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A Perspective on U.S. International Capital Flows
William Poole
I
am very pleased to be here today to visit with
the Tucson Chapter of the Association for
Investment Management Research. I say “visit
with” because I do hope that when I finish speaking
we can engage in some questions and answers
and comments about my chosen topic. International
economic issues—especially trade issues—are hot
topics these days. Through my concentration on
capital markets issues, my intention is to emphasize just how important international capital flows
are to the United States. In the process, I hope to
shed some light, and not just add to the heat, on
trade issues by exploring the intimate connections
between international trade and international capital flows.
Recent economic indicators have suggested
that the long-awaited acceleration of the recovery
from the 2001 recession is under way. According
to the advance estimate from the Department of
Commerce, real GDP growth—the broadest measure of the strength of the economy—increased at a
7.2 percent annual rate in the third quarter, and the
latest employment data show that the accelerated
growth is fueling job creation after many months
of stagnation.
Through all the ups and downs of the U.S.
economy over the past two decades, a staple of the
situation has been a deficit in the U.S. international
trade accounts and a corresponding surplus in the
international capital accounts. Many observers are
troubled by this persistent state of affairs and are
concerned that the trade deficit might derail the
economic recovery. It is common to refer to the situation as an “imbalance,” which naturally implies
that something is wrong. The word “deficit” in “trade
deficit” has the same connotation. I intend to use
the words “surplus” and “deficit” as simple descriptive words and hope that in listening to me you can
consciously ignore the baggage that the words com-
monly carry. My purpose is to analyze the external
imbalance to see why we might, or might not, be
concerned about it.
Before proceeding, I want to emphasize that
the views I express here are mine and do not necessarily reflect official positions of the Federal
Reserve System. I appreciate comments provided
by my colleagues at the Federal Reserve Bank of
St. Louis. Michael R. Pakko, senior economist in the
Research Division, provided special assistance. I take
full responsibility for errors.
To emphasize the importance of thinking
through the analysis and not letting the word “deficit”
decide the issue, consider the situation faced by many
healthy corporations. It is common for a thriving
company to spend more than its revenues, making
up the difference by borrowing. When a company
borrows to finance spending on capital, the company
may be said to have a deficit on current account—
its total spending on goods and services, including
new capital, exceeds its revenues. The company
simultaneously has a surplus on capital account—
more funds are flowing into the company to buy the
company’s shares and bonds than the company is
investing in similar securities issued by others.
Arithmetically, the company has a current account
deficit and a capital account surplus, and thus has
an “imbalance.” Whether the company is suffering from an economic imbalance depends on the
productivity of its capital investments. Sometimes
companies do invest in capital and businesses that
turn out not to yield returns sufficient to service the
debt financing the investments. Such a situation,
when repeated over the years, is not sustainable.
For a company, and as I will argue for a country,
whether continuing infusions of financial capital
are sustainable depends on how the financial capital
is employed.
William Poole is the president of the Federal Reserve Bank of St. Louis. The author thanks colleagues at the Federal Reserve Bank of St. Louis for
comments: Michael R. Pakko, senior economist in the Research Division, provided special assistance. The views expressed are the author’s and do
not necessarily reflect official positions of the Federal Reserve System.
Federal Reserve Bank of St. Louis Review, January/February 2004, 86(1), pp. 1-7.
© 2004, The Federal Reserve Bank of St. Louis.
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CURRENT AND CAPITAL ACCOUNTS
IN THE BALANCE OF PAYMENTS
The most widely cited measure of the U.S. external imbalance is the trade deficit—the difference
between U.S. exports and imports. More generally,
it is useful to concentrate on the broader concept
of the current account, which includes current earnings on capital as well as trade in goods and services.
Putting aside errors and omissions in the data, the
capital account surplus is necessarily equal to the
current account deficit. By the same token, a country with a current account surplus simultaneously
has a capital account deficit—that is, it is importing
more capital claims than it is exporting. In the official statistics reported by the Bureau of Economic
Analysis, this side of the ledger is called the “Capital
and Financial Account.”
A country’s trade balance and its capital account
are clearly very closely related. From an economist’s
perspective, the flows of goods and services that
comprise the trade balance tell only part of the story
of a country’s international economic relations. I’m
going to concentrate on the capital account because
that part of the international economic story is
commonly neglected.
A common mistake is to treat international capital flows as though they are passively responding
to what is happening in the current account. The
trade deficit, it is said, is financed by U.S. borrowing
abroad. In fact, investors abroad buy U.S. assets not
for the purpose of financing the U.S. trade deficit
but because they believe these are sound investments
promising a good combination of safety and return.
Many of these investments have nothing whatsoever
to do with borrowing in the conventional meaning
of the word, but instead involve purchases of land,
businesses, and common stock in the United States.
Foreign auto companies, for example, have purchased land and built manufacturing plants in the
United States. These simple examples should make
clear that a careful analysis of the nature of international capital flows is necessary before offering
judgments about the U.S. external imbalance.
RECENT TRENDS IN THE U.S.
INTERNATIONAL FINANCIAL POSITION
Examining recent trends in the U.S. international
financial position will help to uncover key facts
and issues. There is a huge amount of detailed data
in official U.S. statistics. I’ll draw on some of that
information.
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The capital account measures the change in the
net foreign asset position of a country for a given
period, such as a year. For the United States, the
capital account includes the accumulation of foreign
assets by U.S. residents as well as the accumulation
of U.S. assets by foreigners. In the U.S. balance of
payments accounts, each of these gross asset flows
is broken down into “official” flows—representing
asset purchases by governments and central banks—
and “private” flows—representing the purchases of
individuals and corporate entities. These totals are
further broken down by type of asset—government
securities, corporate bonds, private equity—in tables
reporting the international investment position of
the United States.
The sheer volume of international financial
flows is truly phenomenal. According to the Bank
for International Settlements, in 2001 trade in foreign
currencies averaged $1.2 trillion per day, and trading
in derivatives averaged $1.4 trillion per day. Much
of this daily activity nets out when measuring quarterly and annual flows, but even the quarterly and
annual magnitudes have been quite large. Moreover,
they have been rising significantly over the past
few years. For example, foreign-owned U.S. assets
increased by an average of $155 billion per year
during the 1980s. Since 2000, foreign ownership of
U.S. assets increased at an average rate of $833 billion
per year—more than a fivefold increase. In 2000,
over $1 trillion of assets were sold to foreign entities.
Growth of U.S. ownership of foreign assets has
shown similar, if not quite so remarkable, growth.
Averaging $95 billion during the 1980s, the U.S.
entities have accumulated foreign assets at a rate
of $366 billion per year over the past three years.
Over the entire span of this comparison, the volume
of U.S. assets owned abroad has outpaced our accumulation of foreign assets—a capital account surplus that has moved our country from a positive to
a negative net asset position.
It is sometimes said that the United States has
become a net debtor. The word “debtor” is extremely
misleading in this context, for the U.S. assets owned
by foreigners include equities and physical capital
located in the United States, as well as bonds issued
by U.S. entities. Moreover, the part of the U.S. international financial position that is debt, by which I
mean bonds and other fixed claims such as bank
loans, is predominantly denominated in dollars. A
country with most of its debt denominated in its
own currency is in a very different situation from
one whose debt is denominated in other currencies.
FEDERAL R ESERVE BANK OF ST. LOUIS
The familiar crises experienced by several Asian
countries in 1997-98, by Mexico on several occasions, by Argentina, and by numerous other countries
have all involved situations in which the impacted
countries have had large external debts denominated
in foreign currencies.
The balance-of-payments accounts provide
estimates of annual international investment flows.
These accumulate over time to change the stocks
of assets. Data on the stocks are available and are
referred to as measures of the U.S. international
investment position.
As recently as the early 1980s, the U.S. had a
positive net investment position. As a consequence
of large capital inflows in the 1980s and late 1990s,
the United States today has the world’s largest negative net international investment position. By the
end of 2002, foreigners owned more than $9 trillion
of U.S. assets, based on market values, while U.S.owned assets abroad reached a level of not quite
$6.5 trillion. Hence, at the end of last year, the U.S.
net international investment position represented
a negative net position of $2.6 trillion, about 25
percent of U.S. GDP.
This new role for the United States, with its
negative net international investment position, has
been a source of consternation among those who
see the globalization of financial markets as a worrisome phenomenon. I am much more sanguine
about the U.S. international asset position. To explain
why I view the rapid growth of cross-border financial
market activity in a positive light, I’ll discuss some
basic economic principles that underlie changes in
the U.S. net international position. It would be a
mistake, though, to think that the United States is
in uncharted waters; other prosperous countries
have had large negative international investment
positions without getting into trouble, and the United
States itself was in this position for decades prior
to World War I.
TRADE AND CAPITAL FLOWS
In today’s world, with electronic funds transfers,
financial derivatives, and largely unrestricted capital
flows, investors have a global marketplace in which
to seek profitable returns and diversify risk. In such
an environment, we should consider the possibility
that aggregate patterns of international trade flows
may simply be the by-product of a process through
which financial resources are seeking their most
efficient allocations in a worldwide capital market.
That is, instead of thinking that capital flows are
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financing the current account deficit, it may well
be that the trade deficit is, so to speak, financing
capital flows driven by investors seeking the best
combination of risk and return in the international
capital market.
While such a conclusion is surely an overstatement, I believe that it does contain an important
element of truth. Capital flows are a highly dynamic
feature of the international economy; changes in
investor attitudes and expectations can alter capital
flows quickly and force changes in the trade account.
To paint a more complete picture of the broad nexus
of forces driving trade and investment patterns
around the world, I will describe three complementary views of how cross-border goods and asset flows
are jointly determined.1
Perhaps the most basic model for explaining a
country’s international position could be called
“the trade view,” which focuses explicitly on the
factors determining the import and export of goods
and services. Under this perspective, the emphasis
is on the economic conditions that determine
whether a country runs a deficit in trade. The capital
account simply measures the offsetting financial
transactions that take place; investors are treated
as passive players who finance what is happening
in the dynamic trade sector. This view lends itself
naturally to the application of basic principles of
demand theory. The quantity of goods and services
that a country imports depends on income and the
relative price of imports, which is determined importantly by the exchange rate. Exports depend on the
responses of a country’s trading partners to changes
in their income and exchange rate movements.
Economists who have taken an empirical
approach to estimating these demand relationships
have found that the trade view can explain much
about the fluctuations in trade and capital flows
that we observe across countries. But their estimates
have also presented a puzzle: U.S. import demand
responds more strongly to changes in income growth
than corresponding income responses in other
countries. This finding means that, in the long run,
with exchange rates settling at their equilibrium
values and U.S. and foreign growth rates equal,
the U.S. is predicted to run a persistently widening
current account deficit. Alternatively, a widening
deficit could be halted by a persistent depreciation
1
In describing these three views and highlighting the importance of
international capital flows, I draw on the work of Catherine L. Mann,
a former economist at the Fed who is now a Senior Fellow at the
Institute for International Economics in Washington, D.C. (Mann, 2002).
J A N UA RY / F E B R UA RY 2 0 0 4
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of the dollar, or by suffering a persistently slower
growth rate than the rest of the world.
The conclusion is that either the United States
is destined to face some combination of these undesirable outcomes—a continuously depreciating
currency and/or lower GDP growth than the rest of
the world—or the demand equations of the trade
view are missing something. What might be missing is some important factor outside the trade view
that can explain the recent historical trend of a
widening U.S. current account deficit in an environment in which U.S. GDP growth is on average higher
than growth in much of the rest of the world and
in which the dollar, despite short-run fluctuations,
is on average relatively strong and not persistently
depreciating.
A second perspective of current account/capital
account determination is best explained through
accounting identities of the National Income and
Product Accounts. The National Accounts are structured such that the total output—the GDP—of the
United States is divided into principal components
of consumption, investment, spending by government on goods and services, and exports. Total
income from production can be either consumed
or saved. These relationships imply that a current
account deficit must equal the difference between
U.S. domestic investment, or capital formation,
and total U.S. saving by both the private sector and
government.
This view suggests several explanations for U.S.
current account deficits. One explanation that gained
popularity in the 1980s was that large, persistent
government budget deficits reduced national saving
and thereby induced an inflow of financing from
abroad. This “twin-deficit” argument has some
appeal, particularly in that it suggests a key role for
capital account flows. The argument is that claims
on U.S. assets are exported to help finance government budget deficits. Indeed, the growth of the U.S.
capital account surplus has included a vast accumulation of U.S. Treasury debt by foreigners. It is estimated that over $1.4 trillion of U.S. Treasury debt
is currently held by foreigners, representing about
37 percent of the total outstanding. It is important
to recognize, however, that foreign purchases of
any U.S. assets, and not just Treasury bonds, serve
to help finance the government budget deficit.
The twin-deficits explanation, however, is clearly
inadequate. While this explanation appeared to fit
the facts of U.S. experience in the 1980s, the relationship breaks down when examining other episodes.
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One recent example is the United States during the
late 1990s, when the current account deficit persistently widened while the government budget moved
from deficit to surplus. In other countries that have
experienced large swings in government deficits
and current account deficits, the twin-deficits theory
doesn’t seem to hold up in terms of timing or magnitude either.
Another explanation suggested by the savings/
investment view is that periods of high investment
demand—like the late 1990s in the United States—
fully absorb domestic savings and require additional
external financing. This explanation puts a completely different spin on current account deficits. If
we are exporting claims on U.S. assets—financing
abroad by selling bonds, equities, and claims on
productive facilities—to fund productive investment
opportunities, the payoff from those investments
will finance the obligations incurred. This is a classic
example of how financial markets can be used to
exploit productive opportunities that might otherwise be unavailable.
From this perspective, the profitability of U.S.
investment opportunities makes United States something of an “oasis of prosperity,” attracting savings
from around the world from those who wish to
share in the returns and safety of investing in U.S.
markets. On this view, trade and current account
deficits are induced by the dynamic role of the
United States in world capital markets.
And yet this savings/investment view also
appears incomplete and not in accord with recent
facts. The U.S. external imbalance has continued to
widen in recent years despite the fact that growth
in the investment component of GDP dropped
precipitously during the recent recession and has
only recently shown signs of picking up. Moreover,
returns in the U.S. equity market were pretty miserable from early 2000 until quite recently. Again, we
seem to be left with only part of the story.
A third view of the U.S. external imbalance can,
I believe, help complete the story. Just as the savings/
investment view exploits the accounting identities
of the National Accounts, an “international capital
markets view” can be derived from the identity that
one country’s deficit is balanced by another country’s surplus. From this perspective, capital account
adjustment can play an important independent
role that is determined by the motivations of both
foreign and domestic investors. In particular, we
can think of capital market flows as the equilibrium
outcome of investors worldwide seeking to acquire
FEDERAL R ESERVE BANK OF ST. LOUIS
portfolios that balance risk and return through
diversification.
THE U.S. ROLE IN INTERNATIONAL
CAPITAL MARKETS
Current commentary on international economic
issues pays far too little attention to the role of the
United States in international capital markets. The
globalization of financial markets—spurred by
technological advances and liberalization of capital
flow restrictions worldwide—has created entirely
new investment opportunities for investors in both
the United States and abroad. These new opportunities have undoubtedly given rise to a re-balancing
of portfolios, and there are reasons to believe that
this process might be associated with a net export
of claims on U.S. assets—a capital account surplus.
U.S. financial markets are among the most
highly developed in the world, offering efficiency,
transparency, and liquidity. Moreover, the U.S. dollar
serves as both a medium of exchange and a unit of
account in many international transactions. These
factors make dollar-denominated claims attractive
assets in any international portfolio. No capital market in the world has a combination of strengths
superior to that of the United States. Our advantages
include the promise of a good return, safety, secure
political institutions, liquidity, and an enormous
depth of financial expertise. The United States has
worked hard for generations to create outstanding
capital markets; our latest efforts to improve corporate governance should be viewed as simply another
chapter in an ongoing story.
For some purposes, it is useful to think of U.S.
financial markets as serving as a world financial
intermediary. Just as a bank, or a mutual fund,
channels the savings of many individuals toward
productive investments, the U.S. financial markets
play a similar role for many investors from around
the world. In the process, individuals, companies,
and governments around the world accumulate
dollar-denominated assets to serve as a vehicle for
facilitating transactions and storing liquid wealth
safely.
A bank earns its return on capital by paying a
lower interest rate to depositors than it earns on its
assets. Similarly, the United States earns a higher
return on its investments abroad than foreigners
do on their investments in the United States. Despite
the fact that the U.S. international investment position at the end of 2002 was –$2.6 trillion, U.S. net
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income in 2002 on its investments abroad slightly
exceeded income payments on foreign-owned assets
in the United States.
How is the United States able to earn a significantly higher return on its assets abroad than foreigners earn on their assets in the United States? A
very simple example is currency, which pays a zero
return. At the end of 2002, U.S. currency held abroad
was estimated to be about $300 billion, whereas
only a trivial amount of foreign currency is held in
the United States.
More generally, many private and governmental
investors abroad rely on the U.S. capital market as
the best place to invest in extremely safe and highly
liquid securities. Along a spectrum of safety and
liquidity, these assets include currency, U.S. government obligations, agency debt, and corporate bonds.
U.S. equity markets are also highly liquid. The United
States as a whole earns a return from providing these
safe and liquid investments to the world. Indeed, the
desire of foreigners to hold U.S. Treasury securities
is a testament to the confidence that the world has
in the safety and soundness of our financial system.
Recent data show just how impressive is the
world’s appetite for safe U.S. assets. Over the six
quarters ending with the second quarter of this year,
total outstanding U.S. government debt rose by about
$345 billion, while foreign holdings of such debt
have risen by about $304 billion.
Another force at work may be a gradual breakdown in the home bias to investment. For some
years, international economists have noted that
investors tend to hold portfolios that are weighted
more toward domestic assets than would appear
optimal by the principles of diversification—there
is home-bias to investor behavior. Business cycles
and investment risks are not perfectly synchronized
across countries; a balanced international portfolio
can help to diversify risk. The opening of global
capital markets has allowed investors to exploit
these opportunities, particularly foreign investors
who are able to participate in the relative openness
of U.S. capital markets and the multinational diversification of U.S. corporations.
Another aspect of the situation may be a consequence of demographics. Europe and Japan, especially, have populations that are aging more rapidly
than does the United States. Just as a retired household typically consumes more than its income, drawing down retirement savings in the process, so also
may an entire country draw down international
investments to finance the consumption of its retired
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population. Japan especially has a high saving rate
relative to its domestic investment rate; it is accumulating assets abroad that may be run down in future
years to support its elderly population. This process
is one that will work out over many years. What may
appear to be an “imbalance” this year may make
perfect sense over a long-term horizon.
While the international capital markets view provides a perspective on some unique influences on
U.S. current account/capital account imbalances, it is
entirely consistent with the alternative perspectives.
As foreigners decide to accumulate dollardenominated assets, U.S. interest rates are kept
lower than they otherwise would be, which tends
to increase investment demand in the United States.
This investment demand, incidentally, includes both
corporate demand for capital formation and household demand for new housing. The total demand for
funds also includes the U.S. government’s demand,
which may be temporarily high as a consequence of
the war on terrorism, Iraq, and the 2001-03 period
of recession and slow recovery. These factors are
consistent with the savings/investment perspective
that helps to understand why the United States has
a capital inflow and the associated current account
deficit.
IS THE U.S. EXTERNAL IMBALANCE
SUSTAINABLE?
When considering widening external imbalances
like those that the United States has experienced in
recent years, a natural question is whether or not
current trends are sustainable. Indeed, with a current account deficit equal to 5 percent of GDP and
a negative international investment position that
amounts to 25 percent of GDP, some have drawn
comparisons with countries such as Argentina,
Brazil, and Mexico at times of severe balance of
payments crises.
I consider it highly unlikely that such a crisis
will befall the United States. As a stable, diversified
industrial economy, the United States is not likely to
suffer from a sudden lack of confidence by investors.
In fact, other industrialized economies have incurred
much larger external obligations without precipitating crises. For example, Australia’s negative net
investment position reached 60 percent of GDP in
the mid-1990s, Ireland’s exceeded 70 percent in the
1980s, and New Zealand accumulated a position
amounting to nearly 90 percent of GDP in the late
1990s. Notably, these economies have recently
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been among the most successful—in terms of
economic growth—in the industrialized world.
Indeed, the combination of rising external obligations and prospects for robust growth is entirely
consistent with the view of the capital account I
have discussed today.
Moreover, the international capital markets view
suggests that the United States is not only more
like those countries that have experienced high
levels of debt without obvious ill effects—but that
the U.S. case is, in some sense, unique. The central
role of U.S. financial markets—and of the dollar—
in the world economy suggests that capital account
surpluses are being driven by foreign demand for
U.S. assets, rather than by any structural imbalance
in the U.S. economy itself.
To be sure, no country can permanently incur
rising levels of net external obligations relative to
GDP. If sustained indefinitely, service payments on
ever-increasing obligations would ultimately exceed
national income. Long before that situation of literal
insolvency occurred, however, market forces would
drive changes in exchange rates, interest rate differentials, and relative growth rates in such a way to
move the economy toward a sustainable path. Nevertheless, such adjustments need not be sudden, large,
or disruptive as they have sometimes been for countries with severe balance-of-payments crises.
Not only are there market forces that will restore
equilibrium, should the current situation not correct
itself, but more importantly the international capital
markets may well be looking ahead to changing
circumstances that will reduce the capital flows to
the United States in coming years. I’ve already mentioned the demographic forces at work. Another
possibility is that economic growth will rise elsewhere in the world, raising demands both for U.S.
exports and for international capital to finance
higher growth. Given the strength of U.S. multinational corporations, U.S. firms will share in the
profits from higher growth abroad, and some of
those earnings will be repatriated to the United States.
CONCLUDING COMMENTS
The international financial markets view of
U.S. international capital account determination
that I have described today highlights the dynamic
role of international capital adjustments as investors
exploit the opportunities of globalized financial
markets. Because the technological progress and
capital-market liberalizations that have driven this
process have evolved over time, the process has
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been protracted. Ultimately, however, when portfolio
adjustments have optimally exploited new diversification opportunities, and as growth abroad rises,
the net international investment position of the
United States will stabilize.
If this view is correct, the forces driving the U.S.
capital account represent a persistent, but ultimately
temporary, process that might result in a higher level
of net indebtedness without necessarily posing any
threat to the sustainability of the U.S. international
investment position. Nor will the transition to a
sustainable long-run path necessarily require
wrenching adjustments in domestic or international
markets or in exchange rates.
In the meanwhile, we can all benefit from our
good fortune to have access to increasingly safe,
liquid, and transparent financial markets. The United
States has created for itself a comparative advantage
in capital markets, and we should not be surprised
that investors all over the world come to buy the
product.
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Casino Gaming and Local Employment Trends
Thomas A. Garrett
THE U.S. CASINO INDUSTRY
asino gaming has become a major industry
in the United States over the past two
decades. Prior to the late 1980s, casino
gaming was legal only in Nevada and Atlantic City,
New Jersey. Today, casino gaming is available in 29
states. As a consequence, annual gaming revenue
has grown from $9 billion in 1991 to over $40
billion in 2001.1 Americans spend more money in
casinos than individually on golf, on-screen movies,
CDs and sound equipment, and cable TV.2
The casino industry consists of two major
parties—Indian tribes and publicly traded private
corporations such as Harrah’s Entertainment and
Trump Hotels and Casino Resorts. The Indian Gaming Regulatory Act (Public Law 100-497, passed in
1988) allows Indian tribes to own and operate casinos
on their reservations. Tribal gaming is available in
25 states and generates nearly $13 billion in annual
revenue. Corporate casino gaming is available in 10
states and generated over $27 billion in revenue in
2001.3 Table 1 provides a listing of these states.4
C
1
Casino revenues in this report represent revenue to the casinos after
subtracting player winnings. In comparison, 38 state lotteries generated
nearly $38 billion in 2001; pari-mutuel horse and greyhound racing
generated over $3.25 billion (legal in 43 states) and $550 million (legal
in 15 states), respectively.
2
From the American Gaming Association (www.americangaming.org).
3
West Virginia, Delaware, Rhode Island, Louisiana, Iowa, and New
Mexico offer video lottery terminals (VLTs) and slot machines as part
of their state lottery. These outlets (often called racinos) are usually
located at pari-mutuel racetracks and are not considered corporate
casinos because they are run by the state. The revenue from these
outlets (roughly $500 million annually) is considered a portion of
total lottery revenue.
4
Most data presented in this report are from the following sources:
Bear Stearns 2002-2003 North American Gaming Almanac (Ader, 2003);
The National Gambling Impact Study Commission, Final Report (1999),
www.casino-gambling-reports.com/GamblingStudy/; the American
Gaming Association, www.americangaming.org; and each state’s
gaming commission.
While tribal gaming is available in more states,
corporate casino gaming has traditionally been
perceived as a more appropriate tool for fostering
general economic development through increased
employment and tax revenue.5 The primary reason
for this perception is that states have no power to
tax Indian casino revenue because Indian reservations are sovereign entities, distinct from the state.6
While states and Indian tribes do cooperate on regulation and security issues (dictated by state-tribal
gaming compacts), the relationship between a tribe
and a state is very similar to the relationship between
two states—one state generally cannot legally dictate
what another state can do. Corporate casinos, however, are private industries that are taxed and regulated by the state. These casinos generate much more
revenue and hire more labor from the general labor
market than Indian casinos.
The impact of corporate casino gaming on local
employment is a major issue in the debate over
legalized casino gaming. As a result, the issue has
received careful study.7 This paper explores how
corporate casinos affect employment in six Midwestern counties using various employment data
and forecasting models. Changes in both household
and payroll employment are examined to separate
the effects on the residents and businesses in counties with casinos. Payroll employment changes may
allude to possible interindustry substitution resulting from casino gaming. Also, both urban and
rural “casino counties” are used in the analysis to
5
Indian tribes use their gaming revenue to promote economic development on their reservations. Economic development from corporate
casino gaming, however, has the potential to affect a much greater
population.
6
States have negotiated payments from tribes in return for certain
services such as security and improving and maintaining highway
access to their casinos.
7
Gazel, Thompson, and Rickman (1995), KPMG Management
Consulting (1995), and Blois, Cunningham, and Lott (1995).
Thomas A. Garrett is a senior economist at the Federal Reserve Bank of St. Louis. Molly D. Castelazo provided research assistance.
Federal Reserve Bank of St. Louis Review, January/February 2004, 86(1), pp. 9-22.
© 2004, The Federal Reserve Bank of St. Louis.
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Table 1
State Gaming Summary 2001
State
Land-based casinos
Riverboat casinos
Native American
casinos
Arizona
X
California
X
Colorado
X
Connecticut
X
Florida
X
Idaho
X
Illinois
X
Indiana
X
Iowa
X
Kansas
X
X
Louisiana
X
Michigan
X
X
X
X
Minnesota
X
Mississippi
X
Missouri
X
Montana
X
X
Nebraska
X
Nevada
X
New Jersey
X
X
New Mexico
X
New York
X
North Carolina
X
North Dakota
X
Oklahoma
X
Oregon
X
South Dakota
X
Texas
X
Washington
X
Wisconsin
X
Total
4
6
25
SOURCE: Bear Stearns 2002-2003 North American Gaming Almanac (Ader, 2003, p. 16). The above list does not include those states with
casinos operating as part of a state lottery. States not listed have no corporate or tribal casinos.
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FEDERAL R ESERVE BANK OF ST. LOUIS
Garrett
Table 2
Gaming Revenue for Selected States
State
Colorado
2001 revenue ($ millions)
2000 revenue ($ millions)
$675.3
$631.7
Percent change
6.9%
Connecticut
1,401.6
1,308.7
7.1
Illinois
1,783.8
1,657.8
7.6
Indiana
1,841.8
1,689.7
9.0
922.9
892.6
3.4
Louisiana
1,883.2
1,708.9
10.2
Michigan
1,007.4
742.9
35.6
Mississippi
2,700.8
2,650.4
1.9
Missouri
1,137.1
996.6
14.1
Nevada
9,466.9
9,599.4
–1.4
New Jersey
4,303.9
4,299.6
0.1
27,124.7
26,178.4
3.6
Iowa
Total
NOTE: Tribal and corporate casino revenues are considered in the above figures and represent revenues to the casinos after subtracting
player winnings.
SOURCE: Bear Stearns 2002-2003 North American Gaming Almanac (Ader, 2003, p. 6).
distinguish any potential differences in employment
effects and to address the typical perception that
casino gaming is more often seen as a savior for rural
communities rather than urban communities.
The Spread of Casino Gaming
Nevada was the first state to legalize casino
gaming in 1931 and has the largest gaming market
in the country. The 210 casinos in Nevada generated
over $9.5 billion in revenue during 2001. The largest
concentration of casinos is in Las Vegas, with 14
casinos downtown and 47 on the “Strip” amassing
nearly $5.3 billion in revenue and attracting 35
million visitors annually to fill over 100,000 hotel
rooms. Hotels downtown and on the Strip have
75,000 electronic gaming devices (EGDs—which are
slot machines, video poker games, and any other
electronic game used for wagering) and 3,300 table
games that take up 3.3 million square feet of casino
floor space. Other major markets in Nevada include
Reno ($1 billion in revenue), Laughlin ($500 million
in revenue), and Lake Tahoe ($330 million in revenue).
In 1976, New Jersey became the second state to
legalize casino gaming, but restricted the activity to
Atlantic City. Today there are 13 casinos in Atlantic
City generating nearly $4.3 billion in annual revenue
and attracting 32 million visitors, making Atlantic
City the second largest casino gaming market in the
United States. The Atlantic City market is generally
characterized as a “day-trip” destination, whereas
Las Vegas is typically considered a vacation destination. Atlantic City casinos have 12,000 hotel rooms
and offer 37,000 EGDs, over 1,200 table games, and
nearly 1.3 million square feet of casino floor space.
The early 1990s saw a marked increase in the
number of states that legalized casino gaming.
Riverboat casino gaming first began in Iowa and
Illinois in 1991 and quickly spread throughout the
Midwest.8 Riverboat gaming now also exists in
Indiana, Mississippi, and Missouri. Louisiana and
Michigan legalized land-based casino gaming within
the last decade. States cite the gaming industry’s
potential to create economic growth in the state as
the primary reason for their approval of corporate
casino gaming. The greatest perceived benefits are
employment growth, greater tax revenue to state
and local governments, and growth in local retail
sales. In addition, the increasing fiscal pressures on
state budgets during the 1990-91 recession, the fear
8
In many cases, the riverboat casinos are “fixed in dock,” meaning
that they cannot move freely along a river.
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of lost revenue to neighboring states’ casinos, and
a more favorable public attitude regarding casino
gaming have all increased the appeal and acceptance
of casinos.
Saddled with their current state budget crises,
state legislators have taken up the issue of casino
gaming with a renewed interest. The National
Conference of State Legislatures reported in April
2003 that collective state budget gaps will approach
$70 billion in fiscal year 2004.9 As seen in Table 2,
casino revenues are sizeable, making them an attractive revenue source for state and local governments.
Many states are considering the expansion of casino
gaming, while others such as Pennsylvania are
debating whether to introduce slot machines at
pari-mutuel racetracks. Several states with casino
gaming have increased casino gaming tax rates
within the past year or two. Also, states with Indian
gaming are considering measures to extract revenue
from traditionally tax-exempt Indian casinos. However, the direct taxation of tribal gaming revenue is
likely to be met with serious legal challenges involving the sovereignty of Indian tribes.
CASINOS AND EMPLOYMENT
Local officials and casino proponents often
claim that casinos increase local employment simply
because they create additional jobs within the local
area. However, several factors should be considered
when evaluating the employment effects of casino
gaming. These factors are applicable to any business
or industry, not just casino gaming.
The relationship between casinos and employment involves the location of the casino and the
required skill level of its work force. The general
premise is that casinos increase employment because
a casino’s operation requires labor and this labor
will come from the local area, thus reducing local
unemployment. The question to ask is not only
whether casinos decrease unemployment, but also
for whom they decrease unemployment. Most casino
jobs require some skill, be it accounting, dealing
cards, security, or other expertise. If a casino is planning to move to a rural area that has a relatively lessskilled work force, the casino probably will draw
skilled labor from outside of the area. If this labor
remains outside of the local area and workers commute to the casinos, then unemployment in the local
area will remain unchanged. If some of this skilled
9
Of this total, California accounts for $26 billion. See the National
Conference of State Legislatures State Budget Update (April 2003).
12
J A N UA RY / F E B R UA RY 2 0 0 4
labor decides to move near the casino, then the
unemployment rate in the local area will fall because
the labor force has increased.10 However, unemployment for the original population has remained essentially unchanged—only the new arrivals have found
employment with the casino. It is the employment
of these new arrivals that has decreased the unemployment rate. Thus, the promise of increased
employment for the original population, which is
used as an argument for the construction of casinos,
may not be realized. In a relatively urban area, there
is probably enough variety in the work force to
ensure that skilled labor will be provided locally. In
rural areas, however, most labor may be from outside
of the area, thus leaving unemployment for the
original population unchanged.
While casino employment is used as an indicator
of economic development, true economic development occurs only when there is increased value to
society.11 The introduction of casino gaming may
cause local businesses to close, which will result in
layoffs.12 The net increase in employment in the local
area may thus be less than the number of new casino
jobs. However, casino gaming may increase total
employment when casinos indirectly generate noncasino jobs in the local area as a result of increased
demand for non-casino goods and services. Casino
employees who were previously unemployed or who
recently moved into the area now generate income,
and this income will be spent on goods and services
such as housing and entertainment. An increase
in demand for these services will increase firms’
demand for labor, thereby increasing employment.
These employment “spillovers” essentially result
in a positive or negative multiplier effect. The degree
of this multiplier effect has been disputed in the
literature. Research by Gazel, Thompson, and
Rickman (1995), KPMG Management Consulting
(1995), and Blois, Cunningham, and Lott (1995)
suggests that a positive multiplier effect exists. However, studies by Anders, Siegel, and Yacoub (1998),
Przybylski et al. (1998), and Siegel and Anders (1999)
provide evidence that there is, at least to some degree,
10
Recall that the unemployment rate is the number of unemployed
divided by the labor force (employed+unemployed).
11
An evaluation of the social welfare effects of casino gaming should
consider the benefits of casino gaming beyond employment, as well
as possible costs such as addiction and crime. See Grinols (forthcoming).
12
The influence of casino gaming on businesses and employment certainly reaches beyond county borders. Thus, economic development
in one county could come at the expense of a reduction in economic
activity in a neighboring county.
FEDERAL R ESERVE BANK OF ST. LOUIS
Garrett
Table 3
Statistics for Counties with Casinos
Casino employment
Number of casinos in county
Warren
County,
MS
Tunica
County,
MS
Massac
County,
IL
St. Clair
County,
IL
Lee
County,
IA
St. Louis
County,
MO
2,443
12,689
883
1,184
367
2,050
4
9
1
1
1
1
County employment
25,030
5,636
7,665
108,270
16,708
540,981
County population
49,343
Percent (number) of casino
75 (1,832)
employees from home county
15,081
256,599
33,313
1,015,417
30 (3,807)
9,635
44 (389)
80 (947)
45 (165)
32 (656)
County unemployment rate,
pre-casino (%)
8.8
10.7
9.5
9.4
3.7
3.1
County unemployment rate,
post-casino (%)
4.2
7.1
4.4
5.9
3.3
3.9
State unemployment rate,
pre-casino (%)
8.2
8.2
7.5
7.5
3.7
4.2
State unemployment rate,
post-casino (%)
5.5
5.5
5.4
5.4
3.3
4.7
Employment/population ratio,
pre-casino
0.430
0.302
0.381
0.400
0.477
0.534
Employment/population ratio,
post-casino
0.507
0.591
0.509
0.418
0.449
0.531
First casino opened
2/93
8/92
2/93
7/93
11/94
3/97
NOTE: All employment data are from December 2001, and population data are from 1999. Home-county casino employment was
obtained from contacting casinos. For multiple casinos in a county, the above figure represents the county average.
interindustry substitution between casino gaming
and certain local businesses.
Local Employment—Empirical Analysis
Several academic studies have explored the
impact of casinos on local employment. While their
conclusions are somewhat mixed, the studies generally suggest that casinos do increase employment in
the local area (or at least they do not lead to an
employment decrease). Grinols (1994) studied Illinois
casinos and found that, of the eight casinos in the
state, six have had no significant impact on total
employment since their introduction. Using a different methodology, Hewings, Schindler, and Nafziger
(1996) found that Illinois casinos generated over
17,000 new jobs. In a study of Colorado casinos, the
Center for Business and Economic Forecasting (1995)
found that Native American gaming led to 6,100 new
jobs. Leven and Phares (1997) found that nearly
12,200 new jobs were created as a result of Missouri
casinos.
This section presents two analyses of county
employment changes after the introduction of
casinos. The first analysis uses monthly household
employment data to explore the effect of casinos on
resident employment in each county; the second
analysis uses annual payroll employment data to
detect employment changes in specific industries.
It is important to consider that household and payroll employment data measure employment in different ways, so the figures for each will be neither equal
nor directly comparable. Household employment
is derived from a survey of households and is the
number of people in the county who are employed,
regardless of where they are employed; county payJ A N UA RY / F E B R UA RY 2 0 0 4
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Garrett
roll employment is derived from a survey of firms
and is the number of jobs in the county.
The counties used in the analyses are Warren
County (Vicksburg casino market) and Tunica County
(Tunica casino market) in Mississippi; Massac County
(one casino) and St. Clair County (one casino) in
Illinois; Lee County (one casino) in Iowa; and St. Louis
County (one casino) in Missouri. Of these six counties, St. Louis and St. Clair counties are classified
as urban counties and the rest as rural. Detailed
employment statistics for each of the six counties
are shown in Table 3.
For the first analysis, total household employment is compared before and after casino introduction. For each county, an empirical model is
developed to capture employment changes several
years before casino introduction. These changes
are then used to forecast employment changes from
the date of casino introduction through December
2001 (the end of the sample period). These forecasts
represent the level of employment that would have
existed if the casinos had not been opened. The
difference between the actual and forecasted
employment is the estimated effect of the casinos.
The second analysis uses payroll employment
data to compare county employment in construction, manufacturing, retail trade, services, and
finance before and after casino introduction.13 If
casinos cause an influx of new businesses and/or
residents to the county, employment in these sectors
may have increased since the introduction of casino
gaming. Based on previous studies, this may be
especially true for services and retail trade employment. Conversely, if casinos cannibalize existing
retail and services sector businesses, then employment in these sectors may have decreased since
casino gaming was introduced.
Data and Methodology for Household
Employment Forecasts. Seasonally adjusted
monthly household employment was obtained from
the U.S. Bureau of Labor Statistics for each of the
six counties over the period 1986:01-2001:12. Since
the six counties introduced casino gaming in the
early to mid-1990s, the length of the data series was
chosen to ensure an adequate sample of observations pre- and post-casino adoption.
The behavior of the employment series for each
county prior to casino adoption (see bottom of
13
The analysis does not consider employment in agriculture, government,
or transportation because employment in these sectors is unlikely to
be significantly affected by casino gaming. A description of the businesses included in each of the five sectors can be found at
www.census.gov/epcd/cbp/map/97data/29/189.txt.
14
J A N UA RY / F E B R UA RY 2 0 0 4
Table 3 for casino opening dates) is captured using
an ARIMA( p,d,q) model, which is defined as
x (t)=γ+α1x (t –1)+…+α p x (t –p)
+e (t)+β1e (t –1)+…+βqe (t – q),
where x is county household employment, γ is a
constant term, e(t) is the error term, p is the number
of autoregressive lags, and q is the number of movingaverage lags. Augmented Dickey-Fuller (ADF) tests
for stationarity were conducted on the employment
series (pre-casino adoption) for each of the six counties to determine the order of integration (d ).14 The
ADF tests reveal that employment for St. Clair County
and St. Louis County is stationary in levels, employment for Lee County is trend stationary (a linear
time trend is included in the above equation), and
employment for Tunica, Massac, and Warren counties is first-difference stationary (where x (t)
becomes ∆x (t)=x (t) – x (t –1)).
The Akaike information criterion was used to
determine the model order for each county’s employment series. The appropriate ARIMA models are as
follows: Tunica County ARIMA(2,1,1), Massac County
ARIMA(1,1,0), Warren County ARIMA(2,1,0), St. Clair
County ARIMA(1,0,4), Lee County ARIMA (1,0,0),
and St. Louis County ARIMA(1,0,2).15
Visual inspection of the St. Louis County and
St. Clair County employment series reveals marked
business cycle effects. No discernable effects are
present for the four rural counties. To capture these
effects in the empirical models, the coincident index
for both Missouri and Illinois is included as a variable
in their respective ARIMA model. Based on model
order tests, contemporaneous values of the Illinois
coincident index are included in the St. Clair County
model and contemporaneous and one-lag values of
the Missouri coincident index are included in the
St. Louis County model.16
14
The ADF test results are available from the author.
15
Following Perron (1989), the ARIMA models also account for, if necessary, structural changes in the employment series prior to casino
introduction by including binary dummy variables. Visual inspection
of the data reveals structural breaks in the Massac County and St. Louis
County data. Thus, the equation for Massac County includes a binary
dummy variable that has a value of 1 for 1990:01 and the St. Louis
County equation includes a binary dummy variable that has a value
of 1 over the period 1990:01–1993:01.
16
The coincident index for each state weights changes in payroll
employment, average hours worked in manufacturing, the unemployment rate, and real wages paid. Monthly state-level coincident indices
are available from the Federal Reserve Bank of Philadelphia at
www.phil.frb.org/econ/stateindexes/index.html. See Crone (2002) for
a discussion of regional coincident indices.
FEDERAL R ESERVE BANK OF ST. LOUIS
Garrett
Figure 1
Warren County, MS—Household Employment
Employment
28,000
26,000
24,000
Actual Employment
22,000
20,000
Forecasted Employment (no casinos)
18,000
16,000
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
Figure 2
Tunica County, MS—Household Employment
Employment
7,000
6,000
5,000
Actual Employment
4,000
3,000
Forecasted Employment (no casinos)
2,000
1,000
1986
1987
1988
1989
1990
1991
1992
1993
Using the coefficient estimates from the ARIMA
models, employment is forecasted dynamically from
the month of casino adoption through 2001:12 and
is compared with actual employment since the
beginning of casino operation.17
Results for Household Employment Forecasts
Warren and Tunica Counties, Mississippi. Actual
and forecasted household employment for Warren
and Tunica counties in Mississippi are shown in
Figures 1 and 2. Both are rural counties, and casino
gaming constitutes a major industry in each county.
The figures reveal that employment in both counties
significantly increased since the adoption of casino
gaming. There was a dramatic jump in employment
in Warren County in 1993 and 1994, the two years
in which casinos began operations. Since that time,
employment growth has been relatively flat. Employment in Tunica County has grown steadily since the
first casino was introduced in late 1992, reflecting
the steady increase in the number of casinos in
Tunica County throughout the middle and late 1990s.
Forecasted employment for the 1990s reveals that,
17
Estimates from the ARIMA models are available from the author.
1994
1995
1996
1997
1998
1999
2000
2001
without casino gaming, employment would have
decreased slightly in Warren County (about 7 jobs
per month), but would have increased slightly in
Tunica County (about 3 jobs per month).
As of December 2001, Tunica County household
employment increased by 3,144 since the introduction of the first casino, while the population
increased by 1,172. Warren County employment
increased by 4,225 since the introduction of the first
casino, while its population increased by 910. Therefore, much of the increase in household employment
occurred for pre-casino residents rather than new
residents. The employment-to-population ratios for
both counties have also increased since the introduction of casino gaming (see Table 3). The employmentto-population ratio increased by nearly 27 percentage
points in Tunica County and by over 7 percentage
points in Warren County. Casino employment in
Tunica County is greater than the population of the
county, so the bulk of employees who work in Tunica
casinos live outside of the county. In Warren County,
total casino employment for residents is about
1,800, but the increase in employment since casino
introduction was nearly 5,000 with little change
(910) in population. This suggests that over the
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Figure 3
St. Clair County, IL—Household Employment
Employment
114,000
111,000
Actual Employment
108,000
Forecasted Employment (no casinos)
105,000
102,000
99,000
96,000
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
Figure 4
Massac County, IL—Household Employment
Employment
10,000
8,000
Actual Employment
6,000
Forecasted Employment (no casinos)
4,000
2,000
1986
1987
1988
1989
1990
1991
1992
1993
sample period there was employment growth in
Warren County outside of the casino industry.
St. Clair and Massac Counties, Illinois. Figures 3
and 4 show actual and forecasted employment for
urban St. Clair County and rural Massac County in
Illinois. St. Clair County employment is relatively
more volatile. In a county with over 250,000 people
and household employment near 108,000, the exact
impact of one casino on local employment is hard
to determine given the relative smallness of casino
employment to total employment and the volatility
of overall county employment. Prior to 2000, actual
and forecasted employment trended upward. Beyond
this point, however, actual employment fell below
the forecasted decrease in employment. Total
employment has risen 1,601 since the introduction
of the casino (the casino employs 1,184 people, 947
of whom are from St. Clair County), but the population of St. Clair County has decreased nearly 7,500.
As a result, the employment-to-population ratio has
increased slightly from the pre-casino period (1.7
percentage points). It thus appears that casino gaming has not hurt St. Clair County employment, but
the volatility of total employment and the loss in
16
J A N UA RY / F E B R UA RY 2 0 0 4
1994
1995
1996
1997
1998
1999
2000
2001
population leads one to question the overall ability
of one casino to maintain or foster employment
growth in an urban area.
Employment in rural Massac County markedly
increased when the casino began operations and
has increased steadily since then. Without the introduction of casino gaming, employment forecasts
show a decrease at a rate of about 5 jobs per month.
By the end of 2001, actual employment was higher
than forecasted employment, but the growth in
actual employment has been relatively slow since
the introduction of casino gaming. Employment
increased by 1,927 since the introduction of casino
gaming, which employs 389 persons from Massac
County, and the population of Massac County
increased by 18. As in Warren and Tunica counties,
the vast majority of employment growth in Massac
County occurred for pre-casino residents rather than
new arrivals. In addition, the bulk of employment
growth occurred outside of the casino industry.
The employment-to-population ratio for Massac
County increased nearly 13 percentage points since
the introduction of casino gaming.
Lee County, Iowa. Forecasted and actual employ-
FEDERAL R ESERVE BANK OF ST. LOUIS
Garrett
Figure 5
Lee County, IA—Household Employment
Employment
22,000
Forecasted Employment (no casinos)
20,000
Actual Employment
18,000
16,000
14,000
12,000
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
Figure 6
St. Louis County, MO—Household Employment
Employment
570,000
560,000
550,000
540,000
530,000
520,000
510,000
500,000
1986
Forecasted Employment (no casinos)
Actual Employment
1987
1988
1989
1990
1991
1992
1993
ment for rural Lee County, Iowa, are shown in
Figure 5. Actual employment remained relatively
constant around the time the casino began operations but has steadily decreased since then. Forecasted employment continued a gradual increase
(about 20 jobs per month) since the date of casino
introduction. At the end of 2001, Lee County had
lost 1,846 jobs since the casino began operations
and experienced a population decrease of 1,652.
As a result, the employment-to-population ratio
decreased by nearly 3 percentage points since the
casino was introduced. Unlike rural counties such
as Massac County in Illinois and Tunica and Warren
counties in Mississippi, the introduction of casino
gaming in Lee County has not corresponded to an
increase in employment. It is possible, however,
that the introduction of casino gaming has slowed
the decrease in employment and population in Lee
County.
St. Louis County, Missouri. St. Louis County’s
total household employment is nearly 550,000. As
in urban St. Clair County, household employment
in St. Louis County is quite variable over the sample
period (Figure 6). The impact of one casino employ-
1994
1995
1996
1997
1998
1999
2000
2001
ing 2,050 people, only 32 percent of whom are from
St. Louis County, cannot be accurately inferred from
the data. Employment continued to fall after the
casino was introduced but then slightly increased
above forecasted levels in 2000. It is possible that
the casino has created some jobs, but the direct
impact of the casino on total employment is masked
by highly variable total employment and the relatively small employment contribution made by a
single casino.
Payroll Employment Changes by Sector.
Because the payroll employment data are listed
on an annual basis, this study’s small sample size
is not adequate for running forecast models. Thus,
the analysis involves comparing employment levels
in each sector before and after the introduction of
casinos. Sector employment changes in these two
periods for each of the six counties are shown in
Tables 4 through 9. For each county, services sector
employment excludes casino employment, which
is listed as a separate sector. Recall that changes in
sector employment cannot be directly compared
with household employment changes in the previous section because the two employment measures
are different.
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Table 4
Warren County, MS, Payroll Employment Changes by Sector
Employment
Sector
1993
2001
Gain or loss (% change)
Manufacturing
3,408
5,090
1,682 (49.4)
Retail trade
3,926
2,932
–994 (–25.3)
Services
4,114
7,674
3,560 (86.5)
Financial
597
487
–110 (–18.4)
Construction
363
590
227 (62.5)
Casinos
—
2,443
Total gain or loss
2,443
6,808 (54.9)
NOTE: The first casino opened in February 1993. Services sector employment excludes casino employment.
SOURCE: Data are from the U.S. Census Bureau. 1993: www.census.gov/epcd/cbp/map/93data/28/149.txt.
2001: www.census.gov/epcd/cbp/map/01data/28/149.txt.
Table 5
Tunica County, MS, Payroll Employment Changes by Sector
Employment
Sector
1992
2001
Manufacturing
375
614
Gain or loss (% change)
239 (63.7)
Retail trade
204
374
Services
123
2,441
Financial
77
99
22 (28.6)
Construction
15
60
45 (300.0)
Casinos
—
12,689
Total gain or loss
170 (83.3)
2,318 (1884.5)
12,689
15,483 (1950.0)
NOTE: The first casino opened in August 1992. Services sector employment excludes casino employment.
SOURCE: 1992 data are from GovStats: http://govinfo.kerr.orst.edu/php/commerce/state/show.php. 2001 data are from the U.S. Census
Bureau: www.census.gov/epcd/cbp/map/01data/28/143.txt.
Warren County, Mississippi (Table 4), experienced
a large increase in manufacturing, services, and
construction employment since the introduction
of casino gaming, which constitutes 36 percent of
the total increase in payroll employment. The
increase in manufacturing employment is quite
large, given the national decrease in manufacturing
employment during the 1990s. Moderate decreases
in retail trade and financial employment occurred
within the county over the same time period.
18
J A N UA RY / F E B R UA RY 2 0 0 4
Because casino gaming is a relatively large industry
in Warren County, the findings suggest that the
increase in services sector employment and decrease
in retail trade employment may be attributed to
casino gaming.
Tunica County, Mississippi (Table 5), had employment increases in all five sectors, with the largest
increase in the services sector. Given that casino
gaming is the predominant industry in Tunica
County, the data in Table 5 suggest that employment
FEDERAL R ESERVE BANK OF ST. LOUIS
Garrett
Table 6
St. Clair County, IL, Payroll Employment Changes by Sector
Employment
Sector
1993
2001
Manufacturing
7,318
6,724
Gain or loss (% change)
–594 (–8.1)
Retail trade
18,154
12,872
–5,282 (–29.1)
Services
25,922
39,102
13,180 (50.8)
Financial
3,158
4,274
1,116 (35.3)
Construction
2,626
3,927
1,301 (49.5)
—
1,184
1,184
Casino
Total gain or loss
10,905 (19.1)
NOTE: The casino opened in July 1993. Services sector employment excludes casino employment.
SOURCE: Data are from the U.S. Census Bureau. 1993: www. census.gov/epcd/cbp/map/93data/17/163.txt.
2001: www.census.gov/epcd/cbp/map/01data/17/163.txt.
Table 7
Massac County, IL, Payroll Employment Changes by Sector
Employment
Sector
1993
2001
Manufacturing
736
638
–98 (–13.3)
–342 (–49.2)
Gain or loss (% change)
Retail trade
695
353
Services
874
1,379
Financial
108
198
90 (83.3)
Construction
126
100
–26 (–20.6)
Casino
—
883
883
505 (57.8)
Total gain or loss
1,012 (39.9)
NOTE: The casino opened in February 1993. Services sector employment excludes casino employment.
SOURCE: Data are from the U.S. Census Bureau. 1993: www. census.gov/epcd/cbp/map/93data/17/127.txt.
2001: www.census.gov/epcd/cbp/map/01data/17/127.txt.
increases in the various sectors can be attributed,
in large part, to the introduction of casino gaming.
Overall payroll employment increased by over 1,900
percent since casino gaming was introduced in
1992; a large portion of this increase (82 percent)
is attributed to casino employment.
Casino gaming in St. Clair County, Illinois
(Table 6), contributed to roughly 11 percent of the
gain in payroll employment since casino gaming
was introduced. Services, finance, and construction
employment all increased by an average of 43 percent, but manufacturing and retail trade decreased
by 8 percent and 29 percent, respectively. The
employment impact of casino gaming has been
much smaller than changes in other sectors, but it
still has contributed moderately to net changes in
total payroll employment.
Massac County, Illinois (Table 7), experienced
J A N UA RY / F E B R UA RY 2 0 0 4
19
REVIEW
Garrett
Table 8
Lee County, IA, Payroll Employment Changes by Sector
Employment
Sector
Manufacturing
1994
2001
Gain or loss (% change)
5,991
5,130
–861 (–14.4)
Retail trade
3,144
2,057
–1,087 (–34.6)
Services
3,573
5,229
1,656 (46.3)
Financial
482
558
76 (15.8)
Construction
796
669
–127 (–16.0)
Casino
—
367
Total gain or loss
367
24 (0.17)
NOTE: The casino opened in November 1994. Services sector employment excludes casino employment.
SOURCE: 1994 data are from GovStats: http://govinfo.kerr.orst.edu/php/commerce/state/show.php. 2001 data are from the U.S.
Census Bureau: www.census.gov/epcd/cbp/map/01data/19/111.txt.
Table 9
St. Louis County, MO, Payroll Employment Changes by Sector
Employment
Sector
Manufacturing
1997
2001
Gain or loss (% change)
97,608
59,048
–38,560 (–39.5)
Retail trade
113,407
74,170
–39,237 (–34.6)
Services
207,947
287,982
80,035 (38.5)
Financial
45,162
49,869
4,707 (10.4)
Construction
32,087
39,876
7,789 (24.3)
—
2,050
2,050
Casino
Total gain or loss
16,784 (3.38)
NOTE: The casino opened in March 1997. Services sector employment excludes casino employment.
SOURCE: Data are from the U.S. Census Bureau. 1997: www. census.gov/epcd/cbp/map/97data/29/189.txt.
2001: www.census.gov/epcd/cbp/map/01data/29/189.txt.
an increase in services and financial employment
but a decrease in other sectors. With the introduction
of casino gaming, payroll employment increased
nearly 40 percent. Casino gaming has provided the
largest contribution to the increase in total payroll
employment in Massac County (87 percent). Without
it, the gain in total payroll employment in Massac
County would have been roughly 130 persons.
Without casino gaming, Lee County, Iowa
20
J A N UA RY / F E B R UA RY 2 0 0 4
(Table 8), would have experienced an overall decrease
in payroll employment since casino introduction.
While services and financial employment increased
over the sample period, these increases were met
by larger decreases in manufacturing, retail trade,
and construction employment, resulting in the loss
of 343 jobs. Casino employment of 367 persons
provided a net gain of 24 jobs in Lee County. Household employment and population fell for Lee County,
FEDERAL R ESERVE BANK OF ST. LOUIS
but payroll employment remained relatively constant since casino introduction. This suggests that
either some of the original population in Lee County
moved outside of the county and continues to work
in Lee County or more residents of neighboring
counties now work in Lee County.
Like St. Clair County in Illinois, the casino
industry is a relatively minor employer in St. Louis
County, Missouri (Table 9). However, the 2,050
casino jobs contributed to roughly 12 percent of
the increase in total payroll employment in St. Louis
County (similar to the 11 percent in urban St. Clair
County). Large decreases in manufacturing and
retail trade occurred, but these decreases were met
with slightly larger increases in services, financial,
and construction employment. Thus, even though
casino gaming may be a minor industry in urban
areas, casino gaming can make up a moderate portion of net payroll employment gains or losses.
SUMMARY AND CONCLUSIONS
The employment effects of casino gaming are
difficult to quantify. A casino may draw labor from
outside of the local area, thus leaving local employment conditions unchanged if that labor does not
relocate to the local area. Casinos are only synonymous with economic development if they create a
greater value to society. It is possible that casino
gaming may reduce employment in other local
industries if consumers substitute casino gaming
for other consumption. The net effect of gaming
could be positive or negative depending upon the
degree to which casino gaming substitutes for or
complements consumption at other local businesses.
Determining the possible impact of casino
gaming on local employment involves an examination of employment changes in the local area before
and after the introduction of casino gaming. The
empirical analysis presented here reveals that, in
three of four cases, rural counties that adopted casino
gaming experienced increases in household and
payroll employment. This seems to hold even though
casino employment is dispersed over several counties rather than just the home county. Also, employment gains are much greater in rural counties that
have adopted casino gaming as a major or predominant industry. It is harder to detect the impact of
casino gaming in more-metropolitan counties, where
employment is highly variable and casino gaming
constitutes a small portion of total employment.
However, casino gaming in urban areas can still
constitute a moderate portion of net payroll employ-
Garrett
ment gains or losses even though casino gaming is
a minor industry; still, the impact is much greater
in rural counties with casino gaming.
One question that remains is, How much will
the gaming industry grow in the future? The current
budget crises facing state and local governments
may generate further expansion of casino gaming
across the country. There is little evidence that the
industry has reached the saturation point—a “build
it and they will come” attitude pervades the industry
at the current time. While the evidence here suggests
that rural counties that adopt casino gaming as a
major industry are likely to see large employment
gains, this does not suggest that every county can
become like Tunica, Mississippi. Attitudes regarding
the spread of casino gaming in a given local area,
costly industry regulation, and increasing casino
competition may hinder the growth of gaming in
rural areas.
The degree to which state and local governments
currently rely on casino revenue raises the question
of whether or not the casino industry is recessionproof. One may expect that the growth of the casino
industry is contingent upon economic conditions;
if the industry is highly procyclical, then casino
revenues may do little to lessen the budgetary
impacts of an economic slowdown. This may be
true: In fact, many states with casinos are facing
budget crises similar to those of states without
casinos. However, little research has been done on
this issue. Regardless of what the future holds, there
is little doubt that casinos are here to stay and that
more communities will be faced with the question
of whether to adopt casino gaming.
REFERENCES
Ader, Jason N. Bear Stearns 2002-2003 North American
Gaming Almanac. Las Vegas: Huntington Press, 2003.
Anders, Gary; Siegel, Donald and Yacoub, Munther. “Does
Indian Casino Gambling Reduce State Revenues? Evidence
from Arizona.” Contemporary Economic Policy, July 1998,
16(3), pp. 347-55.
Blois, T.; Cunningham, S. and Lott, W. “The Bridgeport Casino
Proposals: An Economic Evaluation.” Prepared for the
Connecticut Department of Economic and Community
Development and the Connecticut Department of Special
Revenue. Storrs, CT: Connecticut Center for Economic
Analysis, October 1995.
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REVIEW
Garrett
Center for Business and Economic Forecasting, Inc.
Economic Impact of Limited Gaming in Colorado. Report
prepared for the Colorado Casino Owners Association,
Regis University, January 1995.
Crone, Theodore. “Consistent Economic Indexes for the 50
States.” Working Paper No. 02-7/R, Federal Reserve Bank
of Philadelphia, May 2002.
Gazel, R.; Thompson, W. and Rickman, D. “The Economic
Impact of Native American Gaming in Wisconsin.” Gaming
Research and Review Journal, 1995, 2(2), pp. 43-62.
GovStats. http://govinfo.kerr.orst.edu/php/commerce/state/
show.php.
Grinols, Earl. “Bluff or Winning Hand? Riverboat Gambling
and Regional Employment and Unemployment.” Illinois
Business Review, Spring 1994, 51(1), pp. 8-11.
Grinols, Earl. “Cutting the Cards and Craps: Right Thinking
About Gambling Economics” in G. Reith, ed., Gambling:
Debating the Issues, Prometheus Contemporary Issues
Series. New York: Prometheus (forthcoming).
Hewings, G.; Schindler, G. and Nafziger, B. “The Impact of
Riverboat Casino Gambling on the Illinois Economy
1991-1995.” Report to the Illinois Gaming Board. Chicago:
Regional Economics Applications Laboratory, 1996.
Leven, Charles and Phares, Donald. “Casino Gaming in
Missouri: The Spending Displacement Effect and Net
Economic Impact.” Proceedings of the 90th Annual
Conference on Taxation, National Tax Association, Chicago,
November 1997, pp. 431-38.
National Conference of State Legislatures. State Budget
Update. Washington, DC: National Conference of State
Legislatures, February 2003.
National Gambling Impact Study Commission. Final Report.
Washington, DC: National Gambling Impact Study
Commission, 1999.
Perron, Pierre. “The Great Crash, the Oil Price Shock, and
the Unit Root Hypothesis.” Econometrica, November
1989, 57(6), pp. 1361-401.
Przybylski, Michael; Felsenstein, Daniel; Freeman, Daniel
and Littlepage, Laura. “Does Gambling Complement the
Tourist Industry? Some Empirical Evidence of Import
Substitution and Demand Displacement.” Tourism
Economics, September 1998, 4(3), pp. 213-31.
Siegel, Donald and Anders, Gary. “Public Policy and the
Displacement Effects of Casinos: A Case Study of Riverboat
Gambling in Missouri.” Journal of Gambling Studies,
Summer 1999, 15(2), pp. 105-21.
U.S. Census Bureau. www.census.gov.
KPMG Management Consulting. One Year Review of Casino
Windsor. Report prepared for Ontario Casino Corporation,
Toronto, 1995.
22
J A N UA RY / F E B R UA RY 2 0 0 4
U.S. Regional Business Cycles and the Natural
Rate of Unemployment
Howard J. Wall and Gylfi Zoëga
n the late 1960s, Milton Friedman and Edmund
Phelps convinced the economics profession
that there was no long-run trade-off between
inflation and unemployment. A policy that tries to
maintain the unemployment rate below a certain
threshold (dubbed the natural rate of unemployment by Friedman) would lead to rising inflation,
while trying to maintain it above the threshold
would lead to ever-declining rates of inflation. The
proposition of long-run neutrality of inflation and
money growth soon gained wide acceptance, and
work in this area has focused on making the natural
rate of unemployment fully endogenous in generalequilibrium models (Pissarides, 2000; Layard,
Nickell, and Jackman, 1991; and Phelps, 1994).
This theory can be used to show how a variety of
macroeconomic shocks—such as the rate of technical progress, real interest rates, and oil prices—
affect the natural rate and social welfare.
Inflation-targeting central banks often monitor
employment and wage changes in the hope of
preventing wage inflation in the labor market from
generating general price inflation.1 The use of the
notion of an equilibrium level of unemployment
that is independent of current and past monetary
variables has made the estimation of the natural
rate important. This practice relies on representativeagent type models—the ones used to provide
microeconomic foundations for the inflation/
unemployment relationship—to assess the state of
the economy using aggregate data. A central banker
may then use data on aggregate employment, unemployment, and average wage inflation across all
sectors of the economy to assess the position of the
economy in relation to an estimate of the natural
I
1
Such considerations have led to the appointment of a labor economist,
Steve Nickell, to Britain’s Monetary Policy Committee.
rate of unemployment. Most often, the estimate is
the implied natural rate in an econometric model
of the aggregate Phillips curve.
The objective of this article is to show that the
sole reliance on aggregate data may lead to incorrect
inferences about the natural rate of unemployment.
We show how regional business cycles might affect
aggregate wage inflation and how attention to
regional labor market trends can be useful for understanding the aggregate labor market. Moreover, we
show how the natural rate of unemployment may
depend directly on the dispersion of economic
activity across regions.
Our regional approach is in some ways parallel
to the sectoral approach of Lilien (1982), Abraham
and Katz (1986), and Brainard and Cutler (1993).
Lilien (1982) found that a measure of sector-specific
disturbances accounted for a significant portion of
the variation in aggregate employment: When an
industry sheds redundant labor in less time than it
takes for the affected workers to find employment
elsewhere, unemployment rises when the pace of
sectoral reallocation of labor (and capital) increases.
Abraham and Katz (1986) pointed out that Lilien’s
estimates might exaggerate the role of sectoral disturbances by failing to take into account differences
in the sensitivity of different industries to macroeconomic shocks. Brainard and Cutler (1993)
developed a data series to measure the intensity of
reallocation shocks. They constructed a time series
of the variance of sectoral stock market excess
returns and found that they had a modest—though
statistically significant—role in explaining aggregate
employment fluctuations.
Our paper follows recent work illustrating the
significant regional differences in economic conditions, business cycle dynamics, and reactions to
monetary policy. Overman and Puga (2002) demonstrate the increased polarization of unemployment
Howard J. Wall is a research officer at the Federal Reserve Bank of St. Louis. Gylfi Zoëga is a professor of economics at the University of Iceland;
a reader of economics at Birkbeck College, University of London; and an academic adviser to the Central Bank of Iceland. The authors thank seminar
participants at the Central Bank of Iceland, the Federal Reserve Bank of St. Louis, and the Institute for Monetary and Economic Studies of the Bank
of Japan for their comments and suggestions. The views expressed are those of the authors and do not necessarily represent official positions of
the Central Bank of Iceland, the Federal Reserve Bank of St. Louis, or the Federal Reserve System.
Federal Reserve Bank of St. Louis Review, January/February 2004, 86(1), pp. 23-31.
© 2004, The Federal Reserve Bank of St. Louis.
J A N UA RY / F E B R UA RY 2 0 0 4
23
REVIEW
Wall and Zoëga
Figure 1
U.S. Unemployment and Its Coefficient of Variation Across States
12
6
10
5
U.S. Unemployment Rate
(left scale)
8
6
3
4
2
Coefficient of Variation of
State Unemployment Rates (right scale)
2
0
1977:Q2
1
0
1980:Q2
1983:Q2
1986:Q2
1989:Q2
within Europe, where unemployment increasingly
appears in regional clusters that cross national borders. Crone (1998/1999) groups the U.S. states into
regions based on common cyclical behavior, while
Carlino and Sill (2001) find considerable state differences in the volatility of regional cycles. Owyang,
Piger, and Wall (2003) identify distinct state-level
recession/expansion phases, finding a great deal of
business cycle discord among the states and between
individual states and the country as a whole. They
also find significant cross-state differences in the
depths of recessions and the speed of expansions.
Recent research has also found that states and
regions respond differently to monetary policy
(Carlino and DeFina, 1998; Fratantoni and Schuh,
2003; and Owyang and Wall, 2003).
It follows from these studies that the national
economy of the United States is a composite of significantly diverse but interrelated regional economies. In this paper, we show how the diversity in
regional labor market conditions can be used to
enrich policymakers’ understanding of the aggregate
economy. In the next two sections, we briefly lay
out a state-level view of recent U.S. labor market
trends and then describe how differences in regional
business cycles can lead to changes in aggregate
wage inflation. In the final section, we test for the
underlying conditions for this to occur and demonstrate how region-level data can be used to estimate
24
4
J A N UA RY / F E B R UA RY 2 0 0 4
1992:Q2
1995:Q2
1998:Q2
2001:Q2
the aggregate natural rate of unemployment in the
United States.
A STATE-LEVEL VIEW OF U.S.
UNEMPLOYMENT
This article relies on two suppositions about
the dispersion of regional labor market conditions:
(i) that the dispersion is related to aggregate labor
market conditions and (ii) that the dispersion
changes over time. Both suppositions are supported
by Figure 1, which illustrates that the movements
in the aggregate unemployment rate over the past
25 years have largely been in synch with changes
in the dispersion of state unemployment rates (as
measured by the cross-state coefficient of variation).
Correspondingly, the 1990s saw steadily declining
aggregate unemployment alongside a convergence
of state unemployment rates. The only period during
which aggregate unemployment was out of synch
with the coefficient of variation was in 1986-87,
when a handful of states had sudden increases in
unemployment following the crash of energy prices
in 1986.2 Along with the country as a whole, all
other states saw falling unemployment during this
period.
2
These states were Alaska, Alabama, Colorado, Louisiana, Mississippi,
Texas, and Wyoming.
FEDERAL R ESERVE BANK OF ST. LOUIS
Wall and Zoëga
Figure 2
Changes in State Unemployment Rates Around Recessions
1981:Q3 to 1982:Q4
Change in Unemployment Rate
5.97 to 7.59 (1)
4.37 to 5.97 (7)
2.77 to 4.37 (19)
1.17 to 2.77 (16)
–0.43 to 1.17 (7)
1990:Q2 to 1992:Q3
Change in Unemployment Rate
4.37 to 6.62 (2)
2.1 to 4.37 (15)
–0.17 to 2.1 (31)
–2.44 to –0.17 (2)
2000:Q4 to 2002:Q1
Change in Unemployment Rate
2.09 to 3.22 (7)
0.95 to 2.09 (19)
–0.19 to 0.95 (19)
–1.33 to –0.19 (5)
J A N UA RY / F E B R UA RY 2 0 0 4
25
Wall and Zoëga
Figure 2 provides more evidence of the potential
importance of regional labor market variation by
showing the distribution of changes in state unemployment surrounding the three most recent
recession episodes.3 Associated with the 1981-82
recession, the U.S. unemployment rate rose by about
3.3 percentage points from the third quarter of 1981
to the fourth quarter of 1982. Over the same period,
29 states saw smaller increases in their unemployment rates, 14 of which saw increases that were less
than half as large (Nevada actually saw a small
decrease). On the other hand, of the 21 states whose
unemployment rates rose relatively more than the
national average, 6 states saw a rise of at least 4.8
percentage points.
The period surrounding the 1990-91 recession
is perhaps the most regionally distinct of the three
most recent recessions. The aggregate unemployment rate rose by 2.3 percentage points from the
second quarter of 1990 to the third quarter of 1992.
The brunt of the increase was felt on the coasts,
where most states saw increases in their unemployment rates that were much larger than average—
particularly the large states of California, New York,
North Carolina, and Washington. In contrast, a significant majority of states (36), mostly located in
the vast middle of the country, saw a milder than
average increase in unemployment. In fact, four
states actually saw their unemployment rates fall
during the period.
Associated with the 2001 recession was a run-up
in unemployment that began in the fourth quarter
of 2000 and continued well after the end of the
recession. By the first quarter of 2002, the fact of a
regionally diverse unemployment experience, and
an increasing coefficient of variation, had become
clear. By that time, the aggregate unemployment
rate had risen by 1.6 percentage points, although
35 states saw smaller increases than this, and 6 saw
declines. The states hit most severely were scattered
across the country, with pockets in the Great Lakes
region, the Atlantic seaboard, the western Plains,
and the Southwest.
HOW REGIONAL BUSINESS CYCLES
MIGHT MATTER
Here, we describe how a nonlinear relationship
between inflation and measures of labor market
3
As determined by the NBER, the dates for these recessions are July 1981
through November 1982, July 1990 through March 1991, and March
2001 through November 2001.
26
J A N UA RY / F E B R UA RY 2 0 0 4
REVIEW
pressures—such as vacancies, unemployment, and
employment growth—would mean that differences
in regional business cycles are able to affect measures of aggregate conditions. Such nonlinearities
are standard in the theory of unemployment, and
it is not difficult to find empirical evidence backing
them up.
Numerous statistical studies of the distribution
of wage changes point to a potential role for asymmetric wage adjustments and heterogeneity (see, for
example, McLaughlin, 1999; and Card and Hyslop,
1997). These studies show that the distribution of
wage changes is skewed away from small increases
and absolute cuts and toward large increases. There
is a thinning of the left-hand tail to the left of the
zero-inflation point, thereby indicating nominal
wage rigidity. As McLaughlin (1999) documents,
the skewness of the distribution exists even in the
absence of any nominal wage rigidity: Even if the
distribution is truncated at zero wage increases,
the distribution is still skewed. According to survey
results from Truman Bewley (1999), managers are
hesitant to cut wages because of considerations
about worker morale. Wage cuts are likely to introduce personnel and incentive problems beyond the
intended effect on turnover. It follows that in an
economy where some sectors and/or regions are
declining and others are expanding, the relative
wage cuts occurring in the former are smaller than
the wage increases offered in the latter.
This microeconomic evidence suggests that
regional labor market disaggregation may have a
role in illuminating aggregate labor market outcomes. This can be illustrated most simply with
the textbook version of the Phillips curve that traces
its origins to Phelps (1968). In this model, wage
inflation persists because firms cannot adjust instantaneously to changes in vacancies. This might be
due to the costs of setting wages or because wage
setting is staggered over time. Thus, for a given
unemployment rate, the rate of wage inflation is an
increasing function of the number of vacancies that
firms would like to fill and of inflation expectations.
There is a critical vacancy rate, v–, at which actual
wage inflation equals expected wage inflation. When
the vacancy rate is above v–, there is unexpected
wage inflation. Conversely, when the vacancy rate
is below v–, there is unexpected wage deflation.
The microeconometric evidence we cite above
suggests that the slope of the relationship between
wage inflation and the vacancy rate differs above and
below v–. This is because firms are more reluctant
FEDERAL R ESERVE BANK OF ST. LOUIS
Wall and Zoëga
to cut expected wages than to raise them. So, starting
from v–, a decrease in the vacancy rate will lead to
wage deflation that is smaller in absolute terms than
the wage inflation that would follow an equivalent
increase in the vacancy rate. In other words, the
relationship between wage inflation and the vacancy
rate is convex because it is flatter for vacancy rates
below v–.
To see how this convexity matters, consider an
economy with two equal-sized regions, both with
vacancy rates of v–. Now consider equal but oppositesigned changes in the regions’ vacancy rates (i.e.,
the changes are mean-preserving). One region experiences unexpected wage inflation that is greater in
absolute terms than the unexpected wage deflation
in the other. Thus, a mean-preserving increase in
the dispersion of regional vacancy rates is associated
with higher average wage inflation. More generally,
with a strictly convex relationship between wage
inflation and the vacancy rate, the larger is the dispersion of regional vacancy rates, the higher is the
aggregate wage inflation for any given aggregate
vacancy rate.
CONVEXITY AND THE NATURAL RATE
IN THE UNITED STATES
The discussion above describes how aggregate
wage inflation can be affected by the dispersion of
regional labor market conditions when the regionlevel relationship between wage inflation and labor
market conditions is convex. To test for this convexity, we use state unemployment rates and rates
of growth of employment as our measures of state
labor market conditions. Unfortunately, there are
no state-level data for vacancies. This gives rise to
the following equation, which we estimate with
state-level panel data:
(1)
˙
˙
N
˙ it
w
N
= α 0i + α1 it + α1 it
wit
Nit
Nit
+ α 2uit + α 2uit2 + α 3
2
˙ te
w
+ ε it .
wt
In (1), i refers to the state, t refers to the time period,
ẇit /wit is wage inflation, α 0i is a state fixed effect,
Ṅit /Nit is employment growth, u it is the unemployment rate, and ẇ te/wt is expected aggregate wage
inflation. We use quarterly data from 1977:Q3 to
2002:Q1. Our wage measure is hourly earnings in
manufacturing, employment data are from the
establishment survey, and the unemployment rate
is from the household survey. Expected wage inflation at the aggregate level is measured by actual
consumer price inflation (CPI) lagged one quarter.
We estimate (1) with feasible generalized least
squares (FGLS) to correct for state-specific autocorrelation and heteroskedasticity that is correlated across
states.4
As reported in Table 1 and illustrated by Figures
3 and 4, the coefficients for employment growth
and the unemployment rate (in levels and squared)
imply a convex relationship between wage inflation
and regional labor market conditions. However, the
coefficient on the squared employment term is not
statistically significant at traditional levels, so the
relationship is not statistically different from linearity. On the other hand, the convexity of the relationship between wage inflation and the unemployment
rate is statistically significant.
The weight of this empirical evidence indicates
that the relationship between labor market conditions and wage inflation is convex, meaning that
changes in the dispersion of conditions across states
will have repercussions at the aggregate level. In
particular, divergent regional business cycles cause
measured wage inflation to rise for a given aggregate
unemployment rate. In other words, the aggregate
unemployment rate at which wage inflation is
unchanged will be higher. These results suggest
one possible reason for the non-inflationary boom
that took place in the United States in the 1990s.
Recall Figure 1, which shows that the coefficient of
variation of state unemployment rates fell throughout the period, indicating a convergence of economic activity. Consistent with our discussion, this
decreased dispersion was accompanied by a falling
aggregate unemployment rate but no increase in
wage inflation.
To explore this possibility further, we estimate
a relatively simple Phillips curve for the United States,
including features common to Phillips curve models5:
4
We are able to correct for this most-general form of heteroskedasticity
because our time series is relatively long for a cross-state panel. A useful
rule of thumb is that this is possible if there are twice as many time
periods as cross-sectional units (Beck and Katz, 1995), which our panel
just satisfies.
5
The variety of Phillips curve specifications is vast; Staiger, Stock, and
Watson (2001) alone includes dozens of different Phillips curve specifications and estimates. As Phelps (1968) noted 35 years ago, and which
is no less true today, “The numerous Phillips-curve studies of the past
ten years have…[offered] countless independent variables in numerous
combinations to explain wage movements. But it is difficult to choose
among these econometric models, and rarely is there a clear rationale
for the model used” (p. 678).
J A N UA RY / F E B R UA RY 2 0 0 4
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Wall and Zoëga
Figure 3
Figure 4
Wage Inflation and Employment Growth
Wage Inflation and the Unemployment Rate
Wage Inflation
1.2
0
2
6
Unemployment Rate
10
14
18
1.0
–0.1
0.8
–0.2
0.6
–0.3
0.4
–0.4
0.2
–5
–3
0.0
–1
–0.2
–0.5
1
3
5
7
9
Employment Growth
11
–0.6
Wage Inflation
Table 1
Wage Inflation and Vacancies in a State Panel
Coefficient
Employment growth
Employment growth squared
Standard error
t
0.0365*
0.0146
2.50
0.0047
0.0036
1.31
–0.0679*
0.0207
3.28
Unemployment rate squared
0.0021*
0.0012
1.66
Expected wage inflation
0.5907*
0.0293
20.14
Unemployment rate
State fixed effects (48)
Yes
Observations
4,752
Estimated covariances
1,176
Estimated autocorrelations
Log-likelihood
48
–4,587.42
NOTE: * Indicates statistical significance at the 10 percent level. The estimator is FGLS and corrects for state-specific autocorrelation
and heteroskedasticity with cross-state correlations. Quarterly state-level data, 1977:Q3–2002:Q1. Indiana and Kansas are excluded
because of missing earnings data in early years of the sample. For space considerations, we do not report the estimates of the state
fixed effects.
(2)
ẇt
− θte = α0 − α1lnut + λ Xt + BΦ
Φ + πte + εt .
wt
In (2), the dependent variable is nominal hourly
wage growth averaged over years t and t+1 net of
expected productivity growth, θ te, measured by the
trend growth of output per worker in the nonfarm
business sector. We also include a vector of demographic variables, Φ , to control for changes in the
composition of the labor force (Phelps and Zoëga,
1997; Shimer, 1999; Francesconi et al., 2000; and
28
J A N UA RY / F E B R UA RY 2 0 0 4
Staiger, Stock, and Watson, 2001). Following Staiger,
Stock, and Watson (2001), these variables are the
percentages of the adult population that are high
school dropouts, college graduates, white, female,
and aged 25-54. Expected wage inflation, π te, is
measured by average CPI inflation for years t –1
and t –2.
Our innovation is to include Xt , the coefficient
of variation of state unemployment rates, which
we expect to be positively related to wage inflation: Even if the aggregate unemployment rate is
FEDERAL R ESERVE BANK OF ST. LOUIS
Wall and Zoëga
Table 2
U.S. Phillips Curve Estimation
Constant
Log unemployment rate
Coefficient of variation
and demographics
Demographics only
–112.326* (57.196)
–51.097 (68.513)
–3.300* (0.741)
–3.036* (0.958)
Coefficient of variation of state unemployment rates
0.263* (0.080)
—
High school dropouts
0.957* (0.542)
1.098 (0.817)
College graduates
White
0.542* (0.218)
–0.044 (1.057)
0.486* (0.242)
–0.082 (1.389)
Female
1.645 (1.751)
0.798 (2.561)
Aged 25-54
0.240* (0.116)
–0.005 (0.119)
Expected wage inflation
0.452* (0.059)
Observations
19
0.326* (0.090)
19
Log-likelihood
7.781
1.566
R2
0.944
0.8927
NOTE: White-corrected standard errors are in parentheses. * Indicates significance at the 10 percent level. Yearly aggregate data,
1982-2000.
unchanged, an increase in the dispersion of labor
market conditions will raise the aggregate rate of
wage inflation.
In choosing the time frame for estimating (2),
we are hampered by the lack of state-level data
before 1977 and demographic variables after 2000.
In addition, to eliminate the estimation problems
associated with the so-called monetarist experiment
period, we include only 1982 and later. Despite
these restrictions, we obtain the fairly reasonable
results reported by Table 2.
Results for our more general specification—
which includes demographic variables and the
coefficient of variation of state unemployment
rates—indicate that the education and age variables
have all been important in determining the rate of
wage inflation. More importantly for our present
purposes, the results are consistent with our hypothesis that the regional dispersion of economic activity
can affect aggregate wage inflation: The coefficient
on the coefficient of variation of state unemployment
is positive and statistically significant.
Table 2 also reports the results when the aggregate Phillips curve is estimated under the restriction
that the coefficient of variation of state unemployment does not matter statistically. From these results
it is clear that this restriction is not supported. When
the coefficient of variation is excluded, the coefficient on only one of the demographic variables—
the share of college graduates—is anywhere close
to being statistically significant. In addition, the constant term becomes smaller and statistically insignificant, making it very difficult to use the results to
calculate a natural rate of unemployment. In sum,
as supported by a likelihood-ratio test rejecting the
null hypothesis that the restriction does not have a
statistically significant effect, the estimates with the
coefficient of variation are preferred.
According to Ball and Mankiw (2002), the primary source of the changes in the natural rate of
unemployment in the 1990s was the acceleration
of productivity growth (see also Pissarides, 2000;
and Hoon and Phelps, 1997). An additional factor
was the changing composition of the labor force
(Phelps and Zoëga, 1997; Shimer, 1999; and
Francesconi et al., 2000). Our Phillips curve estimation indicates that the convergence of state labor
market conditions also had a role. The extent of this
role can be obtained by examining the natural rates
of unemployment implied by our Phillips curve
estimation. Specifically, solving equation (2) by
assuming that expected wage inflation is equal to
last year’s wage inflation, it can be rewritten as
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Wall and Zoëga
Figure 5
The Falling U.S. Natural Rate, 1982-2000
9
8.9
8
Trend Unemployment Rate
7
6.7
6
Trend Natural Rate
Trend Natural Rate
with 1982 Demographics
5.4
5
4.7
4.2
4
1982
(3)
1985
1988
ẇ
∆ t = − α1 log(ut ) − log(utn ) + ε it ,
wt
(
)
where utn=exp[(α 0+λ X+BΦ
Φ)/α 1] is the time-variant
natural rate of unemployment.6
The trend natural rate from our estimation and
the actual trend unemployment rate are illustrated
in Figure 5. According to our results, the natural
rate fell steadily between 1982 and 2000, from 6.7
percent to 5.4 percent. Although relatively large,
because the period’s demographic changes worked
to increase the natural rate, this 1.3-percentagepoint drop understates the importance of changes
in the dispersion of state-level unemployment rates.
To remove the effect of these changes, the dashed
blue line in Figure 5 is what the trend natural rate
of unemployment would have been if the demographic variables had remained fixed at their 1982
levels.7 As the figure indicates, if all else had remained
constant, changes in the dispersion of state unem6
7
See Staiger, Stock, and Watson (1997) for an analysis of the precision
of natural rate estimates.
Note that because our dependent variable in (2) is wage inflation net
of productivity growth, the trend natural rates shown in Figure 5 are
also net of the effect of productivity changes.
30
J A N UA RY / F E B R UA RY 2 0 0 4
1991
1994
1997
2000
ployment rates would have lowered the trend natural
rate to 4.7 percent by 2000.
CONCLUSIONS
Using state-level data, we find that there is a
convex relationship between unexpected wage
inflation and labor market conditions—as measured
by the unemployment rate and employment growth.
This convexity suggests that increases in the crossstate dispersion of unemployment rates and employment growth mean a higher level of aggregate wage
inflation even if aggregate unemployment and
employment growth are unchanged. Finally, we
include the coefficient of variation of state unemployment rates in our estimation of an aggregate Phillips
curve. From this, we find that the convergence of
state labor market performance between 1982 and
2000 was responsible for a 2-percentage-point drop
in the natural rate of aggregate unemployment.
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Ball, Laurence and Mankiw, N. Gregory. “The NAIRU in
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Fall 2002, 16(4), pp. 115-36.
Lilien, David M. “Sectoral Shifts and Cyclical Unemployment.”
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777-93.
Beck, Nathaniel and Katz, Jonathan N. “What To Do (and
Not To Do) with Time-Series Cross-Section Data.”
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pp. 634-47.
McLaughlin, Kenneth J. “Are Nominal Wage Changes
Skewed Away From Wage Cuts?” Federal Reserve Bank
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Bewley, Truman F. Why Wages Don’t Fall During a Recession.
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Brainard, S. Lael and Cutler, David M. “Sectoral Shifts and
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Card, David and Hyslop, Dean. “Does Inflation ‘Grease the
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Carlino, Gerald and DeFina, Robert. “The Differential
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Carlino, Gerald and Sill, Keith. “Regional Income Fluctuations:
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Crone, Theodore M. “Using State Indexes to Define Economic
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Measurement, 1998/1999, 25(3/4), pp. 259-75.
Francesconi, Marco; Orszag, J. Michael; Phelps, Edmund S.
and Zoëga, Gylfi. “Education and the Natural Rate of
Unemployment.” Oxford Economic Papers, January 2000,
52(1), pp. 204-23.
Fratantoni, Michael and Schuh, Scott. “Monetary Policy,
Housing, and Heterogeneous Regional Markets.” Journal
of Money, Credit, and Banking, August 2003, 35(4), pp.
557-89.
Hoon, Hian Teck and Phelps, Edmund S. “Growth, Wealth
and the Natural Rate: Is Europe’s Jobs Crisis a Growth
Crisis?” European Economic Review, April 1997, 41(3-5),
pp. 549-57.
Layard, Richard; Nickell, Stephen and Jackman, Richard.
Unemployment. Oxford: Oxford University Press, 1991.
Owyang, Michael T.; Piger, Jeremy and Wall, Howard J.
“Business Cycle Phases in U.S. States.” Working Paper
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Owyang, Michael T. and Wall, Howard J. “Regional Disparities
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Overman, Henry G. and Puga, Diego. “Unemployment
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Phelps, Edmund S. “Money-Wage Dynamics and LaborMarket Equilibrium.” Journal of Political Economy, JulyAugust 1968, 76(4, Part 2), pp. 678-711.
Phelps, Edmund S. Structural Slumps. Cambridge, MA:
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Phelps, Edmund S. and Zoëga, Gylfi. “The Rise and
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Pissarides, Christopher A. Equilibrium Unemployment
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Shimer, Robert. “Why Is the U.S. Unemployment Rate So
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Staiger, Douglas; Stock, James H. and Watson, Mark W.
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Staiger, Douglas; Stock, James H. and Watson, Mark W.
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Subjective Probabilities: Psychological Theories
and Economic Applications
Abbigail J. Chiodo, Massimo Guidolin, Michael T. Owyang, and Makoto Shimoji
C
onventional economic analysis of individual
behavior begins with the assumption that
consumers maximize expected utility, optimizing their planning for the future. Economists
incorporate this assumption in models by endowing
consumers in those models with the skills of a good
statistician—that is, the ability to make rational (and
often complicated) calculations. While not always
realistic (perhaps never), this assumption facilitates
the use of economic models that may work well in
the real world. However, in some cases, these models
cannot explain some of the evidence uncovered in
psychological experiments. In other words, the
traditional statistics-based approach sometimes fails
to predict individual behavior and aggregate market
outcomes that are consistent with the empirical
evidence. For instance, observed stock prices and
portfolio choices fail to conform to the implications
of well-known frameworks, such as the capital asset
pricing model (CAPM). Such cases have encouraged
a branch of economics that borrows ideas from
psychology to explain these discrepancies.1
In this area of study, researchers replace the
assumption that individuals use complicated statistical formulas to maximize expected utility with the
likelihood that they use simple rules of thumb
instead, rules that have been identified by psychological research. Psychologists have found evidence
that individuals estimate the probability of future
outcomes in a nonstatistical, or subjective, manner.
Kahneman and Tversky (1973) and Kahneman,
Slovic, and Tversky (1982), among others, have introduced the idea of subjective probability heuristics—
rules that people tend to rely on when assessing
the likelihood of alternative events. Psychological
1
This vein of research is, in some part, attributed to the cross-disciplinary
work of Amos Tversky and 2002 Nobel laureate Daniel Kahneman.
research has shown that the use of these rules can
create different outcomes from what statisticians
(and economists) might expect, both in the estimated
probabilities and in observed behavioral patterns.
Behavioral theories of decisionmaking therefore ask whether economic phenomena may be
explained by models in which
• Some, but not necessarily all, agents either
fail to update their probabilistic beliefs by
applying the appropriate statistical rules or
subsequently fail to maximize a standard
expected utility objective.
• The remaining fully rational agents, then,
cannot completely exploit and eliminate the
biases caused by the actions of agents who
are not perfectly rational.
While these heuristics are drawn from psychological studies, they may be supported by economic
models with boundedly rational agents (Simon, 1955).
In other words, agents do not always have the time
or the cognitive ability to process all of the data
provided by the economic environment with the
necessary accuracy. Instead, people might employ
these heuristics to arrive at analyses that are less
costly to calculate than optimal decisions (Evans and
Ramey, 1992); and, often, the optimal decisions
themselves are impossible to calculate for difficult
problems. Thus, boundedly rational agents do not
maximize expected utility as an economist would
generally assume. Instead, they maximize perceived
expected utility, a quantity based not on actual probabilities but on their beliefs about those probabilities
(Rabin, 1998, 2002).
In this article, we focus on the nature and
application of psychological rules for probability
formation and the biases from anticipated economic
Abbigail J. Chiodo was a research associate at the Federal Reserve Bank of St. Louis while this article was written. Massimo Guidolin is an assistant
professor of economics at the University of Virginia. Michael T. Owyang is an economist at the Federal Reserve Bank of St. Louis. Makoto Shimoji is
an associate professor, International Graduate School of Social Sciences, Yokohama National University. Kristie M. Engemann and Mark L. Opitz
provided research assistance.
Federal Reserve Bank of St. Louis Review, January/February 2004, 86(1), pp. 33-47.
© 2004, The Federal Reserve Bank of St. Louis.
J A N UA RY / F E B R UA RY 2 0 0 4
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Chiodo et al.
outcomes that can result from their use.2 We examine three heuristics that have been identified by
psychologists: the representativeness heuristic (RH),
the availability heuristic (AH), and anchoring and
adjustment (AA). We review the psychological evidence supporting the common use of these heuristics
in estimating subjective probabilities. Finally, we
consider a financial application that uses heuristics
to estimate probabilities with potentially important
economic implications. We then show the effect of
these heuristics on people’s probability judgments.
PSYCHOLOGICAL EVIDENCE
Economics has a long history of exploring
human behavior in decisionmaking. Economic
models often require agents to form expectations
under uncertainty, e.g., expected inflation in macroeconomic models, expected returns in financial
models, or expected utility in decision/choice models.
However, when faced with calculating expectations,
economists often assume that the probabilities are
known or can be inferred (rationally) through learning. What is meant by this? An economic agent might
maximize his expected utility over n uncertain outcomes, defined as
n
(1)
EU = ∑ piU i ,
i =1
where pi is the probability of outcome i and Ui is
the utility from outcome i.
Psychologists, however, have found that people
neglect some available information in their decisionmaking process—that is, they do not update probabilities as new information arrives, as an agent
adhering to rational expectations would. Consistent
with Rabin’s idea of perceived expected utility, agents
might maximize
n
(2)
EU p = ∑ ˆpiU i ,
i =1
where p̂i is the subjective probability of outcome i.
The difference between equations (1) and (2) is solely
in the agent’s assessment of the likelihood that i will
be realized. In this section, we explore how economists and psychologists view pi and p̂i differently.
2
Sherman and Corty (1984) and Camerer (1995) provide surveys of
the psychological evidence on the heuristics discussed here. Another
strand of the recent behavioral literature focuses on the effects of
nonexpected utility preferences for optimal decisions. We do not
discuss these contributions and concentrate instead on the process
of belief formation.
34
J A N UA RY / F E B R UA RY 2 0 0 4
Representativeness
Tversky and Kahneman (1974) suggest that
people typically rely on the representativeness
heuristic (RH) when answering “probabilistic questions” such as “What is the probability that event A
originates from process B?” That is, the RH is used
when a person must determine such probabilities
based on the degree to which A resembles B.
RH is used when an agent must update a subjective probability with new information. Economists
sometimes assume that agents employ Bayes’s law
when updating probabilities. Bayes’s law defines
the probability of an event X, conditional on observing A, as
(3)
p ( X| A) =
p ( A| X ) p( X )
,
p ( A)
where p(A|X) is the conditional probability of A
given X and p(X) and p(A) are population parameters
typically referred to as base rates.
While Bayes’s law is a useful statistical rule,
psychologists have found that people tend to act in
a decidedly non-Bayesian fashion and have identified
a number of subjective probability biases grouped
under the umbrella of RH.
Tversky and Kahneman (1974) and Kahneman,
Slovic, and Tversky (1982) note that using RH when
determining probability can lead to insensitivity to
prior probability, or base-rate frequency, of the
outcomes.3 In one example, subjects were asked to
identify a described individual as either a lawyer or
an engineer. The subjects were given descriptions
that included phrases such as “he wears glasses” or
“he wears a pocket protector.” Subjects were first told
that the individual in question was drawn from a
random sample composed of 100 people, 70 of
which were engineers and 30 of which were lawyers.
Then, the base rates were reversed. The subjects
were told that, of the 100 people in the sample, 70
were lawyers and 30 were engineers. Kahneman,
Slovic, and Tversky found that the subjects’ probability judgments did not differ when the base rate
was changed, even though Bayes’s law indicates
that the conditional probabilities cannot be equal
if the base rates change.
Grether (1980, 1992) and El-Gamal and Grether
(1995) designed experiments that determine that
RH “is a good descriptive model of behavior under
3
Sherman and Corty (1984) provide a comprehensive review of the
biases that are attributed to RH.
FEDERAL R ESERVE BANK OF ST. LOUIS
uncertainty for untutored and unmotivated (or at
least not financially motivated) individuals” (Grether,
1980, p. 538). Specifically, they show that subjects
under-use base rate information when making subjective probability judgments for events that have
little or no consequence or cost. Borgida and Brekke
(1981) have also shown that, while most people do
not neglect base rates entirely, they are typically
under-used.
Availability
The availability heuristic (AH) describes a
method by which a person determines the likelihood
of an event according to the ease with which he or
she can recall instances that match the event. That
is, one’s experiences and conditioning affect how a
person determines the likelihood that an event will
occur. For example, one might estimate the risk of
a burglary in a certain neighborhood by the number
of burglaries one can recall (including any personal
experience).
A similar method is the simulation heuristic, by
which people will determine the likelihood of events
based on the ease with which they can simulate (or
imagine) the outcome in their minds. An example
of this is a person who determines the probability
that the value of a certain stock will decline based
on the number of different scenarios he or she can
easily imagine that would cause such an occurrence.
While AH can often be helpful in making decisions and estimates, Tversky and Kahneman (1974)
list several biases that can result from AH. These
include biases (i) due to the retrievability of instances
(examples easily brought to mind are often judged
to be more likely than they actually are), (ii) due to
imaginability (easily imagined outcomes can give the
illusion that they are more common), and (iii) due
to illusory correlation (one event more strongly
implies another if the two events frequently occur
simultaneously).
Tversky and Kahneman (1973) outline several
studies used to demonstrate the AH and its subsequent biases. For example, subjects were read lists
of names of both sexes, some of which were names
of very famous people (Richard Nixon and Elizabeth
Taylor, for example). Afterward, some were asked
to estimate if there were more males or females on
the list. People tended to estimate, sometimes incorrectly, that there were more of whichever sex had
more famous people in the list. The famous names
were easier to remember and therefore more
prominent in the minds of the subjects. Tversky
Chiodo et al.
and Kahneman conclude, then, that people make
estimates based on AH, which (in this case) led to
the retrievability bias.
AH has been applied to marketing and advertising to investigate the effect of retrieval on the subjective assessment of product failure. Folkes (1988)
presents four studies in which subjects were asked
to predict how likely various products were to fail.
Different scenarios and distinctive brand names
were used to make some products or instances more
memorable. Folkes found that these judgments were
biased in ways described by the AH—that more
memorable products (memorable for various reasons) influenced the subjects’ decisions. Rabin (1998)
points out that people often give too much weight
to memorable evidence, even when better sources
of information are available. He notes that one may
allow a dramatic personal story from a friend regarding an instance of product failure to be more influential than consumer reports with general statistics
regarding that product.
Recently, Mullainathan (2002) developed a model
of memory limitations based on two psychological
concepts that can have properties similar to AH.
The first concept, rehearsal, is the assumption that
remembering an event, story, or some form of information one time makes it easier to remember again.
Mullainathan points out that rehearsal is used by
students who study for a test by reading over the
material and then quizzing themselves to help them
remember it. The second concept, associativeness,
is the process by which current events can trigger
memories of past events that have similar aspects.
Thus, even uninformative information—information
that does not change the likelihood of an event—
can influence beliefs by changing perceptions of
the past. Mullainathan suggests that people respond
“too much” because news resurrects memories that
reinforce beliefs.4
Anchoring and Adjustment
The final heuristic we address is anchoring and
adjustment (AA), which Tversky and Kahneman
(1974) define. According to this heuristic, individuals
make estimates based on a starting point (the anchor)
and update (adjust) their subjective probability based
on new information. While this does not seem to
differ from RH or even from Bayesian updating,
4
Mullainathan considers an application of this model to individuals’
consumption decisions. He suggests that individuals react more to
their private information than to aggregate information because
aggregate information is forgotten.
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Chiodo et al.
psychologists have shown that individuals have a
propensity to bias their estimated probabilities
toward the anchor. That is, individuals do not adjust
enough to new information, making the value of
the anchor more critical.
An individual’s initial guess (the anchor) can
be subjective (interpreted) or objective (e.g., taken
from base rates). Often, the anchor depends on the
manner in which the question is asked or how the
information is given. For example, Tversky and
Kahneman (1974) asked subjects to estimate the
percentage of African countries in the United Nations
by first giving them a number (determined randomly
by spinning a wheel) and then asking the subjects
whether that number was higher or lower than the
percentage of African countries. Different initial
values led to strikingly different estimates. While
the median estimate was 25 percent for groups
that received 10 as the starting value, the median
estimate was 45 percent for those given a starting
value of 65—illustrating the bias toward the anchor.
A starting value can also be the result of a subject’s (usually incomplete) computation. Tversky and
Kahneman (1974) give the example of two groups
being asked to estimate 8! in a limited amount of
time. While one group was given 1*2*3*4*5*6*7*8
as the problem, the other group was given
8*7*6*5*4*3*2*1. Note that the product of the first
few steps of multiplication (performed left to right)
of the descending sequence is much higher than
that of the ascending sequence. As predicted, the
median estimate of the group shown the descending
sequence was much higher than the median estimate
of the group shown the ascending sequence.
This example illustrates how subjects tend to
focus on only part of a problem. For instance, the
probability of success at any one stage of an event
is often used as a starting point (an anchor) to determine the probability of overall success. However,
their assessment of the probability for an event with
multiple stages is often skewed because they do
not deviate enough from that anchor. Tversky and
Kahneman (1974) refer to research that shows how
anchoring biases the estimation of probability for
different types of events—specifically, that subjects
overestimate conjunctive events and underestimate
disjunctive events. For example, suppose there is a
bag of marbles, half of which are red and half of
which are black: People will overestimate the probability of, for instance, drawing a red marble from
the bag seven times in succession after replacing
the drawn marble (a conjunctive event); they will
36
J A N UA RY / F E B R UA RY 2 0 0 4
underestimate the probability of drawing a red
marble from the bag at least once in seven successive
tries after replacing the drawn marble (a disjunctive
event). The anchor for both events is the probability
of drawing a red marble on any try. Success in a
conjunctive event may be likely for only one of
several required outcomes, yet subjects stick close
to their anchor and thus overestimate the probability
of overall success. Conversely, subjects tend to underestimate the likelihood of success beyond the anchor
when multiple attempts are allowed to achieve
merely one successful outcome.
ILLUSTRATIVE APPLICATIONS
To demonstrate the effect of heuristic biases
on probability judgments, we offer the following
illustrations.
Disaster Insurance
The biases resulting from these heuristics have
some implications in the earthquake insurance
market. A large earthquake in one area certainly
qualifies as the kind of salient event mentioned in
the discussion of the AH. After all, graphic pictures
and information from the media or personal stories
from friends affected by the earthquake are likely to
be easily remembered when estimating one’s own
need for earthquake insurance. Psychology theory
implies, then, that a large earthquake should cause
people to overestimate the probability that they will
need earthquake insurance, which could explain the
“gains by losses” phenomenon: In the event of an
earthquake, an insurance company must pay out on
claims, incurring a loss; if an earthquake causes an
increase in demand for insurance, however, insurance companies can benefit, overall, by experiencing significant gains during the period after the
earthquake.
Consider an actuarially fair earthquake insurance
policy with premium π and payout Y. By definition,
the actuarially fair premium must be a function of
the payout and the risk of the event being insured
against. In this case, the premium should exactly
offset the expected payouts.
Suppose now that, given the premium, a person
must decide whether to purchase insurance based
on the perceived likelihood of a loss. Irrelevant information, such as an earthquake in another part of
the country, does not affect the probability of a loss.
However, a person employing heuristics might
assume a greater likelihood of a local earthquake—
FEDERAL R ESERVE BANK OF ST. LOUIS
making the insurance contract more attractive to her.
Thus, if persons employed the heuristics, we would
expect demand for insurance to rise after the occurrence of a similar event.
In fact, Kunreuther et al. (1978) finds that people
tend to discount the likelihood of a disaster (e.g., a
flood or an earthquake) until the event occurs. After
people “update” their assessment, purchases of
insurance contracts rise. Moreover, Shelor, Anderson,
and Cross (1992) and Aiuppa, Carney, and Krueger
(1993) found that insurers’ stock prices increased
after the 1989 earthquake in San Francisco, due to
an increased demand for coverage. However, Yamori
and Kobayashi (2002) find no such benefit to insurance companies in Japan after the 1995 HanshinAwaji earthquake. Yamori and Kobayashi note that
unique attributes of Japanese earthquake insurance
may be the reason for the difference between the
United States and Japan in stock market reactions
to large earthquakes. Namely, the Japanese government sets the insurance industry premium levels at
“no loss and no profit.” Interestingly, while studies
have shown the positive link between earthquakes
and insurance stock prices in the United States, other
studies indicate no such relationship for hurricanes.5
Product Liability
A second application for the heuristics involves
market attitude with regard to product reputation,
specifically, shocks to reputation. We can model
market behavior after a product failure as a temporary shift in demand that results in lower sales and
falling retail and stock prices.
Airplane Crashes. News agencies report airplane crashes in detail, often exhaustively and over
an extended period of time. These reports provide
vivid images to the public.6,7 As a consequence,
people may avoid air travel, at least for some
amount of time. Without an AH, such tragedies
would have little effect on people’s belief regarding
air travel safety because these events are rather
uncommon and it is widely known that air transportation has been much safer than any type of
5
See Lamb (1995) and Cagle (1996) for details.
6
By “airplane crashes,” we do not mean the consequence of terrorism
or hijacking, which are due to external forces.
7
In the previous case, we argued that some of the events are consistent
with the presence of the AH. In this section, we also survey several
examples of product detection, e.g., product recalls. Although most
of the failures are also life-threatening, like the examples above, there
is no evidence of spillover effects in the industry as a whole, unlike
the examples above.
Chiodo et al.
ground transportation in the United States. Because
the change in people’s beliefs regarding the overall
safety of air travel would be minimal, this type of
tragedy would be interpreted as idiosyncratic to a
particular airline. In this case, it is therefore possible that other airlines (the rivals of the airline that
experienced a crash) would benefit from such an
event. If an AH does exist among the potential
customers, however, the demand for air travel as a
whole would decline. This externality would harm
the market as a whole, and, as a consequence, other
carriers would lose profits as well.
Borenstein and Zimmerman (1988) found that
“an airline’s shareholders suffer a statistically significant wealth loss when the airline experiences a
serious accident...[although] the average loss in
equity value is much smaller than the total social
costs of an accident” (p. 913). In addition, they found
that (i) such accidents have little or no effect on
demand and (ii) that there is little evidence of a
externality effect (positive or negative) caused by
such accidents on the demand for other airlines.
This study suggests that the market barely reacts to
these events.
A subsequent study by Mitchell and Maloney
(1989) partitioned the sample into “at-fault” crashes
(those caused by pilot error) and all other crashes
and tested whether these two distinct groups receive
different reactions from the market. Contrary to
the study by Borenstein and Zimmerman (1988),
they found a statistically significant negative reaction
in the former group.8 However, these studies do not
offer an insight regarding the effect of an AH.
Nethercutt and Pruitt (1997) reported a finding
similar to that of Mitchell and Maloney (1989) by
examining the ValuJet accident in 1996. In their study,
they found two things: (i) not only the shareholders
of ValuJet but also those of other “low cost” carriers
suffered losses due to this accident and (ii) the shareholders of the major airlines indeed received statistically significant gains after this event. At first sight,
this result seems to suggest the nonexistence of an
AH. However, their study does not distinguish the
switching effect from the spillover effect; hence, it
does confirm that the former dominates the latter,
but has nothing to say about the effect of an AH.
The study by Bosch, Eckard, and Singal (1998)
partially answers the question raised above. The
authors consider the market overlaps of airlines in
8
See also Broder (1990).
J A N UA RY / F E B R UA RY 2 0 0 4
37
REVIEW
Chiodo et al.
the context of a recent airplane crash and examine
whether customers respond to a commercial airline
crash by switching to rival airlines and/or flying less.
They find that passengers who do choose to fly will
travel on the airlines that have not had a recent crash,
but even these airlines suffer a negative spillover—
namely, fewer passengers overall. With market overlap, the coexistence of the switching effect and the
spillover effect offset each other and we can observe
only the net effect of these two together. However,
with little overlap, the switching effect is limited
and hence we can test if the spillover effect exists.
Indeed, Bosch, Eckard, and Singal found negative
spillover effects after airplane crashes, consistent
with the existence of the AH.
Firm Bankruptcy. Lang and Stulz (1992) studied
the effect of one firm’s bankruptcy announcement
on the other firms in the same industry. They listed
two effects of such an announcement9:
Contagion Effect. A change in the value of competitors that cannot be attributed to wealth redistribution from the bankrupt firm. This may happen
because investors think that firms with characteristics similar to those of the bankrupt firm are less
profitable than expected.
Competitive Effect. A change in the value of
competitors that can be attributed to wealth redistribution from the bankrupt firm. This may happen,
for example, if investors think that the bankrupt firm
is doing poorly because other firms are doing well.
As for the first effect, they found that “on average,
the market value of a value-weighted portfolio of
the common stock of the bankrupt firm’s competitors decreases by 1% at the time of the bankruptcy
announcement and the decline is statistically significant” (p. 46). They also reported that “the effect
appears to be greater for highly leveraged industries”
(p. 46). For the second effect, they found that “the
value of competitors’ equity actually increases by
2.2% in more concentrated industries with low
leverage” (p. 47).
These types of effects may be due to other
announcements or events such as defective products
and recalls.10 In addition, even though the same
types of effects are observed, they may arise from
other sources. In the following, we discuss such
9
Note that contagion affects all the relevant firms in the same negative direction, whereas the competitive effect does not.
10
For example, Ford Motor Company experienced a decline in sales
after the Firestone tires used on Ford products were declared faulty
by the media.
38
J A N UA RY / F E B R UA RY 2 0 0 4
possibilities, as well as the possibility that some of
the events may be attributed to the existence of
heuristics we study in this paper.
A FINANCIAL APPLICATION
We now consider an application of heuristic
probability judgments in an asset pricing model.11
A formal description can be found in the appendix.
Recently, Barberis and Thaler (2002) have stressed
how behavioral approaches that focus on the mechanism of expectation formation cannot be applied
to explanations of well-known aggregate puzzles in
finance, such as the equity premium, excess volatility,
and predictability issues. Although it is acknowledged
that many models developed to investigate the crosssection of asset returns may often be used to also
explain aggregate puzzles, much remains to be
achieved by this strand of literature.12 In this section
we discuss a number of asset pricing puzzles that
can be explained by subjective probability biases.13
How Do Subjective Probabilities Affect
Asset Prices?
Assume there are two assets: a single-period,
risk-free discount bond in zero net supply and a
publicly traded stock (or stock index) in exogenous,
unit supply. The stock pays out an infinite stream
of perishable, real dividends, the growth rates of
which randomly switch between two values: dh in
the good state (an expansion) and dl in the bad state
(a recession).
Individuals use both informative and uninformative variables to determine probability estimates.
For simplicity, assume that the only informative
variable is dividends. Dividends are informative
because they directly relate to the payouts produced
by the stock. Therefore, the information set is com11
Barberis and Thaler (2002) and Hirshleifer (2001) are recent survey
papers on the field of behavioral finance. See Mullainathan (1998)
for an application of the AH to finance.
12
Several papers have used nonexpected utility preferences consistent
with the psychological and experimental evidence to approach the
same phenomena (for instance, Barberis, Huang, and Santos, 2001,
and Benartzi and Thaler, 1995). These papers are often considered to
belong to the behavioral camp.
13
It goes without saying that a vast literature has developed over the
past two decades that approaches the same puzzles we discuss; these
have used types of frictions (transaction costs, information asymmetries
and incomplete information, nonstandard preferences, etc.) that do
not involve either the process of expectation formation or the ability
of investors to rationally use the available information. The surveys
in Campbell (2000) and Cochrane (2001) offer highly readable accounts
and references.
FEDERAL R ESERVE BANK OF ST. LOUIS
posed of the sequence of realized high and low
dividend growth rates plus a set that collects all the
relevant realizations of the uninformative variables.
Examples of uninformative variables are past stock
prices because stock prices fail to add any predictive
power for future cash flows produced by the stock
currently owned. Alternatively, investors might use
past levels of the price-dividend ratio to forecast
future dividend growth because this ratio has been
found to successfully predict stock prices in the
empirical literature. In practice, stock market participants will directly care about the probability for
dividends only. However, depending on the way
subjective probabilities are formed, investors might
indirectly also care about the joint probability distribution of dividends and the uninformative variables,
in the sense that they might use uninformative
events to predict dividends.
The Heuristics-Based Solution
Suppose that the probability of an increase in
dividends is unknown and must be subjectively
calculated based on past observations.14 A representative agent believes that the value of the stock
depends not only on past dividend payments but
also on the irrelevant information she has in her
information set.15 Since events that are recent are
more likely to be remembered, the further back in
time an observation on the dividend growth rate is,
the more unlikely it is that it will belong to the
recalled information set. However, agents recall
events that bear a high resemblance to current
events, even when the similarity is defined not only
in terms of dividends, but also in terms of other,
irrelevant variables (e.g., past asset prices). For
instance, an investor is more likely to recall a big
drop in a company’s dividend when it is associated
14
Barsky and DeLong (1993) present a discounted model in which
investors form extrapolative expectations and generate excess volatility of stock prices. However, their paper does not impose much structure on belief formation and fails to link the extrapolation process to
the experimental psychology literature.
15
For a heuristic rule to have an effect on equilibrium outcomes, irrational
traders need not be completely weeded out of the economic system
(through bankruptcy or reduction to a marginal role in determining
equilibrium results). Although the debate in the economics literature
is not settled yet, important papers in finance (DeLong et al., 1990a,b,
1991) shed light on the subject: namely, that the price biases created
by simple heuristics (such as the case with random trading of securities)
create situations in which the exploitation of less-rational investors
is risky and therefore fails to be implemented on the scale necessary
to completely annihilate the effects of the biases (Shleifer and Vishny,
1997). Therefore, heuristics might appear in the aggregate and a representative agent is a useful shortcut to model such a situation.
Chiodo et al.
with a deep international crisis, even though the
political variables need not carry information useful
in predicting future economic conditions or the
profitability of the company.
The appendix shows that, under these assumptions, the heuristic-based equilibrium stock price
differs from the full-information equilibrium price
because it stops being a fixed multiple of dividends;
on the contrary, the heuristic-based equilibrium
price-dividend ratio now contains a time-varying
component, fitting the empirical finding that pricedividend ratios are subject to long swings. The variation in the price-dividend ratio derives from changes
in the investors’ memory-based (or subjective) expectation of dividends. For instance, particularly bad
dividends may depress stock prices to the point that
investors start recollecting previous bad times when
the observed mean dividend growth was low. This
happens because, when the AH is present, low
growth tends to make other episodes of low growth
salient and to bring up memories of other recessions;
this happens also because poor dividend growth
depresses stock prices and makes other recessionary
episodes more memorable. These biases depress the
subjective dividend expectations and cause deeper
persistent declines in stock prices.
Excess Volatility of Stock Prices
We now investigate a few qualitative implications
for stock prices. Since Shiller (1981) and LeRoy and
Porter (1981), researchers have observed that stock
prices tend to be much more volatile than the underlying economic fundamentals (dividends or aggregate consumption) would dictate. Recent research
has examined this issue with mixed success (see
Brennan and Xia, 2001, Bullard and Duffy, 2001,
and Timmermann, 2001). Under full-information
rational expectations, this finding represents a
puzzle.16 The heuristics-based approach illustrates
how the excess stock volatility puzzle can be easily
resolved when the price-dividend ratio is timevarying as a result of limited memory and of avail16
Barberis and Thaler (2002) informally discuss a psychological model
that could explain the excess volatility puzzle: Investors perceive a
disproportionate volatility of the dividend growth rate when they are
exuberant, i.e., when they observe dividend increases that convince
them, too quickly, that mean dividend growth has increased. Although
Barberis and Thaler notice that a similar story may be derived as an
application of the RH, they do not present a formal model that maps
heuristics into beliefs. Shiller (2003) has recently used the excess volatility puzzle as a workhorse to introduce behavioral finance research to
overcome the traditional efficient market hypothesis.
J A N UA RY / F E B R UA RY 2 0 0 4
39
REVIEW
Chiodo et al.
ability, representativeness, and anchoring biases.
The appendix provides a formal treatment.
Since high dividends are generally accompanied by high stock prices and low dividends by low
stock prices, a high growth realization will make
past high dividend growth rates more memorable
because of the AH. This is because, if a high dividend
growth rate causes an increase in stock prices, other
episodes of bull markets and good fundamentals
will be recalled. Such an event is likely to increase
the subjective expectation of dividends and the
price-dividend ratio. A similar reasoning applies to
situations of low fundamentals and stock prices,
i.e., they will generally make “bad times” more
memorable and depress the expectation of future
dividends. Therefore we expect positive covariation
between dividend growth and the price-dividend
ratio, which makes stock prices much more volatile
than what is implied by full-information rational
expectations. In this sense, heuristics-based asset
pricing makes the solution of the volatility puzzle
not only possible, but likely.
Bubbles and Crashes
A related topic is the tendency of stock markets to experience long periods of sustained (but
hardly rational) increases in prices, followed by
quick outbursts that often lead to sudden crashes.
With reference to these phenomena, economists
have developed both a literature on the theoretical
conditions under which price bubbles may form and
thrive (see Tirole, 1985) and a more recent empirical
literature that describes markets as going through
a sequence of “bulls” and “bears” (see Perez-Quiros
and Timmermann, 2000). Unfortunately, the former
mostly stresses the delicacy of bubbles, while the
latter falls short of providing answers to our questions because it focuses on the microfoundations
of bulls and bears. When investors use heuristics,
bubbles and crashes occur in equilibrium more
frequently.
Suppose the current period is characterized by
good economic fundamentals and hence positive
stock returns. In particular, some degree of exogenous optimism may easily project good dividend
growth in high stock returns. At this point the following mechanism is triggered: A high current stock
price elicits memories of previous periods of fast
economic growth and “good” fundamentals. When
past stock prices are also used to calculate expectations of future dividend growth, high current prices
will also make past bull market periods more mem40
J A N UA RY / F E B R UA RY 2 0 0 4
orable. Hence, past high-dividend periods will be
assigned an abnormally high probability and will
end up being over-represented in the recalled information set. As a result, expected dividends will be
irrationally high. Unless the next-period dividend
is particularly unfavorable, this sustains high demand
for equities and stock prices: This is the beginning
of the bubble. In such an environment it would be
possible for stock prices to increase at such a pace
that (given agents’ imperfect memory), in practice,
only very recent bull periods would be recalled and
used in forming expectations. Here, it is as if the
market enters an entirely different world: Optimism
dominates to the point where price increases are a
foregone conclusion (c.f., the “New Economy”).17
The effect is further enhanced when anchoring
is strong: If the run of price increases is sufficiently
protracted, agents’ subjective perception of the
probability of good economic fundamentals will
become increasingly difficult to move.18 What ends
a bubble? Potentially, a sufficiently negative realization of fundamentals growth. Such an epiphany
could suddenly make investors recall past cases in
which bull markets turned into bear markets. In
other cases, it is sufficient that some variables,
although irrelevant for pricing (political variables,
for instance), may suddenly make investors aware
that bad outcomes are possible. When this happens,
the bubble bursts, often plunging into a catastrophic
crash.
One phenomenon that has not been well
explained by the theoretical literature on bubbles
is the possibility of protracted periods of depressed
stock prices, far below their most moderate rational
levels—a sort of negative bubble (Weil, 1990). An
advantage of heuristic-based asset pricing is the
ability to generate episodes of irrationally low stock
prices. Starting with poor underlying growth and
some pessimism, markets may quickly plunge into
spells in which investors focus only on past negative
news and periods and, hence, systematically underestimate the mean dividend growth rate so that
stock prices are too low given the quality of the
underlying fundamentals. Strong anchoring may
complete the picture, thus damping investors’ expectations for growth prospects.
17
See, for instance, The Economist, “Beyond the Business Cycle?”
October 23, 1999, and the “new era” theories discussed in Shiller
(2000).
18
Intuitively, anchoring makes bubbles harder to ignite but also harder
to burst. Given the available empirical evidence, the behavior of
financial markets is highly consistent with strong anchoring.
FEDERAL R ESERVE BANK OF ST. LOUIS
Chiodo et al.
The Inflation–Stock Returns Puzzle
CONCLUSION
It is conventional wisdom to prefer nominal
stock returns and inflation to be positively and
highly correlated; rational markets, then, should
price equities based on their discounted, expected
nominal cash flow payments. Therefore, ruling out
deeper macroeconomic effects (e.g., sectoral shifts
and other distortions), an increase in current and
expected inflation ought to increase expected nominal dividend payments and cause upward adjustment
of observed stock prices. Empirical research in the
past 20 years has found very limited support for the
hypothesis that stock returns can protect shareholders from inflation. Normally, positive but moderate correlations have been found. In other words,
the Fisher equation systematically fails for nominal
stock returns.19 Heuristic-based asset pricing offers
an easy way to rationalize such a phenomenon.
Suppose that inflation not only influences nominal dividend levels, but also acts as a variable in the
set of uninformative information. In particular,
assume that investors have convinced themselves
that high inflation is always accompanied by subsequent increases in the level of real interest rates that
depress economic growth. Interestingly, this conjecture does not need to be supported by the data,
or it might be supported only by old data. Inflation
is just an additional variable that becomes informative of future economic growth only because
investors think it is. In this case, a high current inflation rate is essentially bad news: It makes past periods
of poor growth and recession more memorable (via
availability) and accelerates inflation (via representativeness). In practice, two effects take place at once:
On one hand, inflation raises expected nominal
dividends; on the other hand, inflation induces a
pessimistic change in the agent’s recalled information set, lowering expected real dividends. The net
effect is unclear but is consistent with the fact that
nominal stock returns do not seem to react much
to inflation news.20
In this article, we surveyed some of the research
that has highlighted the crossover between economics and psychology. The assumptions economists
have traditionally imposed in their models maintain
that individuals are rational (and selfish) and construct their beliefs according to probability theory,
following Bayes’s law. For most economic applications, this type of assumption fits well. However,
there remain situations in which nonrational or
quasirational behavior on the part of the median
agent is observed. In these situations (e.g., hazard
insurance and asset pricing), assuming that people
behave rationally leads to puzzles—such as the
inflation–stock returns puzzle, bubbles and crashes,
and excess stock price volatility—that are yet unexplained using standard economic theories.
Economists have more recently begun to
acknowledge irrationality as a source of interest
for these economic applications. Accounting for all
idiosyncratic effects is literally impossible and, moreover, undesirable. Economic theory adequately
explains many types of behavior, including consumption behavior, for example. However, there remain
some systematic deviations from rational behavior,
which the standard models do not fully capture. The
heuristics that psychologists suggest are examples
of this. Incorporating these types of behavioral rules
in our research could not only broaden how we
approach and analyze subjects but also may greatly
increase the power of our conclusions. We find, for
example, that the puzzles in the asset pricing literature (such as those listed above) can be accounted
for by adding a heuristic probability rule to the standard asset pricing framework. Thus, while behavior
might not be a solution that is broadly cast, we
propose that its importance, in some circumstances,
may warrant further investigation.
19
20
Equivalently, empirical studies have found negative correlation
between real stock returns and inflation, both expected and unexpected. See, for instance, Nelson (1976) and Fama and Schwert
(1977) for early evidence.
Geske and Roll (1983) propose a theoretical model in which the only
exogenous shocks are disturbances to the real level of economic
activity. Since they assume monetary policy acts counter-cyclically,
the negative correlation between real stock returns and inflation
derives from the fact that bad news on fundamentals forecasts higher
future monetary growth and inflation. However, the recent debate
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Appendix
A MODEL
Pr[ XT = 1| ˜XT −1,Y
˜T ] = Pr[ XT = 1| YT ] .
Consider an event χ that agents are attempting
to forecast with an associated indicator XT member
of {0,1}, where XT=1 if event χ occurs in period T.
An agent’s subjective probability, her estimate of the
probability that XT=1 conditional on the information
set ΩT , is determined by a function P : ΩT → [0,1],
which maps the information set into the probability
space. The agent’s information set consists of past
realizations of XT ,
The rational expectations solution can then be
written
P R :YT → [0,1],
where the function P R follows Bayes’s law (3). Thus,
a rational agent with information ΩT has subjective
probability
Pr[ XT = 1| YT ] =
X
˜ T −1 = {X1, X2 ,..., XT −1},
as well as current informative and uninformative
information,
Y
˜T = {Y1,Y2 ,...,YT}, and
˜ZT = {Z1, Z2 ,..., ZT},
respectively.21 Suppose further that the event χ is
serially uncorrelated and that information useful
in forecasting χ in period t is useful only for that
period.22 That is, we assume that
Now consider a model in which the agent
employs the heuristics outlined in the previous
sections. We follow Mullainathan (2002) in assuming
that the memory processes of agents is incomplete,
i.e., that agents forget some realizations of XT. That
is, the agent’s recalled information set, Ω̂T , can be
written as
(4)
Here, information is uninformative if Pr [ XT=1|ZT ]=Pr [ XT=1].
(5)
22
These assumptions are employed for simplicity of exposition and are
not necessary for the development of the model.
and
J A N UA RY / F E B R UA RY 2 0 0 4
ˆ = {X
ˆ T ,YT , ZT} ,
Ω
T
where
21
44
Pr[YT | XT = 1]Pr[ XT = 1]
.
Pr[YT ]
ˆ T = {X1‡,T , X2‡,T ,..., XT‡−1,T}
X
FEDERAL R ESERVE BANK OF ST. LOUIS
Xt with probability pt|T
.
Xt‡,T =
0 with probability 1 − pt ,T
Essentially, Xt‡,T is a combination of two indicators:
whether the event occurs in time t and whether time
t is remembered in time T. The likelihood that an
event that occurred in period t is recalled in period T
is a function of the time since its last recall, associated events in time t (that is, Yt and Zt ), and the
current environment, YT and ZT. Define α t ,T =
α (Yt , Zt ,YT , ZT ), where the function α (·) measures
the distance between the points (Yt , Zt ) and (YT , ZT )
in Cartesian space. We can then write the likelihood
of recalling the event of time t at a later time T as
(6)
pt ,T = F ( Xt‡,T −1,α t ,T ) ,
, ) has the following properties:
where the function F(··
F1(··
, )>0 and F2(··
, )<0. The former indicates that
periods recalled in period T–1 are more likely to be
recalled in T. The latter stipulation indicates that it
is more likely that t will be recalled the closer that
the current environment is to elements temporally
associated with period t.
In this framework, the agent forms an estimate
of the likelihood of χ in time T based, in part, on
how closely T resembles any time t<T in which χ
occurred through the closeness function α (·).
Limited memory makes the probability judgments noisy and biased toward salient events that
may or may not be informative. Elements of the
agent’s information set are a subset of the total information available. Thus, the agent’s update has the
property that forgetting the occurrence of an event
in the past will decrease the subjective probability
estimate.
Additionally, salience increases the perceived
probability, since salience increases the likelihood
of recall. Moreover, since the information set varies
over time, the volatility of the estimated probability
is greater than the volatility of a learned probability
with perfect recall (e.g., OLS learning). In the perfect
recall case, information gathered over time reduces
the volatility. In the limited-memory case, information that is forgotten biases the subjective probability
down, while recalled probability biases it up, each
period inducing higher volatility.
Agents make errors in neglecting base rates and
consequently bias subjective probabilities upward
when they perceive that new information is relevant.
It can be shown that, regardless of the direction new
information should move the posterior probability,
Chiodo et al.
agents employing an updating function that neglects
base rates necessarily overestimate the value of the
new information. Agents’ subjective probabilities
are biased toward their anchor.
A Formal Financial Application
This appendix develops a formal application of
the heuristic probability judgments in an asset pricing model. We will initially follow Lucas (1978) to
develop a simple general equilibrium framework
to study the effects of subjective probabilities.
There are two assets: a risk-free, discount bond
1
with a price Bt and interest rate rt f =
− 1; and a
Bt
stock with price St. The stock pays out an infinite
` , whose
stream of perishable, real dividends, {Ds}s=t
D
growth rates, dt ; t − 1, follow a Bernoulli process:
Dt −1
d h with probability π D
dt =
0 ≤ π D ≤ 1 .23
d t with probability 1 − π D
Agents’ information set consists of a finite sample
space, ΩT , comprising all sequences of the form
ω T = {X{d1 = dh }, X{d2 = dh },..., X{dT = dh },
X{z1 = z h }, X{z 2 = z h },..., X{z T = z h }},
where X{·} denotes a standard indicator function.
Each ω T provides a record of possible sequences
of dividend growth rates and realizations of an
uninformative variable Zt. In our previous notation,
ΩT ={X̃T , Z̃T}. For simplicity, the only informative
variable is dividends. Also, assume that the uninformative variable Zt follows another binomial distribution independent of dividends, i.e., the rate of change
z
of Zt, zt ; t − 1, follows a Bernoulli process:
z t −1
z h with probability π Z
zt =
0 ≤ π Z ≤ 1.
z l with probability 1 − π Z
Therefore, the joint probability measure of each
realization ω T is given by
(9)
P (ω T ) = [π Dj (1 − π D )T − j ].[π Zi (1 − π Z )T − i ]
0 ≤ j ≤ T 0 ≤ i ≤ T,
where ω T is any state characterized by both j occur23
Without loss of generality, assume that d h>d1>–1, so that dividends
are nonnegative provided D0>0.
J A N UA RY / F E B R UA RY 2 0 0 4
45
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Chiodo et al.
rences of high dividend growth and i occurrences
of a high rate of growth of Z. While the marginal
probability for dividends is
P ({X{d1 = dh }, X{d2 = dh },..., X{dT = dh }}) = [π Dj (1 − π D )T − j ],
since D and Z are independent.
From basic asset pricing principles, in the
absence of risk aversion, we can find the price of
both assets as the present discounted value of the
future stream of cash flows generated by each of
them:
St = Et [ β ( St + 1 + Dt + 1)]
Bt = Et [ β ] = β ,
1
, ρ >0 is the subjective rate of
1+ ρ
impatience and Et[·] denotes the conditional expectation operator measurable with respect to available
information. Under the assumption of risk neutrality,
this simple asset pricing model is a specialization
of a classical present-discounted value dividend
model (see Lehmann, 1991) to the binomial distribution case.
In the full-information case where the parameters (πD , dh , dl , πz , zh , zl ) of the joint process for D and
Z are known to the agent, a solution for asset prices
can be obtained easily using the method of undetermined coefficients. Since the lattices for D and Z
are independent, Z does fail to convey any useful
information concerning D and an agent will rationally base her portfolio and pricing decisions on the
marginal probability measure for D only, a standard
(transformation of a) binomial distribution parameterized by {πD , dh , dl }. It is then possible to demonstrate that
j
T
StFI = lim Et ∑ β j ∏ Dt + i / Dt + i −1 . Dt .
T→ `
j =1 i =1
This solution for the equilibrium stock price under
full information shows that the stock price is a
simple, constant multiple of dividends. ΨFI denotes
the constant pricing kernel or, equivalently, the pricedividend ratio. The explicit solution to (10) can then
be derived as
(11)
StFI = Ψ FI Dt =
1 + dl + π ( dh − dl )
1 + E [ dt ]
Dt ,
Dt =
ρ − dl − π ( dh − dl )
ρ − E [dt ]
while the full-information bond price,
46
J A N UA RY / F E B R UA RY 2 0 0 4
1
> 0.
1+ ρ
Equivalently, the time-invariant equilibrium riskfree rate, r FI, is simply ρ>0. Since r FI=ρ, it is
straightforward to rewrite (11) as
StFI =
1 + E [dt ]
Dt ,
r FI − E [ dt ]
which shows the exact equivalence between the
solution under full-information rational expectations
and the classic Gordon’s (1959) formula, popular
in applied corporate finance.
The Heuristics-Based Solution
where β =
(10)
B FI =
BtFI,
is
Suppose that π D is unknown and must be
subjectively calculated in a recursive fashion. A
subjective assessment of π D at time t is equivalent
to calculating a probability function P̂ S(Ω̂ t );
Pr[Xt+k=1|Ω̂ t ] for all k ≥ 1, where Ω̂ t is as defined
in (4). The agent believes that the value of the stock
depends not only on future dividend payments, i.e.,
ˆ ) ; Pr[ X = 1| X
ˆ t ; Z˜ t ] for all k ≥ 1 ,
Pˆ S (Ω
t
t +k
but also on irrelevant information she uses. Assume
that the agent’s information set is Ω̂ t ={X̂t, Z̃t},
where
ˆ t ;{X*j ,t}tj =1
X
(12)
Xt with probability p j ,t
X*j ,t =
0 with probability 1 − p j ,t
and
p j ,t = θ t − jα ( Z j , Zt ) with
dα ( Z j − Zt )
d( Z j − Zt )
< 0, and θ < 1.
The parameter θ is an additional, subjective discount
factor applied to information flows: Since θ<1, the
further back in time an observation on the dividend
growth rate is, the more unlikely it is that it will
belong to the recalled information set Ω̂ t . α (Zj – Zt )
might be simply taken to be the inverse of the
Euclidean distance between Zj and Zt 24:
1
α ( Z j − Zt ) ;
.
1 + ( Z j − Z t )2
24
In the presence of a drifting process for Z, it would be advisable to
de-mean Zt by subtracting δ t and de-mean Zj by subtracting δ j, where
δ is the drift.
FEDERAL R ESERVE BANK OF ST. LOUIS
Chiodo et al.
The current observation on the dividend growth
rate belongs to Ω̂ t since α (Zj – Zt )=θ 0=1. Also, the
probability that Xj ,t is a member of Ω̂ t is a function
not only of the growth rate of Z but its level as well.
Under our binomial assumptions, maximumlikelihood delivers the following (recalled) sample
proportion estimator:
Excess Volatility of Stock Prices
From (10) it follows that26
1 + rtFI ;
Ψ FI dt +
*
ˆ ) = πˆ S (Ω
ˆ )=
Pˆ S (Ω
t
D
t
∑tj =1 X j ,t
,
∑tj =1 I{x*
j,t = x j,t }
where I{x*j,t=xj,t} is another indicator variable that
takes a value of 1 when Xj,t is a member of Ω̂t (it was
recalled) and zero otherwise.
It is now straightforward to calculate the incomplete information, equilibrium asset prices in the
presence of heuristic biases. When ρ>π̂ DS (Ω̂t ) dh+
(1 – π̂ DS (Ω̂t )) dl , the heuristic-based stock price, S tH, is
given by
(13)
ˆ ;θ ,γ ,α (.)) D
StH (θ ,γ ,α (.)) = Ψ H (Ω
t
t
S ˆ
1 + dl + πˆ D (Ωt )( dh − dl )
=
D
ˆ )( d − d ) t
ρ − d − πˆ S (Ω
l
=
D
t
h
ˆ tS [dt +1 ]
1+ E
D,
ˆ tS [dt +1 ] t
rH − E
25
The notation stresses that heuristic-based stock prices do depend on
the strength and structure of the assumed biases, as represented by
the parameters θ, γ , and the functional form of α (·). ÊtS[·] is an expectation taken with respect to the subjective probability assessment of
the agent.
1
1
d = Ψ FI + FI dt . Ψ FI dt ,
FI t
Ψ
Ψ
so that the volatility of gross stock returns, 1+r tFI, is
a constant factor Ψ FI times the volatility of the
rate of growth of fundamentals. Since empirical
research has shown stock returns to be over ten
times more volatile than fundamentals, this reveals
an inconsistency, as Ψ FI >10 implies ΨFI >100,
too high a price-dividend ratio.
To the contrary, (13) shows that the excess stock
volatility puzzle disappears when the price-dividend
ratio, Ψ, that maps dividends into equilibrium stock
prices is time-varying, as a result of limited recall
capabilities. In this case
1
1 + rtH = ΨtH + H dt .ΨtH dt
Ψt
l
while the full-information bond price, B tH, is r H=
ρ>0.25 Equation (13) differs from the full-information
result as the equilibrium stock price stops being a
fixed multiple of dividends; on the contrary, Ψ tH is
time-varying, fitting the empirical observations that
price-dividend ratios are subject to long swings. The
variation in the price-dividend ratio derives from
changes in the memory-based conditional expectation, Ê tS[dt+1]. More generally, observe that even
in the absence of strong changes in dividends, (12)
itself implies that Ψ tH ought to display considerable
variability.
StFI + Dt Ψ FI Dt + Dt
=
=
StFI−1
Ψ FI Dt −1
so that
Var [1 + rtH ] = Var [ ΨtH ] + Var [dt ] + 2Cov[ ΨtH, dt ] .
When Cov [ Ψ tH, dt ]>0, an increase of the volatility
of stock returns (as a result of heuristic biases) will
obtain in a full-information framework. Such a case
is highly likely under the heuristic rules of our
framework.
26
The approximation is justified by realistic values of the price-dividend
ratio in excess of 20 to 30.
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48
J A N UA RY / F E B R UA RY 2 0 0 4
The Efficient Market Hypothesis and Identification
in Structural VARs
Lucio Sarno and Daniel L. Thornton
F
or a variety of reasons economists have long
been interested in measuring the economy’s
response to exogenous shocks. The shocks
are thought to result, for example, from specific
unexpected policy actions, sources that are exogenous to the domestic economy (such as an oil price
shock), or sudden changes in technology. The economic structure (or data-generating process) that
determines any economic outcome must be inferred
from the observed data, and a structural interpretation of the data is obtained from economic theory.
However, there are alternative economic theories
and, consequently, alternative structural interpretations of the same observations. Hence, economists
are faced with the very difficult problem of discriminating among these interpretations and, consequently, identifying the specific source of the shock
or the economy’s response to it.
Before a structural model can be evaluated, it
must be identified. A structural model is identified
when one can obtain the structural parameters from
the estimates of the reduced-form parameters. A
model is “just identified” when there is a one-to-one
correspondence between the structural parameters
and the reduced-form parameters. On the other
hand, a model is over-identified if there is more
than one set of structural parameters that is consistent with a given set of reduced-form parameters,
whereas it is unidentified when there is no way to
obtain the structural parameters from the estimated
reduced-form parameters.1
Generally speaking, there have been two broad
approaches to identification, the Cowles Commission
(CC) methodology and the so-called structural vector
1
When a model is over-identified, there is a set of over-identifying
restrictions that can be tested as part of a structural model evaluation.
autoregression (SVAR) methodology.2 As a consequence of Sims’s (1980) critique of the CC methodology, the SVAR methodology has become arguably
the most widely used method of structural analysis.
Both methodologies assume that the structural economy can be approximated by a linear, dynamic
system of structural equations with an additive
stochastic structure. In applications of the CC
methodology, identification was typically achieved
by placing restrictions (typically homogenous, i.e.,
zero, restrictions) on some of the coefficients of a
dynamic structural model of the economy. While it
was well understood that identification could be
achieved by placing restrictions on the stochastic
structure of the model, this was seldom done in
practice.3
In contrast, in the SVAR methodology (which is
attributed to Bernanke, 1986; Blanchard and Watson,
1986; and Sims, 1986) identification is achieved by
imposing contemporaneous restrictions on both
the structure of the economy and the stochastic
structure of the model.4 Exclusion restrictions on
the structural dynamics—which were frequently
imposed in applications of the CC methodology—
are never imposed.
The restrictions that the SVAR methodology
imposes on the structural shocks have often been
2
The Cowles Commission methodology is attributable to various
researchers who were in one way or another connected to the Cowles
Commission for Research in Economics. For a summary of this methodology, see Koopmans (1949). For an early application of it, see Klein
(1950).
3
See Koopmans (1949) for a discussion of variance-covariance
restrictions.
4
We note that there are identification schemes that impose no contemporaneous restrictions. This literature includes the work of Blanchard
and Quah (1989) and Shapiro and Watson (1988). This methodology
is not discussed here. See Keating (1992) for an excellent survey of
structural VAR approaches to identification.
Lucio Sarno is a professor of finance, Finance Group, Warwick Business School, University of Warwick, and a research affiliate, Centre for Economic
Policy Research (CEPR), London. Daniel L. Thornton is a vice president and economic advisor at the Federal Reserve Bank of St. Louis. The authors
thank Martin Sola, Hiroshi Fujiki, Oscar Jorda, and Yi Wen for comments. John Zhu provided research assistance.
Federal Reserve Bank of St. Louis Review, January/February 2004, 86(1), pp. 49-60.
© 2004, The Federal Reserve Bank of St. Louis.
J A N UA RY / F E B R UA RY 2 0 0 4
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REVIEW
Sarno and Thornton
criticized (e.g., Bernanke, 1986; Stock and Watson,
2001), and Cooley and LeRoy (1985) have noted that,
in the absence of these restrictions, the estimated
shocks from the SVAR would be linear combinations
of all the structural shocks in the reduced-form
VAR. This paper extends and refines Cooley and
LeRoy’s observation by noting that if the VAR includes
one or more efficient market variables (EMVs)—
variables that reflect all information relevant for
their determination—the covariance restrictions
that are typically employed in a SVAR identification
are inappropriate and may have to be replaced with
alternative restrictions. Our paper is close in spirit
to those of Wallis (1980) and Pesaran (1981) in the
rational-expectations literature; however, we focus
on SVARs rather than on more general structural
rational-expectations models.
Strictly speaking, our analysis applies only to
VARs that include variables that are efficient in the
strong form of the efficient market hypothesis (EMH).
We argue, however, that our analysis is likely to
have implications for VARs that include variables
that meet the less stringent requirements of semistrong market efficiency. The potential importance
of our critique for applied work is illustrated with
a SVAR model that is widely used to identify the
effects of monetary policy shocks on the economy.
The paper begins with a brief discussion of the
CC and SVAR approaches to identification. We then
discuss (i) the EMH and the various forms of market
efficiency and (ii) the effect of including an EMV in
a SVAR model. The implications of our analysis for
applied work are illustrated with a widely used
SVAR model.
THE CC AND SVAR METHODS OF
IDENTIFICATION
Both the CC and SVAR methods of identification
assume that the economy can be approximated by
a general linear structural model of the economy
of the form
(1)
AYt=BYt –1+Dvt,
where Yt is an N ×1 vector of endogenous variables
and vt is a vector of i.i.d. structural shocks, with mean
zero and a constant covariance matrix.5 Bernanke
5
The first-order autoregressive structure is used because any higherorder autoregressive process can be written as a first-order process.
For presentation purposes, however, we will assume that the model
is strictly first order.
50
J A N UA RY / F E B R UA RY 2 0 0 4
(1986, p. 52) notes that these shocks are “primitive”
exogenous forces, not directly observed by the
econometrician, which “buffet the system and
cause oscillations.” He notes that “because these
shocks are primitive, i.e., they do not have a common
cause, it is natural to treat them as approximately
uncorrelated.” Hence, it is reasonable to assume
that Evt vt′=Λ, where Λ is a diagonal matrix. This
noncontroversial assumption is common to both
the CC and SVAR approaches.
The reduced-form of the structural model (i.e.,
what economists observe) is given by
Yt=A –1BYt –1+A –1Dvt
(2)
or
(3)
Yt=ΓYt –1+ut,
where Γ=A B and ut=A –1Dvt .
The economic model is (exactly) identified when
it is possible to obtain estimates of the structural
parameters (i.e., the elements of A, B, D, and Λ from
the reduced-form parameters) and vice versa (i.e.,
when there is a one-to-one correspondence between
the structural and reduced-form parameters). Identification is achieved by placing restrictions on A, B,
and D.6
In the CC methodology, identification was typically achieved by imposing restrictions on A and B.
While it was widely understood that identification
could be achieved by imposing restrictions on D or
Λ, such restrictions were seldom imposed in practice. There are N2 unique elements of Γ=A –1B, but
N2 elements in each of A and B. Hence, the necessary
(order) condition for (exact) identification using the
CC methodology is that there are as many zero elements (in the case of homogenous restrictions) in
B as there are non-zero elements in A. That is, there
must be a total of N2 restrictions imposed on A and
B—the fewer the restrictions imposed on A, the
more restrictions must be imposed on B. If these
restrictions are linearly independent (the rank condition for identification), it is possible to go from the
reduced-form parameters to the structural parameters and vice versa.
In response to Sims’s (1980) claim that the
restrictions placed on B were “incredible,” the SVAR
literature has taken a different approach to identification. No restrictions are placed on B. Instead,
identification is achieved by placing restrictions on
–1
6
Restrictions can also be imposed on Λ. For example, one might assume
that the variance of one structural shock is some multiple of another.
This possibility is ignored for ease of presentation.
FEDERAL R ESERVE BANK OF ST. LOUIS
the elements of A and D. To see how the model is
identified in the SVAR literature, note that Eut ut ′=
A –1DΛD′A′–1=Σ, where Σ is a real symmetric matrix
of rank N. An estimate of Σ is obtained by estimating
the reduced-form model, i.e.,
ˆ ,
ˆ tu
ˆ t′ = Σ
∑Tt =1 Eu
where ût is the vector of residuals obtained by estimating equation (3). There are at most N(N+1)/2
unique, non-zero elements of Σ̂. In contrast, there
are N2 parameters in A, N elements in Λ, and N2
elements in D. Consequently, there are 2N2+N
structural parameters, so that (3N2+N)/2 restrictions
are needed to satisfy the necessary (order) conditions for identification. Hence, identification can
be achieved by imposing (3N2+N)/2 restrictions on
the 2N2 elements of A and D.
It is frequently assumed in the SVAR literature
that D=I. With this assumption, there are only
(N2+N)/2 restrictions that need to be imposed on A.
N of these restrictions can be obtained by assuming
that the diagonal elements of A are equal to unity
(these are normalization restrictions), which leaves
N(N–1)/2 required restrictions.7 In the case of recursive structural VARs (RSVARs), these restrictions
come from assuming that A is lower triangular.8
THE EMH
The assumption that SVAR models impose on
A and D to achieve identification may not hold if the
VAR includes one or more EMVs. To see why, it is
useful to briefly discuss the EMH (Samuelson, 1965;
and Campbell, Lo, and MacKinlay, 1997). Malkiel
(1992, p. 739) states that a “market is said to be efficient with respect to an information set, φ, if security
prices would be unaffected by revealing that information to all participants.” The degree of market
efficiency is usually categorized by the nature of
the information set. Markets are said to be efficient
in the weak form if the information set only includes
the history of prices or returns. For the semi-strong
form of market efficiency, the information set is all
7
8
Even in cases where D ≠ I, there is a one-to-one correspondence
between the structural shocks and the variables in the VAR (e.g.,
Bernanke, 1986). This is a consequence of the requirement that D
must be N × N.
This is often referred to as a Wold causal chain in honor of Herman
Wold, who advocated the theoretical desirability of recursive models
in economics, e.g., Wold (1954). In the case of non-recursive structural
VARs, the necessary condition for identification is usually achieved by
imposing N(N–1)/2 homogenous (or in some cases, non-homogenous)
restrictions that are rationalized on the basis of economic theory.
Sarno and Thornton
publicly available information. When market prices
reflect the information known to any market participant, they are said to be efficient in the strong
form.9
Market efficiency is also characterized by the
speed with which information is reflected in market
prices (e.g., Chordia, Roll, and Subrahmanyam, 2002;
and Schwert, 2002). A shock that is initially reflected
in only one asset price may, over time, be reflected
in other asset prices. The faster the information is
reflected in other prices, the more efficient the
market is said to be. Financial markets are thought
to be efficient with respect to publicly announced
(or known) information, in that such information is
thought to be rapidly, if not immediately, reflected
in asset prices (Malkiel, 1992; and Campbell, Lo, and
MacKinlay, 1997). It may take longer for information
that is not publicly announced to be incorporated
in asset prices; however, a shock that initially affects
only one asset price may create arbitrage opportunities. As market participants respond to such
opportunities, prices of other assets change. Hence,
the longer the period of time over which economic
data are averaged, the more likely it is that asset
prices will reflect information that is and is not
publicly announced.
THE EMH AND THE SVAR
IDENTIFICATION
By definition, an EMV responds contemporaneously to all shocks that are relevant for its determination. This means that none of the elements of
the row of A –1D corresponding to the EMV are zero.
It is not important whether the response of the EMV
to structural shocks is due to the form of A or D ;
nevertheless, if the assumptions made about the
form of A are such that the rows of A –1 corresponding to the EMVs are zero, the elements of the rows
of D corresponding to these variables must be
non-zero.
To better understand why this is so, consider a
simple three-variable structural model of the economy represented by equation (1). We initially assume
that no identifying restrictions are imposed, so that
a11 a12
A −1 = a21 a22
a
a
31 32
9
a13
a23 ,
a33
See Malkiel (1992) for details.
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Sarno and Thornton
b11 b12
B = b21 b22
b31 b32
b13
b23 ,
b33
1 d12
D = d21 1
d31 d32
d13
d23 .
1
and
The diagonal elements of D are normalized to unity
under the assumption that the structural shocks
are unique. Now assume that the second variable
in the VAR, Y2, is an EMV.
For the sake of illustration, assume that D=I,
so that the reduced-form error is given by
(4)
u1,t a11ν1,t + a12ν 2,t + a13ν 3,t
ut = u2,t = a21ν1,t + a22ν 2,t + a23ν 3,t ,
u3,t a31ν1,t + a32ν 2,t + a33ν 3,t
where v1, v2, and v3 denote the first, second, and
third primitive structural shocks, respectively.
Note that the reduced-form shocks are related
to the structural shocks solely by the structure of A.
While the point made above applies to any SVAR
model, for ease of illustration, we assume a RSVAR,
i.e., A is assumed to be lower triangular. With this
assumption, equation (4) reduces to
(5)
a11ν1,t
ut =
a21ν1,t + a22ν 2,t
.
a ν + a ν + a ν
32 2,t
33 3,t
31 1,t
Under these assumptions, the first shock is reflected
only in the first reduced-form residual, the first and
second structural shocks are reflected in the second
reduced-form residual, and so on and so forth.
Note that equation (5) is incompatible with our
assumption that Y2 is an EMV because, under the
assumptions made about A and D, Y2 responds only
to the first and second structural shocks. Hence,
given the assumptions made about the structure
of A, the EMH requires alternative assumptions be
made about the structure of D.
In the case of a RSVAR, one way the model
can be made consistent with the EMH is by letting
the EMV appear last in the Choleski ordering. The
placement of the variables in the ordering in RSVARs
is usually based on economic arguments, however.
Hence, changing the recursive ordering in a RSVAR
52
J A N UA RY / F E B R UA RY 2 0 0 4
is tantamount to making different assumptions
about the structure of the economy. Hence, while
placing the EMV last in the recursive ordering overcomes the problem we discuss in this paper, it need
not be the “correct” solution.
Alternatively, one could maintain the Choleski
ordering and relax the assumptions on D. In this
example this can be achieved by assuming that
d23 ≠ 0. In this case, the reduced-form errors would
now be given by
(6)
ν1,t
ut =
a21ν1,t + ν 2,t + d23ν 3,t
.
a31d21ν1,t + a32ν 2,t + ( a32 d23 + 1)ν 3,t
Y2,t responds to the third structural shock due to the
assumption that d23 ≠ 0. If the model were exactly
identified, however, an additional restriction must
be imposed on either A or Λ (e.g., σ 2vi=σ 2vj for some
i and j ) to satisfy the necessary conditions for
identification.
Note that if there are two or more EMVs in the
VAR, placing these variables last in the Choleski
ordering will not overcome the problem unless one
of the EMVs deviates from the other by an idiosyncratic shock.10 If the recursive structure of A is
maintained, identification will have to be achieved
by imposing additional restrictions on either A or Λ.
IMPLICATIONS OF THE EMH FOR
APPLIED WORK
How important is our analysis of the EMH for
applied work? This is a difficult question to answer
for at least two reasons. First, in general, the answer
depends on the nature of the variables included in
the SVAR and the structural restrictions imposed
for identification. Consequently, the importance of
including an EMV in the SVAR must be analyzed on
a case-by-case basis.
Second, strictly speaking, our analysis holds
only if the SVAR includes a variable that is efficient
in the strong form of the EMH, and strong-form
market efficiency is a stringent condition that is
unlikely to be satisfied in the real world. We believe
that our critique may apply to SVARs that include
financial market variables that are likely to be efficient in the weak form or in the semi-strong form
of the EMH, such as stock prices, interest rates, or
possibly exchange rates.
10
For example, the expectations hypothesis holds.
FEDERAL R ESERVE BANK OF ST. LOUIS
Hence, one area of research where we believe
that our analysis is likely to apply is the relatively
large body of empirical work devoted to identifying
the effects of monetary policy shocks using RSVARs.
In a large strand of this literature, U.S. monetary
policy shocks are identified using time series on a
short-term interest rate—most often the effective
federal funds rate—at monthly or lower frequencies,
using a RSVAR (e.g., Christiano, Eichenbaum, and
Evans, 1996, 1999).
While it is perhaps unlikely that short-term
interest rates reflect all market information, there
is considerable evidence to suggest that they reflect
all publicly available information rather quickly.
That is, short-term interest rates (and interest rates,
more generally) are likely to satisfy the conditions
for the semi-strong form of market efficiency.
Further, these markets are dominated largely by
public information, with private information playing
a limited role relative to, for instance, the stock
market. Indeed, the evidence suggests interest rates
respond quickly to information that market participants believe is important for determining the stance
of monetary policy. For example, interest rates
responded quickly to unexpected changes in the
stock of money during the period when the Fed was
implementing monetary policy by targeting M1 from
October 1979 through October 1982 (e.g., Cornell,
1982, 1983; Roley and Walsh, 1985; and Thornton,
1989). There is also a large body of literature showing
that interest rates respond rapidly to a variety of
macroeconomic information, albeit different information at different times (see Fleming and Remolona,
1997, for a summary of this literature), and respond
intra-day to a number of macroeconomic announcements (e.g., Fleming and Remolona, 1999). To the
extent that shocks to macroeconomic variables also
reflect such information, the identifying restrictions
imposed in the RSVAR will be violated.
The longer the period of time over which interest
rates are averaged, the more likely it is that all rates
will reflect information that was initially reflected
in only one rate. That is, it becomes more likely that
interest rates will reflect information that is not
publicly known. Hence, the covariance restrictions
frequently imposed for identification are more problematic the longer the period of time over which
interest rates are averaged.
Some analysts might argue that our conclusion
that short-term nominal interest rates are likely to
satisfy the EMH runs counter to the treatment of
short-term rates in many monetary policy analyses,
Sarno and Thornton
where the short-term interest rate is treated as a
choice variable of the central bank. In this case, the
short-term rate need not be an EMV because changes
in it are made entirely in response to past information. However, if one takes seriously the evidence
that interest rate rules are forward looking (e.g.,
Clarida, Gali, and Gertler, 2000), it is plausible that
the short-term interest rate is consistent with the
EMH even if it is determined solely by decisions of
the central bank. Consequently, regardless of
whether the short-term interest rate is determined
by the market or determined by the central bank, it
seems possible that the interest rate behaves in a
manner consistent with the EMH under certain
assumptions.11,12
To investigate the significance of our critique
for applied work, we estimate a seven-variable VAR
similar to that estimated by Christiano, Eichenbaum,
and Evans (1999). The variables used are industrial
production, Y; the price level as measured by the
consumer price index, CPI; the Journal of Commerce
commodity price index, CP ; the effective federal
funds rate, FF ; nonborrowed reserves, NBR; total
reserves, TR; and the broad monetary aggregate, M2.
With the exception of CP and NBR, the variables are
identical to those used by Christiano, Eichenbaum,
and Evans (1999). All of the variables except the
funds rate are in natural logs. The data are monthly
for the period 1959:01 to 2001:07. Following
Christiano, Eichenbaum, and Evans (1999), the lag
order is 12.13
Christiano, Eichenbaum, and Evans employ the
Choleski factorization with the ordering {Y, P, CP,
FF, NBR, TR, M2}. Our analysis suggests, however,
that if FF is an EMV, it should come last in the
11
Applying the EMH only to financial prices is at odds with some recent
New Keynesian literature. Some of the models in this literature employ
forward-looking relations for output (and inflation) that resemble
asset-pricing conditions (e.g., Estrella and Fuhrer, 2002). Of course,
extending our analysis to such variables would make the identification
problems discussed here even more severe because EMH-type behavior
might be expected of other variables in the VAR besides financial
prices or interest rates.
12
If the above argument applies, it applies primarily to the federal funds
rate and then only over periods when the Fed explicitly targeted the
funds rate. Moreover, Sims (1998) found that the qualitative results
were unaffected by using either the Fed’s discount rate or the commercial paper rate. We confirmed his finding; however, these results
are not reported. The impulse response functions obtained using the
federal funds rate were very similar to those obtained using a variety
of other short-term rates.
13
Qualitatively and quantitatively similar results are obtained with
shorter lag lengths.
J A N UA RY / F E B R UA RY 2 0 0 4
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Sarno and Thornton
Figure 1
Impulse Response Functions for Y with FF Fourth and Last in the
Cholesky Ordering
0.4
0.2
0.0
–0.2
FF Last
–0.4
FF Fourth
–0.6
90% Confidence Band
–0.8
–1.0
–1.2
–1.4
–1.6
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41
Figure 2
Impulse Response Functions for CPI with FF Fourth and Last in the
Cholesky Ordering
0.6
0.4
0.2
0.0
–0.2
FF Last
–0.4
FF Fourth
90% Confidence Band
–0.6
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41
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J A N UA RY / F E B R UA RY 2 0 0 4
FEDERAL R ESERVE BANK OF ST. LOUIS
Sarno and Thornton
Figure 3
Impulse Response Functions for CP with FF Fourth and Last in the
Cholesky Ordering
2
1.5
FF Last
1
FF Fourth
0.5
90% Confidence Band
0
–0.5
–1
–1.5
–2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41
Figure 4
Impulse Response Functions for NBR with FF Fourth and Last in the
Cholesky Ordering
1.5
FF Last
1
FF Fourth
90% Confidence Band
0.5
0
–0.5
–1
–1.5
–2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41
J A N UA RY / F E B R UA RY 2 0 0 4
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Sarno and Thornton
Figure 5
Impulse Response Functions for TR with FF Fourth and Last in the
Cholesky Ordering
1.5
FF Last
1
FF Fourth
90% Confidence Band
0.5
0
–0.5
–1
–1.5
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41
Figure 6
Impulse Response Functions for M2 with FF Fourth and Last in the
Cholesky Ordering
0.8
0.6
FF Last
FF Fourth
0.4
90% Confidence Band
0.2
0
–0.2
–0.4
–0.6
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41
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FEDERAL R ESERVE BANK OF ST. LOUIS
Sarno and Thornton
Figure 7
Impulse Response Functions for FF with FF Fourth and Last in the
Cholesky Ordering
1.4
FF Last
1.2
FF Fourth
1
90% Confidence Band
0.8
0.6
0.4
0.2
0
–0.2
–0.4
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41
Choleski ordering. Hence, we compare the results
with two orderings: {Y, P, CP, FF, NBR, TR, M2} and
{Y, P, CP, NBR, TR, M2, FF}.
Figures 1 through 7 show the impulse response
functions of each of the variables to a one-unit shock
to the funds rate when the funds rate is fourth in
the ordering (the solid black line) and when the
funds rate is last in the ordering (the solid gray line);
they also show the 90 percent confidence interval
(the dashed lines) for the impulse response functions
obtained when FF comes last in the Choleski ordering. The confidence intervals are obtained by bootstrapping the model using 500 iterations. The effect
of placing the funds rate in the middle rather than
last in the recursive ordering is sometimes large—
particularly for a funds rate shock on output, where
the effect with the funds rate in the middle drifts
to the lower bound of the 90 percent confidence
interval.
The effect is also large for NBR. This is not surprising because there is a strong and contemporaneous link between NBR and the funds rate (Pagan
and Robertson, 1995; and Thornton, 2001). Thornton
(2001) has shown that this relationship is due to the
Fed’s operating procedure, which caused NBR to
respond contemporaneously and endogenously to
changes in the funds rate over much of this period.
In any event, when the funds rate is last in the ordering, the contemporaneous relationship between
the funds rate and NBR is accounted for in the funds
rate equation. With the contemporaneous relationship between the funds rate and NBR accounted
for in the funds rate equation, shocks to the funds
rate have no significant effect on NBR. Moreover,
consistent with Thornton’s (2001) analysis of the
Fed’s operating procedure, the effect of shocks to the
funds rate on NBR and TR is similar.
It is well known that the response to a shock
may vary with the Choleski ordering. In this respect,
these results are perhaps not surprising. We have
provided a rationale for why the response is likely
to change with the recursive ordering in some cases.
Hence, these results raise doubts about the implications obtained from RSVARs. Note that while we
obtained different results by placing the potential
EMV last in the Choleski ordering, we are not advocating this as a “solution” to the problem of identification when RSVARs contain a potential EMV. We
are only suggesting that these results are consistent
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Sarno and Thornton
with our overall conclusion that special care should
be taken when identifying SVARs that include an EMV.
Of course, if the VAR includes two or more financial market variables, such as interest rates, stock
prices, or exchange rates, identification is even more
complicated.14 Such variables may be efficient at
least in the semi-strong form of the EMH and, hence,
will quickly reflect publicly known information.
For example, a policy or other announcement that
affects interest rates is likely also to affect stock
prices or exchange rates. Garfinkel and Thornton
(1995), who investigated the relationship between
the federal funds rate, the overnight repo rate, and
the 3-month T-bill rate using weekly average and
daily data, found that shocks to interest rates that
cause a differential between the funds rate and other
rates were quickly eliminated. They also found that
the idiosyncratic shocks to interest rates, as they
identify them, are not correlated with three measures
of monetary policy actions, suggesting that monetary
policy actions were quickly reflected in market
interest rates, including the federal funds rate. Consistent with these results, Sarno and Thornton (2003)
found that disturbances to the equilibrium between
the daily funds rate and the 3-month T-bill rate dissipate very rapidly.
The problem is that if economic variables contemporaneously reflect the same information,
structural identifying assumptions that impose the
condition that shocks do not affect such variables
contemporaneously will be violated. While the
importance of this critique for applied work is an
empirical question, the empirical analysis presented
here supports the argument that covariance restrictions imposed in the SVAR literature may be inappropriate and that greater caution should be exercised
in choosing the identifying restrictions in such
models.
EMH because EMVs, as we term them, respond to
all information.
While, strictly speaking, our analysis applies
only to variables that are efficient in the strong form
of the EMH, the longer the period of time over which
the data are measured, the more likely it is that the
variables that are efficient in the semi-strong or weak
forms of the EMH will reflect information that was
initially known only to relatively few market participants. Hence, our analysis is likely to have implications for empirical analyses that use variables that
are efficient in the semi-strong or weak forms of
the EMH, especially when data are measured at
monthly and quarterly frequencies and for markets
where public (as opposed to private) information is
dominant.
We illustrate the potential importance of our
analysis by estimating a RSVAR often used to
identify the effects of monetary policy shocks on
the economy. Our results suggest that some of the
effects of monetary policy shocks, so identified,
are sensitive to whether the interest rate is ordered
in the middle of the VAR, as is most often the case,
or at the end (which avoids the problem in RSVARs
that include only one EMV). This does not imply that
one can simply overcome the problem by putting
the EMV last in the Choleski ordering. It does, however, support our conclusion that researchers need
to be extremely careful when using the standard
contemporaneous identifying restrictions employed
in the SVAR methodology when the VAR includes
one or more variables that may satisfy some form
of the EMH. Caution is particularly required when
the data employed are at the monthly or quarterly
frequency, as is often the case in applied macroeconomics and monetary economics.
SUMMARY AND CONCLUSIONS
Bernanke, Ben S. “Alternative Explanations of the MoneyIncome Correlation.” Carnegie-Rochester Conference
Series on Public Policy, Autumn 1986, 25(0), pp. 49-99.
The SVAR methodology identification is frequently applied by imposing restrictions that prevent
economic variables from responding contemporaneously to one or more structural shocks. This paper
shows that such restrictions are not applicable if
the variable is efficient in the strong form of the
14
In an effort to estimate the effect of monetary policy actions—shocks
to the federal funds rate—on the yield curve, Evans and Marshall
(1998) estimate a number of SVARs that include the effective federal
funds rate and a “long-term rate,” with maturities ranging from one
month to ten years. Evans and Marshall use three alternative identifying assumptions, including a Choleski ordering.
58
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