogeneous
in important ways. If investors are subject to large idiosyncratic risks in their labor
income and can share these risks only indirectly by trading a few assets such as stocks
23 Recentworksurveyedby Shiller(1999)attempts to placethe behaviorof noise traders on a firmer
psychologicalfolmdation.BenartziandThaler(1995),fbr example,arguethatpsychologicalbiasesmake
noise tradersreluctantto hold stocks,and that this helpsto explainthe equitypremiumpuzzle.
Ch. 19: Asset Prices, Consumption,and the Business Cycle 1291
and Treasury bills, their individual consumption paths may be much more volatile
than aggregate consumption. Even if individual investors have the same power utility
function, so that any individual's consumption growth rate raised to the power -y would
be a valid stochastic discount factor, the aggregate consumption growth rate raised to
the power -y may not be a valid stochastic discount factor.
This problem is an example of Jensen's Inequality. Since marginal utility is
nonlinear, the average of investors' marginal utilities of consumption is not generally
the same as the marginal utility of average consumption. The problem disappears when
investors' individual consumption streams are perfectly correlated with one another as
they will be in a complete markets setting. Grossman and Shiller (1982) point out
that it also disappears in a continuous-time model when the processes for individual
consumption streams and asset prices are diffusions.
Recently Constantinides and Duffle (1996) have provided a simple framework within
which the effects of heterogeneity can be understood. Constantinides and Duffle
postulate an economy in which individual investors k have different consumption levels
Ckt. The cross-sectional distribution of individual consumption is lognormal, and the
change from time t to time t + 1 in individual log consumption is cross-sectionally
uncorrelated with the level of individual log consumption at time t. All investors have
the same power utility function with time discount factor 6 and coefficient of relative
risk aversion y,
In this economy each investor's own intertemporal marginal rate of substitution
is a valid stochastic discount factor. Hence the cross-sectional average of investors'
intertemporal marginal rates of substitution is a valid stochastic discount factor. I write
this as
M,+~ = 6E,\~ L\~-k, ) / '
(72)
where E[ denotes an expectation taken over the cross-sectional distribution at time t.
That is, for any cross-sectionally random variable Xk~,
K
1 ~Xkt,E:x,, - lim
k-I
the limit as the number of cross-sectional units increases of the cross-sectional sample
average of Xkt24. Note that E[Xkt will in general vary over time and need not be
lognormally distributed conditional on past information.
24 Constantinidesand Duffle(1996)present a morerigorousdiscussion.
1292 J.Y. Campbell
The assumption of cross-sectional lognormality means that the log stochastic
discount factor, m[+1 = log(M~ 1), can be written as a function of the cross-sectional
mean and variance of the change in log consumption:
mr+t = -log(b)- yEt+jAck, t+1 + Var~+lAck,t+l, (73)
where Var[ is defined analogously to E[ as
K
Var/Xl, = lim 1 ~(X~ lEt&,)2 '
K--,ooK
k=l
and like E[ will in general vary over time.
An economist who knows the underlying preference parameters of investors but
does not understand the heterogeneity in this economy might attempt to construct a
representative-agent stochastic discount factor, M/~, using aggregate consumption:
/E/+l[G,t+l] ) r
-'uF+'l - b k (74)
The log of this stochastic discount factor can also be related to the cross-sectional
mean and variance of the change in log consumption:
me+]=-log(b)-yEt+,Ack, t+l- (~)[Vart+lck, t+1- Var/c?,l]
--log(O)-yE2i.,Ack,,+,- (7)[Var,*~_iAc'k,,+,],
(7s)
where the second equality follows from the relation ck,tH ckf+ Ack,t+l and the fact
that Ack,t+l is cross-sectionally uncorrelated with ckt.
The diflbrence between these two variables can now be written as
m/~1 I~A Y(Y+ 1) .-m"l = 2 Vart+lACk, t kl. (76)
The time series of this difference can have a nonzero mean, helping to explain
the riskfree rate puzzle, and a nonzero variance, helping to explain the equity
premium puzzle. If the cross-sectional variance of log consumption growth is
negatively correlated with the level of aggregate consumption, so that idiosyncratic risk
increases in economic downturns, then the true stochastic discount factor m[+1 will be
more strongly countercyclical than the representative-agent stochastic discount factor
constructed using the same preference parameters; this has the potential to explain the
high price of risk without assuming that individual investors have high risk aversion.
Mankiw (1986) makes a similar point in a two-period model.
Ch. 19: Asset Prices, Consumption,and the Business Cycle 1293
An important unresolved question is whether the heterogeneity we can measure
has the characteristics that are needed to help resolve the asset pricing puzzles. In
the Constantinides-Duffie model the heterogeneity must be large to have important
effects on the stochastic discount factor; a cross-sectional standard deviation of log
consumption growth of 20%, for example, is a cross-sectional variance of only 0.04,
and it is variation in this number over time that is needed to explain the equity premium
puzzle. Interestingly, the effect of heterogeneity is strongly increasing in risk aversion
since Var~*+lAck,t+l is multiplied by y(g + 1)/2 in Equation (76). This suggests that
heterogeneity may supplement high risk aversion but cannot altogether replace it as
an explanation for the equity premium puzzle 25.
It is also important to note that idiosyncratic shocks have large effects in the
Constantinides-Duffie model because they are permanent. Heaton and Lucas (1996)
calibrate individual income processes to micro data from the Panel Study of Income
Dynamics (PSID). Because the PSID data show that idiosyncratic income variation
is largely transitory, Heaton and Lucas find that investors can minimize its effects on
their consumption by borrowing and lending. This prevents heterogeneity from having
any large effects on aggregate asset prices.
To get around this problem, several recent papers have combined heterogeneity with
constraints on borrowing. Heaton and Lucas (1996) and Krusell and Smith (1997) find
that borrowing constraints or large costs of trading equities are needed to explain the
equity premium. Constantinides, Donaldson and Mehra (1998) focus on heterogeneity
across generations; in a stylized three-period overlapping generations model they find
that they can match the equity premium if they prevent young agents from borrowing
to buy equities.
All of these models assume that agents have identical preferences. But heterogeneity
in preferences may also be important. Several authors have recently argued that trading
between investors with different degrees of risk aversion or time preference, possibly
in the presence of market frictions, can lead to time-variation in the market price of
risk [Aiyagari and Gertler (1998), Grossman and Zhou (1996), Sandroni (1997), Wang
(1996)]. This seems likely to be an active research area in the next few years.
5.3. Irrational expectations
So far I have maintained the assumption that investors have rational expectations and
understand the time-series behavior of dividend and consumption growth. A number of
papers have explored the consequences of relaxing this assumption. [See for example
25 Lettau (1997) reaches a similar conclusion by assuming that individuals consume their income,
and calculating the risk-aversioncoefficientsneeded to put model-based stochastic discount factors
inside the Hansen-Jagannathanvolatility bounds. This procedure is conservativein that individuals
trading in financialmarkets are normallyable to achievesome smoothingof consumptionrelativeto
income.NeverthelessLettaufindsthathigh individualrisk aversionis stillneededto satisfythe Hansen,~
Jagannathanbounds.
1294 JY CampbeH
Barberis, Shleifer and Vishny (1998), Barsky and DeLong (1993), Cecchetti, Lam and
Mark (1998), Chow (1989), or Hansen, Sargent and Tallarini (1997)] 26
In the absence of arbitrage, there exist positive state prices that can rationalize the
prices of traded financial assets. These state prices equal subjective state probabilities
multiplied by ratios of marginal utilities in different states. Thus given any model of
utility, there exist subjective probabilities that produce the necessary state prices and
in this sense explain the observed prices of traded financial assets. The interesting
question is whether these subjective probabilities are sufficiently close to objective
probabilities, and sufficiently related to known psychological biases in behavior, to be
plausible.
Many of the papers in this area work in partial equilibrium and assume that stocks
are priced by discounting expected future dividends at a constant rate. This assumption
makes it easy to derive any desired behavior of stock prices directly from assumptions
on dividend expectations. Barsky and DeLong (1993), for example, assume that
investors believe dividends to be generated by a doubly integrated process, so that
the dividend growth rate has a unit root. These expectations imply that rapid dividend
growth increases stock prices more than proportionally, so that the price-dividend ratio
rises when dividends are growing strongly. If dividend growth is in fact stationary, then
the high price-dividend ratio is typically followed by dividend disappointments, low
stock returns, and reversion to the long-run mean pric~dividend ratio. Thus Barsky
and DeLong's model can account for the volatility puzzle and the predictability of
stock returns.
In general equilibrium, dividends are linked to consumption so investors' irrational
expectations about dividend growth should be linked to their irrational expectations
about consumption growth, interest rates are not exogenous, but like stock prices, are
determined by investors' expectations. Thus it is significantly harder to build a general
equilibrium model with irrational expectations.
To see how irrationality can affect asset prices, consider first a static model in which
log consumption follows a random walk (q} = 0) with drift g. Investors understand
that consumption is a random walk, but they expect it to grow at rate ~ instead of g.
Equation (37) implies that the log price-dividend ratio is
Pet - det -- i - p + ~ -- (77)
Equation (21) implies that the riskless imerest rate is
0-1 2 0 2
rL,+1 - - log 6 + ~ + ~-- ow- ~-~- o7, (78)
26 There is also import.
Ch. 19: Asset Prices, Consumption, and the Business Cycle 1295
and the rationally expected equity premium is
4Et[r~,,+,l - rf, t-t-1 -t- T = ~I-~0"2-I- ~L(M- D)" (79)
The first term on the right-hand side of Equation (79) is the standard formula for
the equity premium in a model with serially uncorrelated consumption growth. This is
investors' irrational expectation of the equity premium. The second term arises because
dividend growth is systematically different from what investors expect.
This model illustrates that irrational pessimism among investors @ < g) can lower
the average riskfree rate and increase the equity premium. Thus pessimism has the
same effects on asset prices as a low rate of time preference and a high coefficient of
risk aversion, and it can help to explain both the riskfree rate puzzle and the equity
premium puzzle 27.
To explain the volatility puzzle, a more complicated model of irrationality is needed.
Suppose now that log consumption growth follows an AR(1) process, a special case
of Equation (35), but that investors believe the persistence coefficient to be ~}when in
fact it is q)28. In this case the riskfree interest rate is given by
^
r/;t+l =/~f+ ~(Act-g), (80)
while the rationally expected equity premium is
<
E,fr~,,~,I-,r~;,,,+T=~-(,}-O) ~ ,~- +,~ (A<-g), (81)
where/~f and/J~ are constants. If 0 is larger than ~b, and if the term in square brackets
in Equation (81) is positive, then the equity premium falls when consumption growth
has been rapid, and rises when consumption growth has been weak. This model, which
can be seen as a general equilibrium version of Barsky and DeLong (1993), fits the
apparent cyclical variation in the market price of risk.
One difficulty with this explanation for stock market behavior is that it has strong
implications for bond market behavior. Consumption growth drives up the riskless
27 The effect of pessimism on the averageprice-dividend ratio is ambiguous, for the usual reason that
lower riskfree rates and lower expected dividend growth have offsetting effects. Hansen, Sargent and
Tallarini (1997) alsoemphasizethat irrational pessimism can be observationallyequivalentto lowertime
preference and higher risk aversion.
28 All alternativeformulationwouldbe to assume, followingEquation(35), that log consumptiongrowth
is predicted by a state variablex~that investorsobserve,but that investorsmisperceivetile persistence of
this process to be ~ rather than ~. In this case investorscorrectly forecast consumptiongrowth overthe
next period, but incorrectly forecast subsequent consumption growth. Their irrationality has no effect
on the riskfiee interest rate but causes time-variation in equity and bond premia.
1296 JY. Campbell
interest rate and the real bond premium even while it drives down the equity premium.
Barsky and DeLong (1993) work in partial equilibrium so they do not confront
this problem. Cecchetti, Lain and Mark (1998) handle it by allowing the degree of
investors' irrationality itself to be stochastic and time-varying 29.
6. Some implications tbr macroeconomics
The research summarized in this chapter has important implications for various aspects
of macroeconomics. I conclude by briefly discussing some of these.
A first set of issues concerns the modelling of production, and hence of investment.
This chapter has followed the bulk of the asset pricing literature by concentrating on
the relation between asset prices and consumption, without asking how consumption is
determined in relation to investment and production. Ultimately this is unsatisfactory,
and authors such as Cochrane (1991, 1996) and Rouwenhorst (1995) have argued that
asset pricing should place a renewed emphasis on the investment decisions of firms.
Standard macroeconomic models with production, such as the canonical real
business cycle model of Prescott (1986), imply that asset prices are extremely stable.
The real interest rate equals the marginal product of capital, which is perturbed only by
technology shocks and changes in the quantity of capital; when the model is calibrated
to US data the standard deviation of the real interest rate is only a few basis points.
The return on capital is equally stable because capital can costlessly be transformed
into consumption goods, so its price is always fixed at one and uncertainty in the return
comes only from uncertainty about dividends.
If real business cycle models are to generate volatile asset returns, they must be
modified to include adjustment costs in investment so that changes in the demand for
capital cause changes in the value of installed capital, or Tobin's q, rather than changes
in the quantity of capital. Baxter and Crucini (1993), Jermann (t998), and Christiano
and Fisher (1995), among others, show how this can be done. The adjustment costs
affect not only asset prices, but other aspects of the model; the response of investment
to shocks falls, for example, so larger shocks are needed to explain the cyclical
behavior of investment.
The modelling of labor supply is an equally difficult problem. Any model in which
workers choose their labor supply implies a first-order condition of the form
OU OU
OC~G~- ON,' (82)
where Gt is the real wage and Nt is labor supply. A well-known difficulty in business
cycle theory is that with a constant real wage, the marginal utility of consumption
29 The workofRietz(1988)canbe understoodin a similarway.Rictzarguesthatinvestorsare concerned
about an unlikelybut serious eventthat has not actually occurred. Given the data we have, investors
appearto be irrationalbut in fact, with a longenoughdatasample,they will proveto be rational.
Ch. 19: Asset Prices, Consumption,and the Business Cycle 1297
OU/OCt will be perfectly correlated with the marginal disutility of work -OU/ON~. Since
the marginal utility of consumption is declining in consumption while the marginal
disutility of work is increasing in hours, this implies that consumption and hours
worked will be negatively correlated. In the data, of course, consumption and hours
worked are positively correlated since they are both procyclical.
This problem can be resolved if the real wage is procyclical; then when consumption
and hours increase in an expansion the decline in marginal utility of consumption
is more than offset by an increase in the real wage. In a standard model with log
utility of consumption only a 1% increase in the real wage is needed to offset the
decline in marginal utility caused by a 1% increase in consumption. But preferences
of the sort suggested by the asset pricing literature, with high risk aversion and
low intertemporal elasticity of substitution, have rapidly declining marginal utility
of consumption. These preferences imply that a much larger increase in the real
wage will be needed to offset the effect on labor supply of a given increase in
consumption. Boldrin, Christiano and Fisher (1995) and Lettau and Uhlig (1996)
confront this problem; Boldrin, Christiano and Fisher try to resolve it by using
a two-sector framework with limited mobility of labor between sectors. In their
framework the first-order condition (82) does not hold contemporaneously, but only
in expectation.
Models with production also help one to move away from the common assumption
that stock market dividends equal consumption or equivalently, that the aggregate stock
market equals total national wealth. This assumption is clearly untrue even for the
United States, and is even less appropriate for countries with smaller stock markets.
While one can relax the assumption by writing down exogenous correlated timeseries
processes for dividends and consumption in the manner of section 4.3, it will
ultimately be more satisfactory to derive both dividends and consumption within a
general equilibrium model.
Another important set of issues concerns the links between different national
economies and their financial markets. In this chapter I have treated each national
stock market as a separate entity with its own pricing model. That is, I have assumed
that national economies are entirely closed so that there is no integrated world capital
market. This assumption may be appropriate for examining long-term historical data,
but it seems questionable under modern conditions. There is much work to be done on
the pricing of national stock markets in a model with a perfectly or partially integrated
world capital market.
Finally, the asset pricing literature is important in understanding the welfare costs
of macroeconomic fluctuations. There has recently been a tendency for economists
to downplay the importance of economic fluctuations in favor of an emphasis on
long-term economic growth. But models of habit formation imply that consumers
take fluctuations extremely seriously. Fluctuations have important negative effects on
welfare because they move consumption in the short term, when agents have little time
to adjust; reductions in long-term growth, on the other hand, allow agents' habit levels
to adjust gradually.
1298 J.E Campbell
This conclusion is not an artifact of a particular utility function and habit formation
process. As Atkeson and Phelan (1994) emphasize, it must result from any utility
function that explains the level of the equity premium. The choice between risky stocks
and stable money market instruments offers investors a tradeoff between the mean
growth rate of their wealth and the volatility of this growth rate. The fact that so much
extra mean growth is available from volatile stock market investments implies that
investors find volatility to be a serious threat to their welfare. Economic policymakers
should take this into account when they face policy tradeoffs between economic growth
and macroeconomic stability.
References
Abel, A.B. (1990), "Asset prices under habit formation and catching up with the Joneses", American
Economic Review Papers and Proceedings 80:38 42.
Abel, A.B. (1994), "Exact solutions for expected rates of return under Markov regime switching:
implications for the equity premium puzzle", Journal of Money, Credit and Banking 26:345 361.
Abel, A.B. (1999), "Risk premia and term premia in general equilibrium", Journal ofMonetaryEconomics
43:3-33.
Abel, A.B., N.G. Mankiw, L.H. Sumxners and R.J. Zeckhauser (1989), "Assessing dynamic efficiency:
theory and evidence", Review of Economic Studies 56:1-20.
Aiyagari, S.R., and M. Gertler (1998), "Overreaction of asset prices in general equilibrium", Working
Paper No. 6747 (NBER).
Atkeson, A., and C. Phelan (1994), "Reconsidering the costs of business cycles with incomplete
markets", in: S. Fischer and J.J. Rotentherg, eds., NBER Macroeconomics Annual 1994 (MIT Press,
Cambridge, MA) 187507.
Attanasio, O.R, and G. Weber (1993), "Consumptiongrowth, the interest rate, and aggregation", Review
of Economic Studies 60:631-649.
Backus, D. (1993), "Cox-Ingersoll Ross in discrete time", unpublished paper (New YorkUniversity).
Bansal, R., and W.J.Coleman II (1996), "A monetal7 explanationof the equity premium, tern1premium,
and risk-free rate puzzles", Journal of Political Economy 104:1135-1171.
Barberis, N., A. Shleifer and R.W. Vishny (1998), "A model of investor sentiment", Journal of Financial
Economics 49:307 343.
Barclays de Zoete Wedd Securities (1995), The BZW Equity-GiltStudy: investmentin the London Stock
Market since 1918 (London).
Barsky, R.B., and J.B. DeLong (1993), "Why does the stock market fluctuate?", Quarterly Jomnal of
Economics 107:291-311.
Baxter, M., and M.J. Crucini (t993), "Explaining saving investment correlations", American Economic
Review 83:416-436.
Beaudry, R, and E. van Wincoop (1996), "The intertemporal elasticity of substitution: an exploration
using a US panel of state data", Economica 63:495 512.
Bekaert, G., R.J. Hodrick and D.A. Marshall (1997), "'Peso problem' explanations for term structure
anomalies", Working Paper No. 6147 (NBER).
Benartzi, S., and R.H. Thaler (1995), "Myopic loss aversion and the equity premium puzzle", Quarterly
Journal of Economics 110:73-92.
Black, E (1976), "Studies of stock price volatility changes", Proceedings of the 1976 Meetings of the
Business and Economic Statistics Section (American Statistical Association) 177--181.
Ch. 19: Asset Prices, Consumption, and the Business Cycle 1299
Blanchard, O.J., and M.W. Watson (1982), "Bubbles, rational expectations, and financial markets",
in: E Wachtel, ed., Crises in the Economic and Financial Structure: Bubbles, Bursts, and Shocks
(Lexington Publishers, Lexington, MA).
Boldrin, M., L.J. Christiano and J. Fisher (1995), "Asset pricing lessons for modeling business cycles",
Working Paper No. 5262 (NBER).
Bollerslev, T., R. Engle and J. Wooldridge (1988), "A capital asset pricing model with time varying
covariances", Journal of Political Economy 96:116 131.
Bollerslev, T., R.Y. Chou and K.E Kroner (1992), "ARCH modeling in finance: a review of the theory
and empirical evidence", Journal of Econometrics 52:5-59.
Bray, A., and C.C. Geczy (1996), "An empirical resurrection of the simple consumption CAPM with
power utility", unpublished paper (University of Chicago).
Breeden, D. (1979), "An intertemporal asset pricing model with stochastic consumption and investment
opportunities", Journal of Financial Economics 7:265-296.
Brown, S., W. Goetzmann and S. Ross (1995), "Survival", Journal of Finance 50:853-873.
Campbell, J.Y. (1986), "Bond and stock returns in a simple exchange model", Quarterly Journal of
Economics 101:785-804.
Campbell, J.Y. (1987), "Stock returns and the term structure", Journal of Financial Economics 18:
373~99.
Campbell, J.Y. (1991 ), "A variance decomposition for stock returns", Economic Journal 101:157-179.
Campbell, J.Y. (1993), "lntertemporal asset pricing without consumption data", American Economic
Review 83:487-512.
Campbell, J.Y. (1996a), "Consumption and the stock market: interpreting international experience",
Swedish Economic Policy Review 3:251-299.
Campbell, J.Y. (1996b), "Understanding risk and return", Journal of Political Economy 104:298-345.
Campbell, J.Y., and J.H. Cochrane (1999), "By force of habit: a consumption-based explanation of
aggregate stock market behavior", Journal of Political Economy 107:205-251.
Campbell, J.Y., and A.S. Kyle (1993), "Smart money, noise trading, and stock price behavior", Review
of Economic Studies 60:1-34.
Campbell, J.Y., and N.G. Mankiw (1989), "Consumption, income, and interest rates: reinterpreting the
time series evidence", in: O.J. Blanchard and S. Fischer, eds., National Bureau of Economic Research
Macroeconomics Annual 4:185~ 16.
Campbell, J.Y., and N.G. Mankiw (1991), "The response of consumption to income: a cross-cotmtry
investigation", European Economic Review 35: 723-767.
Campbell, J.Y., and R.J. Shiller (1988), "The dividend-price ratio and expectations of future dividends
and discount factors", Review of Financial Studies 1:195-227.
Campbell, J.Y., and R.J. Shiller (1991), "Yield spreads and interest rate movements: a bird's eye view",
Review of Economic Studies 58:495 514.
Campbell, J.Y., A.W. Lo and A.C. MacKinlay (1997), The Econometrics of Financial Markets (Princeton
University Press, Princeton, NJ).
Carroll, C.D. (1992), "The buffer-stock theory of saving: some macroeconornic evidence", Brookings
Papers on Economic Activity t992(2):61-156.
Cecchetti, S.G., E-S. Lain and N.C. Mark (1990), "Mean reversion in equilibrium asset prices", American
Economic Review 80:3984 18.
Cecchetti, S.G., E-S. Lain and N.C. Mark (1993), "The equity premium and the risk-fiee rate: matching
the moments", Journal of Monetary Economics 31:2t~45.
Cecchetti, S.G., R-S. Lain and N.C. Mark (1998), "Asset pricing with distorted beliefs: are equity returns
too good to be true?", Working Paper No. 6354 (NBER).
Chen, N. (1991), "Financial investment opportunities and the macroeconomy", Journal of Finance
46:52%554.
Chou, R.Y., R.E Engle and A. Kane (1992), "Measuring risk aversion from excess returns on a stock
index", Journal of Econometrics 52:201~24.
1300 J E Campbell
Chow, G.C. (1989), "Rational versus adaptive expectations in present value models", Review of
Economics and Statistics 71:376 384.
Christiano, L.J., and J. Fisher (1995), "Tobin's q and asset returns: implications for business cycle
analysis", Working Paper No. 5292 (NBER).
Cochrane, J.H. (1991), "Production-based asset pricing and the link between stock returns and economic
fluctuations", Journal of Finance 46:209-237.
Cochrane, J.H. (1996), "A cross-sectional test of an investment-based asset pricing model", Journal of
Political Economy 104:572~521.
Cochrane, J.H., and L.R Hansen (1992), "Asset pricing lessons for macroeconomics", in: O.J. Blanchard
and S. Fischer, eds., NBER Maeroeconomics Annual 1992 (The MIT Press, Cambridge).
Constantinides, G.M. (1990), "Habit formation: a resolution of the equity premium puzzle", Journal of
Political Economy 98:519-543.
Constantinides, G.M., and D. Duffle (1996), "Asset pricing with heterogeneous consumers", Journal of
Political Economy 104:219-240.
Constantinides, G.M., J.B. Donaldson and R. Mehra (1998), "Junior can't borrow: a new perspective on
tile equity premium puzzle", Working Paper No. 6617 (NBER).
Cutler, D.M., J.M. Poterba and L.H. Summers (1991), "Speculative dynamics", Review of Economic
Studies 58:529-546.
Deaton, A.S. (1991), "Saving and liquidity constraints", Econometrica 59:1221-1248.
DeLong, J.B., A. Shleifer, L.H. Summers and R.J. Waldmann (1990), "Noise trader risk in financial
markets", Journal of Political Economy 98:703-738.
Dunn, K.B., and K.J. Singleton (1986), "Modeling the term structure of interest rates under non-separable
utility and durability of goods", Journal of Financial Economics 17:27-55.
Epstein, L.G., and S.E. Zin (1989), "Substitution, risk aversion, and the temporal behavior of consumption
and asset returns: a theoretical fiamework", Econometrica 57:937-968.
Epstein, L.G., and S.E. Zin (1991), "Substitution, risk aversion, and the temporal behavior of consmnption
and asset returns: an empirical investigation", Journal of Political Economy 99:263-286.
Estrella, A., and G.A. Hardouvelis (1991), "The term structure as a predictor of real economic activity",
Journal of Finance 46:555-576.
Fama, E.E, and R. Bliss (1987), "The information in long-maturity forward rates", American Economic
Review 77:68(~692.
Fama, E.E, and K.R. French (1988a), "Permanent and temporary components of stock prices", Journal
of Political Economy 96:246-273.
Fama, E.E, and K.R. French (1988b), "Dividend yields and expected stock returns", Journal of Financial
Economics 22:3 27.
Fama, E.E, and K.R. French (1989), "Business conditions and expected returns on stocks and bonds",
Journal of Financial Economics 25:23~49.
Ferson, W.E., and G.M. Constantinides (1991), "Habit persistence and durability in aggregate
consumption: empirical tests", Journal of Financial Economics 29:199-240.
French, K., G.W. Schwert and R.E Stambaugh (1987), "Expected stock returns and volatility", Journal
of Financial Economics 19:3-30.
Frennberg, R, and B. Hansson (1992), "Computation of a monthly index for Swedish stock returns
1919-t989", Scandinavian Economic History Review 40:3-27.
Froot, K., and M. Obstfeld (1991), "Intrinsic bubbles: the case of stock prices", American Economic
Review 81:t189-1217.
Glosten, L, R. Jagannathan and D. Runkle (1993), "On the relation between the expected value and the
volatility of the nominal excess return on stocks", Journal of Finance 48:177%180I.
Goetzmmur, W.N., and R Jorion (1997), "A century of global stock markets", Working Paper No. 5901
(NBER).
Grossman, S.J., and R.J. Shiller (198l), "The determinants of the variability of stock market prices",
American Economic Review 71:222 227.
Ch. 19: Asset Prices', Consumption, and the Business Cycle 1301
Grossman, S.J., and R.J. Shiller (1982), "Consumption correlatedness and risk measurement in economies
with non-traded assets and heterogeneous information", Journal of Financial Economics 10:195-210.
Grossman, S.J., and Z. Zhou (1996), "Equilibrium analysis of portfolio insurance", Journal of Finance
51:1379 1403.
Grossman, S.J., A. Melino and R.J. Shiller (1987), "Estimating the continuous time consumption based
asset pricing model", Journal of Business and Economic Statistics 5:315-328.
Hall, R.E. (1988), "Intertemporal substitution in consumption", Journal of Political Economy
96:221~273.
Hamilton, J.D. (1989), "A new approach to the analysis of nonstationary returns and the business cycle",
Econometa%a 57:357-384.
Hansen, L.P, and R. Jagannathan (1991), "Restrictions on intertemporal marginal rates of substitution
implied by asset returns", Journal of Political Economy 99:225-262.
Hansen, L.P., and K.J. Singleton (1983), "Stochastic consumption, risk aversion, and the temporal
behavior of asset returns", Journal of Political Economy 91:249-268.
Hansen, L.P, T.J. Sargent and T.D. Tallarini Jr (1997), "Robust permanent income and pricing",
unpublished paper (University of Chicago and Carnegie Mellon University); Review of Economic
Studies, fbrthcoming.
Hardouvelis, G.A. (1994), "The term structure spread and future changes in long and short rates in the
G7 countries: Is there a puzzle?", Journal of Monetary Economics 33:255283.
Harvey, C.R. (1989), "Time-varying conditional covariances in tests of asset pricing models", Journal
of Financial Economics 24:289-317.
Harvey, C.R. (1991), "The world price of covariance risk", Journal of Finance 46:111-157.
Hassler, J., E Lundvik, T. Persson and E S6derlind (1994), "The Swedish business cycle: stylized facts
over 130 years", in: V. Bergstr/Sm and A. Vredin, eds., Measuring and Interpreting Business Cycles
(Clarendon Press, Oxford).
Heaton, J. (1995), "'An empirical investigation of asset pricing with temporally dependent preference
specifications", Econometrica 63:681-717.
Heaton, J., and D.J. Lucas (1996), "Evaluating the effects of incomplete markets on risk sharing and
asset pricing", Journal of Political Economy 104:443-487.
Jermann, U.J. (1998), "Asset pricing in production economies", Journal of Monetary Economics 41:
257-275.
Kandel, S., and R.E Stambaugh (t991), "Asset returns and intertemporal preferences", Journal of
Monetary Economics 27:39-71.
Kocherlakota, N. (1996), "The equity premium: it's still a puzzle", Journal of Economic Literature
34:42~ 1.
Kreps, D.M., and E.L. Porteus (1978), "Temporal resolution of uncertainty and dynamic choice theory",
Econometriea 46:185-200.
Kxusell, E, and A.A. Smith Jr (1997), "Income and wealth heterogeneity, portfolio choice, and equilibrium
asset returns", Macroeconomic Dynamics 1:387-422.
Kugler, E (1988), "An empirical note on the term structure and interest rate stabilization policies",
Quarterly Journal of Economics 103:78%792.
La Porta, R., E Lopez-de-Silanes, A. Shleifer and R.W. Vishny (1997), "Legal determinants of external
finance", Journal of Finance 52:1131-1150.
LeRoy, S.E, and R.D. Porter (1981), "The present value relation: tests based on variance bounds",
Econometriea 49:555-577.
Lettan, M. (1997), "Idiosyncratic risk and volatility bounds", unpublished paper (CentER, Tilburg
University).
Lettau, M., and H. Uhlig (1996), "Asset prices and business cycles: successes and pitfalls of the general
equilibrium approach", unpublished paper (CentER, Tilburg University).
Lucas Jr, R.E. (1978), "Asset prices in an exchange economy", Econometrica 46:1429-1446.
1302 J.Y. Campbell
Mankiw, N.G. (1986), "The equity premium and the concentration of aggregate shocks", Journal of
Financial Economics 17:211-219.
Mankiw, N.G., and J.A. Miron (1986), "The changing behavior of the term structure of interest rates",
Quarterly Journal of Economics 101:211228.
Mankiw, N.G., and S.E Zeldcs (1991), "The consumption of stockholders and non-stockholders", Journal
of Financial Economics 29:97-112.
Mehra, R., and E.C. Prescott (1985), "The equity premium puzzle", Journal of Monetary Economics
15:145-161.
Merton, R. (1973), "An intertemporal capital asset pricing model", Econometa@a 41:867-887.
Miron, J.A. (1986), "Seasonal fluctuations and the life cycle-permanent income hypothesis of
consumption", Journal of Political Economy 94:1258 1279.
Nelson, C.R., and R. Startz (1990), "The distribution of the instrumental variables estimator and its
t-ratio when the instrument is a poor one", Journal of Business 63:S125-$140.
Poterba, J.M., and L.H. Summers (1988), "Mean reversion in stock returns: evidence and implications",
Journal of Financial Economics 22:27-60.
Prescott, E.C. (1986), "Theory ahead of business cycle measurement", Carnegie-Rnchester Conference
Series on Public Policy 25:11-66.
Restoy, E, and E Weil (1998), "Approximate equilibrium asset prices", Working Paper No. 6611 (NBER).
Rietz, 32 (1988), "The equity risk premium: a solution?", Journal of Monetary Economics 21:117-132.
Rouwenhorst, K.G. (1995), "Asset pricing implications of equilibrium business cycle models", in:
T.E Cooley, ed., Frontiers of Business Cycle Research (Princeton University Press, Princeton, NJ).
Ryder Jr, H.E., and G.M. Heal (1973), "Optimum growth with intertemporally dependent preferences",
Review of Economic Studies 40:1-33.
Sandroni, A. (1997), "Assetprices, wealth distribution, and intertemporal preference shocks", unpublished
paper (University of Pennsylvania).
Santos, M.S., and M. Woodford (1997), "Rational asset pricing bubbles", Econometrica 65:19 57.
Schwert, G.W. (1989), "Why does stock market volatility change over time?", Journal of Finance
44:1115 1153.
Shiller, R.J. (i 981), "Do stock prices move too much to be justified by subsequent changes in dividends?",
American Economic Review 71:421-436.
Shiller, R.J. (1982), "Consumption, asset markets, and macroeconomic fluctuations", Carnegie Mellon
Conference Series on Public Policy 17:203-238.
Shiller, R.J. (1984), "Stock prices and social dynamics", Brookings Papers on Economic Activity
1984(2):457M98.
Shiller, R.J. (1999), "Human behavior and the efficiency of the financial system", ch. 20, this Handbook.
Singleton, K. (1990), "Specification and estimation ofintertemporal asset pricing models", in B. Friedman
and E Hahn, eds., Handbook of Monetary Economics (North-Holland, Amsterdam).
Sun, T. (I992), "Real and nominal interest rates: a discrete-time model and its continuous-time limit",
Review of Financial Studies 5:581-611.
Stmdaresan, S.M. (1989), "Intertemporally dependent preferences and the volatility of consumption and
wealth", Review of Financial Studies 2:73 88.
Svensson, L.E.O. (1989), "Portfolio choice with non-expected utility in continuous time", Economics
Letters 30:313--317.
The Economist (1987), One Hundred Years of Economic Statistics (The Economist, London).
Tirole, J. (1985), "Asset bubbles and overlapping generations", Econometrica 53:1499-1527.
Vasicek, O. (1977), "An equilibrium characterization of the term structure", Journal of Financial
Economics 5:177-188.
Wang, J. (1996), "The term structure of interest rates in a pure exchange economy with heterogeneous
investors", Journal of Financial Economics 41:75 110.
Weil, E (i989), "The equity premium puzzle and the risk-t?ec rate puzzle", Journal of Monetary
Economics 24:401-421.
Ch. 19: Asset Prices, Consumption, and the Business Cycle 1303
Wheatley, S. (1988), "Some tests of the consumption-based asset pricing model", Journal of Monetary
Economics 22:193~ 18.
Wilcox, D. (1992), "The construction of US consumption data: some facts and their implications for
empirical work", American Economic Review 82:922-941.