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Flation
William Poole and Robert H. Rasche
lation”—not inflation, not deflation—is
lifted from the title of a book by Abba P.
Lerner.1 For the past 35 years in the
United States and, indeed, in most of the world,
policymakers and the public in general have been
focused on the issue of inflation—that is, the continual upward drift in prices of the overwhelming
fraction of goods and services produced in the
economy. Sometimes the drift was more of a gallop.
For most of this period, the upward trend was also
characteristic of the prices of assets such as land,
houses, and equities. Inflation, prevalent though
it has been in our recent economic experience,
has not been the norm for most of U.S. history. In
the early 1930s, exactly the opposite experience
occurred: deflation, or a continual downward drift
in the prices of goods, services, and assets.
Deflation has a frightening history. Simultaneously with the deflation of the early 1930s, the U.S.
unemployment rate soared to about 25 percent in
1933 at the depth of the Great Depression. Although
deflation ended in 1933, the damage to the economy
was so great that poor economic conditions persisted
until the United States became involved in World
War II in 1941. Moreover, the economic history of
the 1990s in Japan is characterized by deflation. The
Japanese economy has stagnated, and unemployment there has risen today to levels not seen in over
40 years. From these and other episodes around
the world, many people associate deflation with
“hard times.”
The purpose of this analysis is not to get into a
discussion of whether a little deflation is compatible
with prosperity, although within limits it may be.
The more important point is that, without question,
substantial deflation is inconsistent with prosperity.
Thus, deflation is every bit as serious an issue as
inflation; however, the U.S. economy today does
not run any significant risk of deflation.
“F
William Poole is the president and Robert H. Rasche is a senior vice
president and director of research at the Federal Reserve Bank of St.
Louis. This article is adapted from a speech of the same title presented
before the International Mass Retail Association Leadership Forum,
January 21, 2002. The authors appreciate comments provided by
colleagues at the Federal Reserve Bank of St. Louis. The views expressed
do not necessarily reflect official positions of the Federal Reserve
System.
© 2002, The Federal Reserve Bank of St. Louis.
Obviously, not everyone agrees with this judgment. Based on a few recent observations of monthto-month price changes, some commentators have
used the “D” word to express their concern about
the current state of the U.S. economy. The objective
in this paper is to explore this subject and, we hope,
make a contribution to public understanding of the
issue.
First, we will elaborate on what we believe is
the appropriate objective for Federal Reserve policy.
Second, we will explain the generally accepted definitions of inflation and deflation, and discuss the
fundamental sources of these phenomena. Third, we
will review aspects of price behavior in our economy
and discuss how data should be interpreted to determine the inflationary or deflationary state of the
economy. Finally, although the issue concerns the
behavior of the aggregate price level, we will examine some particular sectoral price changes to help
better understand the aggregate price level.
THE APPROPRIATE POLICY OBJECTIVE
FOR THE FEDERAL RESERVE
Our monetary policy framework is this. First
and foremost, the central bank must maintain a
commitment to price stability. An operational definition of price stability is an environment in which
the inflation rate, properly measured and averaged
over several years, is zero. All of our inflation data
are subject to measurement errors. Experts in such
measurements generally agree that current price
indexes, despite statisticians’ best efforts, still leave
inflation measures that have some upward bias.
Hence, in terms of the various inflation indexes, we
can say that price stability prevails when broad price
indexes exhibit small positive average values for
measured inflation and that year-to-year fluctuations
around that average are well contained.
If the price level comes unstuck, yielding inflation or deflation, all sorts of other problems will
arise. Nevertheless, within the confines of the goal
of price stability, the central bank has some flexibility to lean against fluctuations in output and employment. However, the central bank ought not to pursue
the goal of stabilizing economic activity so aggressively that it runs any substantial risk of compromising the goal of price stability.
Finally, in leaning against fluctuations in growth
and employment, the central bank ought not to
1
Lerner, Abba P. Flation. New York: Quadrangle Books, 1972.
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Poole and Rasche
have goals for levels of the economy’s growth and
unemployment rates per se. Within a wide range,
no one knows what the economy’s equilibrium rate
of growth is or what rate of unemployment will
clear the labor market in the long run. The biggest
risks of a major monetary policy mistake occur if a
central bank attempts to target the levels of real
variables.
Achieving the objective of price stability, as
defined above, will yield a highly stable economy.
When the market has confidence in Fed policy, shortrun changes—that is, over a few months or even a
few quarters—in the rate of inflation or deflation will
tend to be self-reversing rather than self-reinforcing.
THE DEFINITION AND SOURCES OF
INFLATION AND DEFLATION
At the beginning of the great inflation of 1965-80,
there was a wide disparity of professional opinion
about the fundamental source of inflation or deflation in an economy. One proposition came to be
known as the “monetarist view.” This view held that
sustained inflation or deflation was always a monetary phenomenon; that is, that the only source of
long-run positive or negative trends in the general
level of prices in an economy is the creation of an
excess or insufficient supply of money balances
relative to the growth of the productive capacity of
that economy. Milton Friedman of the University of
Chicago was the most publicly visible proponent
of this proposition. The Federal Reserve Bank of St.
Louis, in particular the president of the Bank at that
time, Darryl Francis, and the Research staff were
vocal advocates of this proposition in the policy
arena during the late 1960s and early 1970s. A reading of the Memorandum of Discussion of the Federal
Open Market Committee (FOMC) for this period
makes clear that there were sharp debates over these
issues. The FOMC is the Fed’s main monetary policymaking body, and the public record of that period
shows that Darryl Francis was a vigorous advocate
of the monetarist view.
The proposition that the central bank is the
source of ongoing inflation or deflation was a distinct minority view 35 years ago. In the FOMC, Darryl
Francis was usually the only one expressing this
view. The development of economic theory and the
economic history of the past three decades have
produced a major change in both professional
thinking and public attitudes toward the sources of
inflation and deflation. Economists are now largely
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in agreement that if the central bank does not achieve
the goal of price stability, no one else can. Many
central banks around the world, starting with the
Reserve Bank of New Zealand in 1990, have acknowledged this responsibility and have adopted explicit
numeric inflation targets.
This view also spread into public thinking about
inflation in the United States. Paul Volcker, former
chairman of the Board of Governors of the Federal
Reserve System, is widely credited for the disinflation
that occurred in the United States in the early 1980s.
Chairman Greenspan is applauded for the additional
progress in the 1990s that brought the U.S. inflation
rate to the lowest level in almost 40 years.
Today the Federal Reserve accepts its responsibility for the trend rate of inflation. However, a central
bank is not responsible for month-to-month wiggles
in the inflation statistics. Nor should a central bank
attempt to react to short-run variations, since the
sources of such noise are beyond its control and
likely to average out over a period of a few months
or at most a couple of years. One obvious reason
for not reacting to short-run developments is that
an unknown part of these changes in the reported
inflation rate is purely measurement error, or statistical noise.
Professional opinion has also changed about the
source of deflation in the 1930s. It is now widely
acknowledged that, at a minimum, the intensity of
the Great Depression was magnified by the failure
of the Federal Reserve to provide sufficient liquidity
to the economy in the face of widespread bank failures. The Federal Reserve in turn has learned from
that experience. When the U.S. economy has been
threatened by liquidity crises in recent years—such
as the stock market crash of 1987, the Asian crises
and Russian default of 1998, and the terrorist attack
of September 11, 2001—the Fed has moved rapidly
to inject large amounts of liquidity into the economy. Liquidity crises have been averted, inflation
has remained low and stable, and deflation has not
occurred.
Experience elsewhere has not been as benign.
Over the period from 1981 through 1990, the
Japanese economy grew at an annual rate of 3.7
percent and the inflation rate (measured by the
gross domestic product [GDP] price index) averaged
1.5 percent per year. The situation in Japan in the
1990s has been remarkably different. The Japanese
economy has struggled in and out of recession, and
real growth from 1991 to 2000 averaged only 1.1
percent. Over the same period, very low inflation
FEDERAL RESERVE BANK OF ST. LOUIS
has turned into deflation. From 1991 to 1996, the
Japanese consumption deflator rose at an average
annual rate of only 0.5 percent; for 1996 to 2000,
the rate was –0.2 percent. Asset prices fell dramatically. The decline of the Nikkei equity price index
from a value of close to 40,000 in late 1989 to its
recent level of less than 10,000 is common knowledge. What is not as well known outside Japan is
that land and real estate prices over the past decade
have experienced equally dramatic declines as those
seen in equity markets. In April 1993 an index of
housing prices in Japan stood at 42.35 million yen.
By April 2001 it had fallen to 36.52 million yen, an
annual average rate of decline of 1.7 percent.2 The
index of residential land prices reached a peak in
March 1991 of 109.7 and fell to 81.7 by September
2001, an annual average rate of decline of 2.4 percent. The decline in commercial land prices was
even larger. From a peak of 111.7 in September 1991,
the index of these prices fell to 49.1 in September
2001, an annual average rate of decline of 5.6 percent.3 In terms of the impact on Japan’s output and
employment, the large deflation of asset prices was
probably more important than the gentle deflation
of goods prices.
What is responsible for the incredible difference in the performance of the Japanese economy
between the 1980s and 1990s? Japan’s money stock
(using Japan’s own preferred measure, M2+CDs)
grew at an average annual rate of 7.9 percent from
1981 through 1990, but only at 2.3 percent per year
over the decade from 1991 through 2000. A conclusion consistent with research on this issue is
that the ongoing stagnation and deflation that the
Japanese economy has experienced in the past
decade is likely related to an insufficient supply of
liquidity by the Bank of Japan. Slow money growth
is not the whole story, but is certainly a significant
part of it.
RECENT PRICE BEHAVIOR IN THE
U.S. ECONOMY
Public discussion of inflation in the United
States generally is focused on the consumer price
index (CPI) published monthly by the Bureau of
Labor Statistics. The monthly change in the overall
CPI is the so-called “headline” inflation number.
The CPI is very visible; it has been widely reported
for years and is used to construct cost-of-living
adjustments in union wage contracts and Social
Security benefits.
Poole and Rasche
Sometimes reference is also made to a “core”
inflation rate, usually measured by the CPI excluding
prices of food and energy products. The rationale
for excluding food and energy prices is that they can
be quite volatile, and hence longer-term inflation
trends can be obscured when they are included.
Starting in 2000, the FOMC chose to focus on a
different measure of inflation: changes in the price
index for personal consumption expenditures in the
national income accounts. This measure of inflation,
which for convenience we will call the “consumption
price index,” is reported monthly by the Bureau of
Economic Analysis of the Department of Commerce.
Although this index receives less public attention
than the CPI, it is preferred by the FOMC because
the methodology used in its construction reduces
the measurement bias relative to that in the CPI;
also, the coverage of goods and services in this index
is believed to better represent consumption patterns.
For example, prices of medical services are included
in the CPI only to the extent that such services are
paid directly by consumers. Prices of all medical
services are included in the consumption price
index whether those services are paid for directly
by consumers or are paid for on behalf of consumers
by third parties such as insurance companies.
In recent years, inflation as measured by the
consumption price index has been lower than that
measured by the CPI.4 Although the following discussion will refer primarily to the consumption price
index, no important issues depend on whether the
focus is on that index or the CPI.
What should we expect to observe in an economy where price stability prevails? If it were possible to measure the average level of prices with little
or no bias in such an economy, then over a period
of time an average measured inflation rate very close
to zero should be observed. From month-to-month
or quarter-to-quarter, positive or negative changes
of the inflation index will occur, but over time these
would average out to about zero.
2
The Housing Loan Progress Association. “Price Survey of the Housing
Market.” <http://jin.jcic.or.jp/stat/stats/>.
3
National Land Agency.
4
In August 2002 the Bureau of Labor Statistics introduced a new measure
of consumer prices—the chained consumer price index for all urban
consumers (C-CPI-U). Monthly data are available from December 1999.
The objective of the new index is to reduce the substitution bias that
is present in the CPI-U. Between December 1999 and December 2000
(the only period for which final estimates of the C-CPI-U are available),
the inflation rate measured by the C-CPI-U differs from that measured
by the consumption price index by only 0.1 percent.
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Poole and Rasche
What about prices of individual goods and services under such conditions? There would likely be
a dispersion of changes in the prices of individual
goods and services around zero. In fact, prices of
some goods and services could be continually falling,
while prices of other goods and services could be
continually rising. It is perfectly normal to experience
divergent trends of individual prices under conditions of overall price stability. Thus, trends in the
prices of individual goods or services cannot be used
to judge whether an economy is experiencing inflation or deflation.
An important influence on inflation data in the
United States over the past three years has been the
behavior of energy prices on world markets. In 1998,
energy prices collapsed as world demand dropped
dramatically in response to the crises in Asian economies. Petroleum inventories rose unexpectedly
and major producers, including OPEC nations, cut
production to stabilize prices and adjust inventories.
In 1999 and 2000, energy prices rose sharply as
economic activity boomed in the United States and
other major industrialized economies at a time when
world inventories of oil were particularly low. Leading up to 2002, as the U.S. economy sank into recession and economic growth slowed in Europe, energy
demand growth slowed and energy prices on world
markets fell again.
The average inflation rate over the four years
1994 through 1997 was 2.7 percent per year as
measured by the consumption price index. The
average inflation rate over the four years from 1998
through 2001 was 1.7 percent per year. The core
inflation component of the consumption price index
has fallen from 2.1 percent in the earlier period to
1.6 percent in the latter period. The conclusion
from these observations is that there has been a
small reduction in trend inflation, whether measured
by the total or the core consumption price index,
over the past four years.
No estimates of the biases in the index are so
large as to suggest that the true rate of inflation is
now negative—that is, the U.S. economy is not in a
deflationary situation. What, then, is the origin of
the “deflation threat” that has been featured in some
economic and newspaper commentaries? Some of
these discussions appear to concentrate unduly on
particular prices and on short-run data collected in
the immediate aftermath of the September 11 terrorist attacks. The change in the price index for personal
consumption expenditures for September 2001
compared with August 2001 was reported at –0.4
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percent. The decline is attributable to falling energy
prices and to a statistical artifact of the decision
made by the Bureau of Economic Analysis in measuring insurance claim payments as a result of the
September 11 attacks. The December 2001 consumption price index showed a decline of 0.2 percent
for the month and led to further press speculation
about deflation. Again, it is necessary to emphasize
that a focus on very short-term movements in the
price indexes can lead to misinterpretation of the
underlying trends of inflation or deflation in an
economy.
CHANGES IN RELATIVE PRICES
One of the great strengths of the U.S. economy
is that prices of individual goods and services fluctuate freely. These price changes allow markets to
signal how our productive resources can be allocated
most efficiently. The disparity among inflation rates
for particular goods and services over longer periods
of time is significant. From 1980 to 2000, the overall consumption price index rose 95 percent. Consider price behavior in a half-dozen categories within
overall personal consumption expenditures. Prices
of personal computers and peripheral equipment
stand out: such prices are estimated to have fallen
by 99 percent since 1980. Note that despite this
dramatic price decline, people do not talk about the
computer industry suffering from deflation. This is
a growth industry, driven by dramatic innovations
and increases in efficiency.
Prices of durable goods are estimated to have
increased by 20 percent since 1980, considerably
slower than the general inflation over this period.
Prices of nondurables are estimated to have increased
by 65 percent since 1980; nondurable goods prices
have risen more than durable goods prices, but still
considerably less than the overall rate of inflation.
Prices of food and beverages are estimated to have
increased 79 percent since 1980, somewhat slower
than the overall rate of inflation.
Consider some examples at the other extreme.
Since 1980, prices of tobacco and smoking products
are estimated to have increased 480 percent and
prices of medical services by 197 percent. In the
tables that show prices by various sectors, wide
differences in experience such as those mentioned
here can be seen.
Are falling prices, or prices that increase slowly
relative to the general rate of inflation, indicative of
“hard times” for particular industries? Sometimes,
but certainly not always. Consider personal comput-
FEDERAL RESERVE BANK OF ST. LOUIS
ers and consumer electronics in general (the latter
is included in the durable goods component of the
consumption price index). These are goods that have
demonstratively high income and price elasticities.
What that means is that the amounts consumers
buy increase a lot as incomes rise and/or prices fall.
Over time, as consumer incomes have increased
and prices have fallen, the size of the market for
these high-elasticity products has increased dramatically. Color TVs, camcorders, VCRs, DVDs, and personal computers, to name a few such products, are
all now common household items in the United
States. Many consumers can remember when these
products were either unknown or owned by relatively
few households.
This is an important point: expansion of the
markets for certain products occurred simultaneously with a fall in prices. Price deflation for these
goods was not inconsistent with prosperity in the
industries producing them. Indeed, declining prices
were essential to expanding these markets. The
fall in prices was the result of rapid productivity
increases from innovations in the production of
these items and/or their components. Firms found
it profitable to cut prices and expand production.
Workers in these industries found their improved
productivity rewarded in higher wages. Consumers,
workers, and shareholders all have benefited, even
though prices have fallen substantially over time.
High-demand elasticities are a critical element
in such success stories. In contrast, consider markets
for basic agricultural products in the United States.
Productivity improvement in U.S. agricultural production over the years has been tremendous. Prices
of these products have also fallen relative to goods
in general over the long run. However, both income
and price elasticities for agricultural products are
relatively low. Hence, economic growth and declining prices have not produced large increases in
consumption. As a result, fewer and fewer workers
have been required over time to produce more than
enough output to satisfy both domestic and foreign
demand. Farms have gone out of business, the number of people engaged in agricultural production
has decreased, and in recent years farm income
has been sustained by large “emergency” farm
appropriations out of the federal budget. Because
of the low price and income elasticities for agricultural goods, deflation in this industry means hard
times for many farmers.
Health care provides a really interesting case
of relative price changes. In part, the rapid rate of
price increase here represents innovation in the
Poole and Rasche
form of new products and/or improved procedures.
Such price changes really reflect significant quality
improvements. Ideally such quality improvements
would be incorporated into the measurement of a
standardized unit of medical services. With some
consumer durables, such as automobiles, statisticians
have been quite successful in measuring quality
improvement. In other areas, capturing quality
change into the measurement of a standard unit of
output is difficult if not impossible.
As an example, consider laparoscopic surgery
to remove the gall bladder. Not that long ago, gall
bladder surgery required a substantial period of
hospitalization, during which patient activity levels
were significantly restricted. Today, with laparoscopic
surgery, the length of the hospital stay is much
shorter and patient discomfort much less. Moreover,
the patient can resume reasonably normal activity,
including going to work, after a short postoperative
period. The patient and/or a third-party payer may
pay the surgeon substantially more today to remove
the gall bladder than 35 years ago, but does this
increase mean that the price properly measured is
dramatically higher? A well-constructed price index
might adjust for the reduction in the pecuniary cost
of confinement—fewer hospital days—from the
improved technology. However, it is unlikely that
any price index would reflect the improved quality
of the procedure represented by the reduced nonpecuniary costs of confinement and the shorter
recovery time now available. Hence the reported
change in the price index for such a procedure
certainly overstates the true rate of price change.
FLATION AND THE FED
The Fed’s goal is to maintain low and steady
inflation, so that expectations of changes in inflation
do not enter importantly in the decisions businesses
and households make. Using several different measures of inflation expectations, it is clear that longterm expected inflation has changed little in recent
years. There is no evidence that changing inflation
expectations figure importantly in economic decisions at this time.
Substantial variability in prices of individual
goods is consistent with stability in the overall inflation rate. The variability serves to allocate and reallocate resources across different sectors of the
economy, according to changes in consumer tastes
and differential trends in productivity advancement.
Simply put, it is normal that some industries are
growing while others are contracting.
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Poole and Rasche
A common business problem is to determine a
successful pricing strategy. One aspect of pricing
strategy is directly relevant to this discussion. When
a firm cuts prices to stimulate sales, it may not be
successful if its customers believe that even deeper
price cuts are around the corner. An expectation of
falling prices may, temporarily, reduce rather than
increase sales. It is for this reason that generalized
deflation can be so dangerous to the economy. A
widespread expectation of falling prices may lead
to declining demand across much of the economy
as people wait for lower prices in the future. Declining demand may force layoffs, which further depress
household and business confidence. Conversely,
inflation expectations can lead to rising demands
and anticipatory buying.
Many analysts seem to view low inflation and
high employment as competing goals. That is certainly not the only possible scenario. Maintaining
low and stable inflation contributes mightily to overall economic stability. Consider the situation in the
weeks following the terrorist attacks of September 11,
2001, when the economic outlook was highly
uncertain. The auto industry was successful in selling
a record number of cars in October 2001 through
price cuts in the form of zero-interest financing. If
consumers had reacted by expecting even deeper
price cuts and had delayed purchases, the situation
in early 2002 would have been very different. Overall, consumers view price cuts in today’s environment as a buying opportunity, not as a forecast of
further price cuts to come.
Clearly, the stability in the overall price environment—stability in longer-run expectations—is what
allows temporary price cuts to work to boost sales
and is an important element in stabilizing the general
economy. The current U.S. situation does not match
cases in the United States and elsewhere that historically have been associated with ongoing deflation.
The Federal Reserve pursued an expansionary monetary policy throughout 2001 that has contributed
to restoring equilibrium to the U.S. economy. What
policy actions will be appropriate going forward will
have to be determined as evidence arrives on the
strength and durability of the economic expansion.
We must be vigilant, but today it is likely that we
enjoy flation—no “in” and no “de.”
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A Case Study of a
Currency Crisis: The
Russian Default of 1998
Abbigail J. Chiodo and Michael T. Owyang
A
currency crisis can be defined as a speculative attack on a country’s currency that can
result in a forced devaluation and possible
debt default. One example of a currency crisis
occurred in Russia in 1998 and led to the devaluation
of the ruble and the default on public and private
debt.1 Currency crises such as Russia’s are often
thought to emerge from a variety of economic conditions, such as large deficits and low foreign reserves.
They sometimes appear to be triggered by similar
crises nearby, although the spillover from these contagious crises does not infect all neighboring economies—only those vulnerable to a crisis themselves.
In this paper, we examine the conditions under
which an economy can become vulnerable to a
currency crisis. We review three models of currency
crises, paying particular attention to the events leading up to a speculative attack, including expectations
of possible fiscal and monetary responses to impending crises. Specifically, we discuss the symptoms
exhibited by Russia prior to the devaluation of the
ruble. In addition, we review the measures that were
undertaken to avoid the crisis and explain why those
steps may have, in fact, hastened the devaluation.
The following section reviews the three generations of currency crisis models and summarizes the
conditions under which a country becomes vulnerable to speculative attack. The third section examines
the events preceding the Russian default of 1998 in
the context of a currency crisis. The fourth section
applies the aforementioned models to the Russian
crisis.
CURRENCY CRISES: WHAT DOES
MACROECONOMIC THEORY SUGGEST?
A currency crisis is defined as a speculative
attack on country A’s currency, brought about by
Abbigail J. Chiodo is a senior research associate and Michael T. Owyang
is an economist at the Federal Reserve Bank of St. Louis. The authors
thank Steven Holland, Eric Blankmeyer, John Lewis, and Rebecca
Beard for comments and suggestions and Victor Gabor at the World
Bank for providing real GDP data.
© 2002, The Federal Reserve Bank of St. Louis.
agents attempting to alter their portfolio by buying
another currency with the currency of country A.2
This might occur because investors fear that the
government will finance its high prospective deficit
through seigniorage (printing money) or attempt to
reduce its nonindexed debt (debt indexed to neither
another currency nor inflation) through devaluation.
A devaluation occurs when there is market pressure to increase the exchange rate (as measured by
domestic currency over foreign currency) because
the country either cannot or will not bear the cost
of supporting its currency. In order to maintain a
lower exchange rate peg, the central bank must buy
up its currency with foreign reserves. If the central
bank’s foreign reserves are depleted, the government
must allow the exchange rate to float up—a devaluation of the currency. This causes domestic goods
and services to become cheaper relative to foreign
goods and services. The devaluation associated with
a successful speculative attack can cause a decrease
in output, possible inflation, and a disruption in
both domestic and foreign financial markets.3
The standard macroeconomic framework
applied by Fleming (1962) and Mundell (1963) to
international issues is unable to explain currency
crises. In this framework with perfect capital mobility, a fixed exchange rate regime results in capital
flight when the central bank lowers interest rates
and results in capital inflows when the central bank
raises interest rates. Consequently, the efforts of the
monetary authority to change the interest rate are
undone by the private sector. In a flexible exchange
rate regime, the central bank does not intervene in
the foreign exchange market and all balance of payment surpluses or deficits must be financed by
private capital outflows or inflows, respectively.
The need to explain the symptoms and remedies
of a currency crisis has spawned a number of models
designed to incorporate fiscal deficits, expectations,
and financial markets into models with purchasing
power parity. These models can be grouped into
three generations, each of which is intended to
explain specific aspects that lead to a currency crisis.
1
Kharas, Pinto, and Ulatov (2001) provide a history from a fundamentalsbased perspective, focusing on taxes and public debt issues. We
endeavor to incorporate a role for monetary policy.
2
The speculative attack need not be successful to be dubbed a currency
crisis.
3
Burnside, Eichenbaum, and Rebelo (2001) show that the government
has at its disposal a number of mechanisms to finance the fiscal costs
of the devaluation. Which policy is chosen determines the inflationary
effect of the currency crisis.
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Chiodo and Owyang
First-Generation Models
(1997), and others are particularly useful in explaining self-fulfilling contagious currency crises. One
possible scenario suggested by these models involves
a devaluation in one country affecting the price level
(and therefore the demand for money) or the current
account by a reduction of exports in a neighboring
country. In either case, devaluation in a neighboring
country becomes increasingly likely.
Eichengreen, Rose, and Wyplosz (1997) find
that a correlation exists between the likelihood of
default across countries. That is, the probability of
a speculative attack in country A increases when
its trading partner, country B, experiences an attack
of its own. They estimate that a speculative attack
somewhere in the world increases the probability
of a domestic currency crisis by about 8 percent.
The spillover from one currency crisis into neighboring countries can be attributed to a number of different scenarios. First, an economic event, such as a
war or an oil price shock, that is common to a geographical area or a group of trading partners can
affect those economies simultaneously; in addition,
an individual shock can be transmitted from one
country to another via trade. Second, a devaluation
or default in one country can raise expectations of
the likelihood of a devaluation in other countries.
Expectations can rise either because countries are
neighboring trade partners or because they have
similar macroeconomic policies or conditions (e.g.,
high unemployment or high government debt). Since
the crises are self-fulfilling, these expectations make
the likelihood of devaluation increase as well. Lastly,
a devaluation can be transmitted via world financial
markets to other susceptible countries. Any combination of scenarios can serve as an explanation of
the apparent international linkages that are responsible for the spread of speculative attacks from one
country to another.
The first-generation models of a currency crisis
developed by Krugman (1979) and Flood and Garber
(1984) rely on government debt and the perceived
inability of the government to control the budget
as the key causes of the currency crisis. These models
argue that a speculative attack on the domestic
currency can result from an increasing current
account deficit (indicating an increase in the trade
deficit) or an expected monetization of the fiscal
deficit. The speculative attack can result in a sudden
devaluation when the central bank’s store of foreign
reserves is depleted and it can no longer defend the
domestic currency. Agents believe that the government’s need to finance the debt becomes its overriding concern and eventually leads to a collapse
of the fixed exchange rate regime and to speculative
attacks on the domestic currency.
Krugman presents a model in which a fixed
exchange rate regime is the inevitable target of a
speculative attack. An important assumption in the
model is that a speculative attack is inevitable. The
government defends the exchange rate peg with its
store of foreign currency. As agents change the composition of their portfolios from domestic to foreign
currency (because rising fiscal deficits increase the
likelihood of devaluation, for example), the central
bank must continue to deplete its reserves to stave
off speculative attacks. The crisis is triggered when
agents expect the government to abandon the peg.
Anticipating the devaluation, agents convert their
portfolios from domestic to foreign currency by buying foreign currency from the central bank’s reserves.
The central bank’s reserves fall until they reach the
critical point when a peg is no longer sustainable
and the exchange rate regime collapses. The key
contribution of the first-generation model is its
identification of the tension between domestic fiscal
policy and the fixed exchange rate regime.4
While the first-generation models help explain
some of the fundamentals that cause currency crises,
they are lacking in two key aspects. First, the standard first-generation model requires agents to suddenly increase their estimates of the likelihood of
a devaluation (perhaps through an increase in
expected inflation). Second, they do not explain
why the currency crises spread to other countries.
The literature on contagious currency crises
has helped clarify the spread of devaluations and
their magnitudes. However, the first two generations
of models have not provided a policy recommendation for the central bank in the face of a crisis. Indeed,
Krugman’s first-generation model suggests that a
crisis cannot be thwarted—that once a devaluation
is expected, it is inevitable. Thus, third-generation
Second-Generation Models
4
The second-generation models suggested by
Obstfeld (1994), Eichengreen, Rose, and Wyplosz
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Third-Generation Models
Obstfeld (1986) outlines a multiple equilibrium model in which a
currency crisis is brought about when government policy (financing
a deficit through seignorage, for example) causes agents to expect a
crisis and push the economy to a bad equilibrium.
FEDERAL RESERVE BANK OF ST. LOUIS
currency crisis models suggested by Krugman (1999)
and Aghion, Bacchetta, and Banarjee (2000, 2001)
examine the effects of monetary policy in a currency
crisis.
These models argue that fragility in the banking
and financial sector reduces the amount of credit
available to firms and increases the likelihood of a
crisis. They suggest that a currency crisis is brought
on by a combination of high debt, low foreign
reserves, falling government revenue, increasing
expectations of devaluation, and domestic borrowing constraints. Firms’ access to domestic loans is
constrained by assuming they can borrow only a
portion of their wealth (somewhat similar to requiring the firm to collateralize all domestic loans). In
these lending-constrained economies, the credit
market does not clear: interest rates rise, but not
enough to compensate investors for the increase in
perceived default risk. Increasing the domestic interest rate, then, does not raise the supply of domestic
lending in the normal fashion. Moral hazard, a firm’s
ability to take its output and default on its loan, forces
banks to restrict lending. Therefore, increasing
the interest rate reduces the amount of loans as it
increases firms’ incentive to default.
These third-generation models offer a role for
monetary policy (aside from the decision to abandon
the exchange rate peg) through a binding credit
constraint in an imperfect financial market. If firms’
leverage in the domestic market is substantially
reduced, they may be forced to accumulate a large
amount of foreign-denominated debt. When, in
domestic markets, the amount of available lending
depends on the nominal interest rate, the central
bank can deepen a crisis by further reducing firms’
ability to invest. The typical prescription for a currency crisis is to raise interest rates and raise the
demand for domestic currency.5 However, in the
third-generation models, an interest rate increase
can greatly affect the amount of lending and further
restrict firms’ access to financial capital. In cases
where lending is highly sensitive to the interest rate,
an increase in the nominal interest rate can be
detrimental, altering the productive capacity of the
economy by stifling investment. The perceived drop
in output puts additional pressure on the exchange
rate, perhaps through actual or expected tax revenue,
exacerbating the crisis. In this situation, an alternative strategy for the central bank is warranted: it is
actually beneficial to lower the interest rate to spur
investment.6
These three generations of models suggest four
Chiodo and Owyang
factors that can influence the onset and magnitude
of a currency crisis. Domestic public and private
debt, expectations, and the state of financial markets
can, in combination with a pegged exchange rate,
determine whether a country is susceptible to a
currency crisis and also determine the magnitude
and success of a speculative attack. In the next
section, we provide an example of a recent currency
crisis, keeping these four factors in mind.
THE RUSSIAN DEFAULT: A BRIEF
HISTORY
After six years of economic reform in Russia,
privatization and macroeconomic stabilization had
experienced some limited success. Yet in August
1998, after recording its first year of positive economic growth since the fall of the Soviet Union, Russia
was forced to default on its sovereign debt, devalue
the ruble, and declare a suspension of payments by
commercial banks to foreign creditors. What caused
the Russian economy to face a financial crisis after
so much had been accomplished? This section
examines the sequence of events that took place in
Russia from 1996 to 1998 and the aftermath of the
crisis. (For a timeline, see Table 1.)
1996 and 1997
Optimism and Reform. In April 1996, Russian
officials began negotiations to reschedule the payment of foreign debt inherited from the former
Soviet Union. The negotiations to repay its sovereign
debt were a major step toward restoring investor
confidence. On the surface, 1997 seemed poised
to be a turning point toward economic stability.
• The trade surplus was moving toward a
balance between exports and imports (see
Figure 1).
• Relations with the West were promising: the
World Bank was prepared to provide expanded
assistance of $2 to $3 billion per year and the
International Monetary Fund (IMF) continued
to meet with Russian officials and provide aid.
• Inflation had fallen from 131 percent in 1995
to 22 percent in 1996 and 11 percent in 1997
(see Figure 2).
• Output was recovering slightly.
5
Flood and Jeanne (2000) argue that increasing domestic currency
interest rates can act only to speed devaluation.
6
The expansionary monetary policy in this case is assumed not to be
inflationary since it only alleviates liquidity constraints.
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Chiodo and Owyang
Table 1
A Timeline of Russian Events
April 1996
Negotiations with the Paris and London Clubs for repayment of Soviet debt begin.
1997
Trade surplus moving toward balance.
Inflation around 11 percent.
Oil selling at $23/barrel.
Analysts predict better credit ratings for Russia.
Russian banks increase foreign liabilities.
Real wages sagging.
Only 40 percent of workforce being paid fully and on time.
Public-sector deficit high.
September/October 1997
Negotiations with Paris and London Clubs completed.
November 11, 1997
Asian crisis causes a speculative attack on the ruble.
CBR defends the ruble, losing $6 billion.
December 1997
Year ends with 0.8 percent growth.
Prices of oil and nonferrous metal begin to drop.
February 1998
New tax code submitted to the Duma.
IMF funds requested.
March 23, 1998
Yelstin fires entire government and appoints Kiriyenko.
Continued requests for IMF funds.
April 1998
Another speculative attack on the ruble.
April 24, 1998
Duma finally confirms Kiriyenko’s appointment.
Early May 1998
Dubinin warns government ministers of impending debt crisis, with reporters in the
audience.
Kiriyenko calls the Russian government “quite poor.”
May 19, 1998
CBR increases lending rate from 30 percent to 50 percent and defends the ruble
with $1 billion.
Mid May 1998
Lawrence Summers not granted audience with Kiriyenko.
Oil prices continue to decrease.
Oil and gas oligarchs advocate devaluation of ruble to increase value of their exports.
May 23, 1998
IMF leaves Russia without agreement on austerity plan.
May 27, 1998
CBR increases the lending rate again to 150 percent.
Summer 1998
Russian government formulates and advertises anti-crisis plan.
July 20, 1998
IMF approves an emergency aid package (first disbursement to be $4.8 billion).
August 13, 1998
Russian stock, bond, and currency markets weaken as a result of investor fears of
devaluation; prices diminish.
August 17, 1998
Russian government devalues the ruble, defaults on domestic debt, and declares a
moratorium on payment to foreign creditors.
August 23-24, 1998
Kiriyenko is fired.
September 2, 1998
The ruble is floated.
December 1998
Year ends with a decrease in real output of 4.9 percent.
NOTE: CBR, Central Bank of Russia.
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FEDERAL RESERVE BANK OF ST. LOUIS
Chiodo and Owyang
Figure 1
Figure 2
Russian Merchandise Trade Balance
CPI Inflation
Percent Change over Previous Year
US$ Millions
30,000
Percent
Exports
250
25,000
200
20,000
150
Imports
15,000
100
10,000
50
5,000
1994:Q1
1996:Q1
1998:Q1
2000:Q1
0
Dec
1995
SOURCE: CBR.
Mar
1997
Jun
1998
Sep
1999
Dec
2000
SOURCE: IMF.
• A narrow exchange rate band was in place
keeping the exchange rate between 5 and 6
rubles to the dollar (see Figure 3).
• And oil, one of Russia’s largest exports, was
selling at $23 per barrel—a high price by
recent standards. (Fuels made up more than
45 percent of Russia’s main export commodities in 1997.)
In September 1997, Russia was allowed to join
the Paris Club of creditor nations after rescheduling
the payment of over $60 billion in old Soviet debt
to other governments. Another agreement for a
23-year debt repayment of $33 billion was signed
a month later with the London Club. Analysts predicted that Russia’s credit ratings would improve,
allowing the country to borrow less expensively.
Limitations on the purchase of government securities
by nonresident investors were removed, promoting
foreign investment in Russia. By late 1997, roughly
30 percent of the GKO (a short-term government
bill) market was accounted for by nonresidents. The
economic outlook appeared optimistic as Russia
ended 1997 with reported economic growth of 0.8
percent.
Revenue, Investment, and Debt. Despite the
prospects for optimism, problems remained. On
average, real wages were less than half of what they
were in 1991, and only about 40 percent of the
work force was being paid in full and on time. Per
capita direct foreign investment was low, and regu-
Figure 3
Exchange Rate
Ruble/US$
35
30
25
20
15
10
5
0
Dec
1995
Mar
1997
Jun
1998
Sep
1999
Dec
2000
SOURCE: IMF (end of period data).
lation of the natural monopolies was still difficult
due to unrest in the Duma, Russia’s lower house
of Parliament. Another weakness in the Russian
economy was low tax collection, which caused the
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Chiodo and Owyang
public sector deficit to remain high. The majority
of tax revenues came from taxes that were shared
between the regional and federal governments,
which fostered competition among the different
levels of government over the distribution. According to Shleifer and Treisman (2000), this kind of
tax sharing can result in conflicting incentives for
regional governments and lead them to help firms
conceal part of their taxable profit from the federal
government in order to reduce the firms’ total tax
payments. In return, the firm would then make
transfers to the accommodating regional government. This, Shleifer and Treisman suggest, may
explain why federal revenues dropped more rapidly
than regional revenues.
Also, the Paris Club’s recognition of Russia as a
creditor nation was based upon questionable qualifications. One-fourth of the assets considered to
belong to Russia were in the form of debt owed to
the former Soviet Union by countries such as Cuba,
Mongolia, and Vietnam. Recognition by the Paris
Club was also based on the old, completely arbitrary
official Soviet exchange rate of approximately 0.6
rubles to the dollar (the market exchange rate at
the time was between 5 and 6 rubles to the dollar).
The improved credit ratings Russia received from
its Paris Club recognition were not based on an
improved balance sheet. Despite this, restrictions
were eased and lifted and Russian banks began
borrowing more from foreign markets, increasing
their foreign liabilities from 7 percent of their assets
in 1994 to 17 percent in 1997.
Meanwhile, Russia anticipated growing debt
payments in the coming years when early credits
from the IMF would come due. Policymakers faced
decisions to decrease domestic borrowing and
increase tax collection because interest payments
were such a large percentage of the federal budget.
In October 1997, the Russian government was counting on 2 percent economic growth in 1998 to compensate for the debt growth. Unfortunately, events
began to unfold that would further strain Russia’s
economy; instead of growth in 1998, real GDP
declined 4.9 percent.
The Asian Crisis. A few months earlier, in
the summer of 1997, countries in the Pacific Rim
experienced currency crises similar to the one that
eventually affected Russia. In November 1997, after
the onset of this East Asian crisis, the ruble came
under speculative attack. The Central Bank of Russia
(CBR) defended the currency, losing nearly $6 billion
(U.S. dollars) in foreign-exchange reserves. At the
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same time, non-resident holders of short-term
government bills (GKOs) signed forward contracts
with the CBR to exchange rubles for foreign currency, which enabled them to hedge exchange rate
risk in the interim period.7 According to Desai
(2000), they did this in anticipation of the ruble losing value, as Asian currencies had. Also, a substantial
amount of the liabilities of large Russian commercial
banks were off-balance-sheet, consisting mostly
of forward contracts signed with foreign investors.
Net obligations of Russian banks for such contracts
were estimated to be at least $6 billion by the first
half of 1998. Then another blow was dealt to the
Russian economy: in December 1997, the prices
of oil and nonferrous metal, up to two-thirds of
Russia’s hard-currency earnings, began to drop.
1998
Government, Risk, and Expectations. With
so many uncertainties in the Russian economy,
investors turned their attention toward Russian
default risk. To promote a stable investment environment, in February 1998, the Russian government
submitted a new tax code to the Duma, with fewer
and more efficient taxes. The new tax code was
approved in 1998, yet some crucial parts that were
intended to increase federal revenue were ignored.
Russian officials sought IMF funds but agreements
could not be reached. By late March the political
and economic situation had become more dire, and,
on March 23, President Yeltsin abruptly fired his
entire government, including Prime Minister Viktor
Chernomyrdin. In a move that would challenge
investor confidence even further, Yeltsin appointed
35-year-old Sergei Kiriyenko, a former banking and
oil company executive who had been in government
less than a year, to take his place.
While fears of higher interest rates in the United
States and Germany made many investors cautious,
tensions rose in the Russian government. The executive branch, the Duma, and the CBR were in conflict.
Prompted by threats from Yeltsin to dissolve Parliament, the Duma confirmed Kiriyenko’s appointment
on April 24 after a month of stalling. In early May,
during a routine update, CBR chair Sergei Dubinin
warned government ministers of a debt crisis within
the next three years. Unfortunately, reporters were
in the audience. Since the Asian crisis had heightened
investors’ sensitivity to currency stability, Dubinin’s
7
The requirement of forward contracts was the CBR’s way of preventing
runs on its foreign currency reserves.
FEDERAL RESERVE BANK OF ST. LOUIS
restatement of bank policy was misinterpreted to
mean that the Bank was considering a devaluation
of the ruble. In another public relations misunderstanding, Kiriyenko stated in an interview that tax
revenue was 26 percent below target and claimed
that the government was “quite poor now.” In actuality, the government was planning to cut government
spending and accelerate revenue, but these plans
were never communicated clearly to the public.
Instead, people began to expect a devaluation of
the ruble.
Investors’ perceptions of Russia’s economic
stability continued to decline when Lawrence
Summers, one of America’s top international-finance
officials, was denied a meeting with Kiriyenko while
in Russia. An inexperienced aide determined that
Summers’s title, Deputy Secretary of the Treasury,
was unworthy of Kiriyenko’s audience and the two
never met. At the same time, the IMF left Russia,
unable to reach an agreement with policymakers
on a 1998 austerity plan. Word spread of these incidents, and big investors began to sell their government bond portfolios and Russian securities,
concerned that relations between the United States
and Russia were strained.
Liquidity, Monetary Policy, and Fiscal Policy.
By May 18, government bond yields had swelled
to 47 percent. With inflation at about 10 percent,
Russian banks would normally have taken the
government paper at such high rates. Lack of confidence in the government’s ability to repay the
bonds and restricted liquidity, however, did not
permit this. As depositors and investors became
increasingly cautious of risk, these commercial
banks and firms had less cash to keep them afloat.
The federal government’s initiative to collect more
taxes in cash lowered banks’ and firms’ liquidity.8
Also, in 1997, Russia had created a U.S.-style treasury system with branches, which saved money
and decreased corruption, yet also decreased the
amount of cash that moved through banks. The
banks had previously used these funds to buy bonds.
Also, household ruble deposits increased by only
1.3 billion in 1998, compared with an increase of
29.8 billion in 1997.
The CBR responded by increasing the lending
rate to banks from 30 to 50 percent, and in two days
used $1 billion of Russia’s low reserves to defend
the ruble. (Figure 4 shows the lending rate.) However,
by May 27, demand for bonds had plummeted so
much that yields were more than 50 percent and
the government failed to sell enough bonds at its
Chiodo and Owyang
Figure 4
Lending Rate
Percent
160
140
120
100
80
60
40
20
0
Jul
1996
Feb
1997
Nov
1997
Mar
1998
Jun
1998
Mar
2000
Nov
2000
SOURCE: CBR.
weekly auction to refinance the debt coming due.
Meanwhile, oil prices had dropped to $11 per
barrel, less than half their level a year earlier. Oil
and gas oligarchs were advocating a devaluation of
the ruble, which would increase the ruble value of
their exports. In light of this, the CBR increased the
lending rate again, this time to 150 percent. CBR
chairman Sergei Dubinin responded by stating
“When you hear talk of devaluation, spit in the eye
of whoever is talking about it” (quoted in Shleifer
and Treisman, 2000, p. 149).
The government formed and advertised an anticrisis plan, requested assistance from the West, and
began bankruptcy processes against three companies with large debts from back taxes. Kiriyenko
met with foreign investors to reassure them. Yeltsin
made nightly appearances on Russian television,
calling the nation’s financial elite to a meeting at
the Kremlin where he urged them to invest in Russia.
In June the CBR defended the ruble, losing $5 billion
in reserves.
Despite all of the government efforts being made,
there was widespread knowledge of $2.5 to $3 billion
8
As a result of a 1998 elimination of tax-offsets paper issued by government agencies to pay for goods and services, the receipts of which
could be used to decrease their tax duties, banks and companies were
forced to provide more cash to pay their taxes, thus lowering their
liquidity.
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Chiodo and Owyang
was down 65 percent with a small number of shares
actually traded. From January to August the stock
market had lost more than 75 percent of its value,
39 percent in the month of May alone. (Figure 5
shows the Russian stock market’s boom and bust.)
Russian officials were left with little choice. On
August 17 the government floated the exchange rate,
devalued the ruble, defaulted on its domestic debt,
halted payment on ruble-denominated debt (primarily GKOs), and declared a 90-day moratorium on
payment by commercial banks to foreign creditors.
Figure 5
The Russian Stock Market
Daily Observations (Sept. 1, 1995=100)
600
500
400
300
The Aftermath
200
100
0
Jan
1996
Dec
1996
Dec
1997
Dec
1998
Dec
1999
Dec
2000
Nov
2001
SOURCE: <http://red-stars.com/financial>.
in loans from foreign investors to Russian corporations and banks that were to come due by the end
of September. In addition, billions of dollars in ruble
futures were to mature in the fall. In July the IMF
approved additional assistance of $11.2 billion, of
which $4.8 billion was to be disbursed immediately.
Yet between May and August, approximately $4
billion had left Russia in capital flight, and in 1998
Russia lost around $4 billion in revenue due to sagging oil prices. After losing so much liquidity, the
IMF assistance did not provide much relief.
The Duma, in an effort to protect natural monopolies from stricter regulations, eliminated crucial
parts of the IMF-endorsed anti-crisis program before
adjourning for vacation. The government had hoped
that the anti-crisis plan would bring in an additional
71 billion rubles in revenue. The parts that the Duma
actually passed would have increased it by only 3
billion rubles. In vain, lawmakers requested that the
Duma reconvene, lowering investors’ confidence
even further.
Default and Devaluation. On August 13, 1998,
the Russian stock, bond, and currency markets
collapsed as a result of investor fears that the
government would devalue the ruble, default on
domestic debt, or both. Annual yields on rubledenominated bonds were more than 200 percent.
The stock market had to be closed for 35 minutes
as prices plummeted. When the market closed, it
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Russia ended 1998 with a decrease in real output of 4.9 percent for the year instead of the small
growth that was expected. The collapse of the ruble
created an increase in Russia’s exports while imports
remained low (see Figure 1). Since then, direct
investments into Russia have been inconsistent at
best. Summarized best by Shleifer and Treisman
(2000), “the crisis of August 1998 did not only undermine Russia’s currency and force the last reformers
from office…it also seemed to erase any remaining
Western hope that Russia could successfully reform
its economy.”
Some optimism, however, still persists. Figure
6 shows Russian real GDP growth, which grew 8.3
percent in 2000 and roughly 5 percent in 2001—
lower but still positive. Imports trended up in the
first half of 2001, helping to create a trade balance.
At the same time, consumer prices grew 20.9 percent
and 21.6 percent in 2000 and 2001, respectively,
compared with a 92.6 percent increase in 1999.
Most of the recovery so far can be attributed to the
import substitution effect after the devaluation; the
increase in world prices for Russia’s oil, gas, and
commodity exports; monetary policies; and fiscal
policies that have led to the first federal budget surplus (in 2000) since the formation of the Russian
Federation.
HOW DO THE THEORIES EXPLAIN
THE RUSSIAN CRISIS?
As discussed earlier, four major factors influence
the onset and success of a speculative attack. These
key ingredients are (i) an exchange rate peg and a
central bank willing or obligated to defend it with a
reserve of foreign currency, (ii) rising fiscal deficits
that the government cannot control and therefore
is likely to monetize (print money to cover the deficit),
(iii) central bank control of the interest rate in a
FEDERAL RESERVE BANK OF ST. LOUIS
fragile credit market, and (iv) expectations of devaluation and/or rising inflation. In this section we discuss these aspects in the context of the Russian
devaluation. We argue that an understanding of all
three generations of models is necessary to evaluate
the Russian devaluation. Krugman’s (1979) firstgeneration model explains the factors that made
Russia susceptible to a crisis. The second-generation
models show how contagion and other factors can
change expectations to trigger the crisis. The thirdgeneration models show how the central bank can
act to prevent or mitigate the crisis.
The Exchange Rate and the Peg
When the ruble came under attack in November
1997 and June 1998, policymakers defended the
ruble instead of letting it float. The real exchange
rate did not vary much during 1997. Clearly a primary component of a currency crisis in the models
described here is the central bank’s willingness to
defend an exchange rate peg. Prior to August 1998,
the Russian ruble was subject to two speculative
attacks. The CBR made efforts both times to defend
the ruble. The defense was successful in November
1997 but fell short in the summer of 1998. Defending the ruble depleted Russia’s foreign reserves.
Once depleted, the Russian government had no
choice but to devalue on August 17, 1998.
Revenue, Deficits, and Fiscal Policy
Russia’s high government debt and falling revenue contributed significantly to its susceptibility
to a speculative attack. Russia’s federal tax revenues
were low because of both low output and the opportunistic practice of local governments helping firms
conceal profits. The decrease in the price of oil also
lowered output, further reducing Russia’s ability to
generate tax revenue. Consequently, Russia’s revenue
was lower than expected, making the ruble ripe for
a speculative attack. In addition, a large amount of
short-term foreign debt was coming due in 1998,
making Russia’s deficit problem even more serious.
Krugman’s first-generation model suggests that a
government finances its deficit by printing money
(seigniorage) or depleting its reserves of foreign
currency. Under the exchange rate peg, however,
Russia was unable to finance through seigniorage.
Russia’s deficit, low revenue, and mounting interest
payments put pressure on the exchange rate. Printing rubles would only have increased this pressure
because the private sector would still have been able
Chiodo and Owyang
Figure 6
Real GDP Growth
Quarterly Change from Previous Year
Percent
11
10
8
6
4
2
0
–2
–4
–6
–8
–10
1995:Q1
1996:Q2
1997:Q3
1998:Q4
2000:Q1
2001:Q2
SOURCE: Russian Statistics Committee and International
Bank for Reconstruction and Development staff estimates.
to trade rubles for foreign currency at the fixed rate.
Thus, whether directly through intervention in the
foreign currency market or indirectly by printing
rubles, Russia’s only alternative under the fixed
exchange rate regime was to deplete its stock of
foreign reserves.
Monetary Policy, Financial Markets,
and Interest Rates
During the summer of 1998, the Russian economy was primed for the onset of a currency crisis.
In an attempt to avert the crisis, the CBR intervened
by decreasing the growth of the money supply and
twice increasing the lending rate to banks, raising
it from 30 to 150 percent. Both rate hikes occurred
in May 1998, the same month in which the Russian
stock market lost 39 percent of its value. The rise
in interest rates had two effects. First, it exacerbated
Russia’s revenue problems. Its debt grew rapidly as
interest payments mounted. This put pressure on
the exchange rate because investors feared that
Russia would devalue to finance its non-denominated
debt. Second, high government debt prevented firms
from obtaining loans for new capital and increasing
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Chiodo and Owyang
eign reserves held by the CBR were so low that the
government could no longer defend the currency
by buying rubles.
Expectations
Three components fueled the expectations of
Russia’s impending devaluation and default. First,
the Asian crisis made investors more conscious of
the possibility of a Russian default. Second, public
relations errors, such as the publicized statement
to government ministers by the CBR and Kiriyenko’s
refusal to grant Lawrence Summers an audience,
perpetuated agents’ perceptions of a political crisis
within the Russian government. Third, the revenue
shortfall signaled the possible reduction of the public
debt burden via an increase in the money supply.
This monetization of the debt can be associated
with a depreciation either indirectly through an
increase in expected inflation or directly in order
to reduce the burden of ruble-denominated debt.
Each of these three components acted to push the
Russian economy from a stable equilibrium to one
vulnerable to speculative attack.
CONCLUSION
In this paper we investigate the events that lead
up to a currency crisis and debt default and the
policies intended to avert it. Three types of models
exist to explain currency crises. Each model explains
some factor that has been hypothesized to cause a
crisis. After reviewing the three generations of currency crisis models, we conclude that four key
ingredients can trigger a crisis: a fixed exchange
rate, fiscal deficits and debt, the conduct of monetary
policy, and expectations of impending default. Using
the example of the Russian default of 1998, we show
that the prescription of contractionary monetary
policy in the face of a currency crisis can, under
certain conditions, accelerate devaluation. While
we believe that deficits and the Asian financial crisis
contributed to Russia’s default, the first-generation
model proposed by Krugman (1979) and Flood and
Garber (1984) and the second-generation models
proposed by Obstfeld (1984) and Eichengreen, Rose,
and Wyplosz (1997) do not capture every aspect of
the crisis. Specifically, these models do not address
the conduct of monetary policy. It is therefore necessary to incorporate both the first-generation
model’s phenomenon of increasing fiscal deficits
and the third-generation model’s financial sector
fragility. We conclude that the modern currency
16
N OV E M B E R / D E C E M B E R 2 0 0 2
crisis is a symptom of an ailing domestic economy.
In that light, it is inappropriate to attribute a single
prescription as the prophylactic or cure for a currency crisis.
REFERENCES
Aghion, Philippe; Bacchetta, Philippe and Banerjee, Abhijit.
“A Simple Model of Monetary Policy and Currency Crises.”
European Economic Review, May 2000, 44(4-6), pp. 728-38.
___________; ___________ and ___________. “Currency
Crises and Monetary Policy in an Economy with Credit
Constraints.” European Economic Review, June 2001, 45(7),
pp. 1121-50.
Ahrend, Rudiger. “Foreign Direct Investment Into Russia—
Pain Without Gain? A Survey of Foreign Direct Investors.”
Russian Economic Trends, June 2000, 9(2), pp. 26-33.
Burnside, Craig; Eichenbaum, Martin, and Rebelo, Sergio.
“On The Fiscal Implications of Twin Crises.” Working
Paper No. 8277, National Bureau of Economic Research,
May 2001.
Desai, Padma. “Why Did the Ruble Collapse in August 1998?”
American Economic Review: Papers and Proceedings, May
2000, 90(2), pp. 48-52.
Economist. “Surplus to Requirements.” 8 July 2000, p. 79.
Eichengreen, Barry; Rose, Andrew and Wyplosz, Charles.
“Contagious Currency Crisis.” March 1997.
<http://www.haas.berkeley.edu/~arose/>.
Fischer, Stanley. “The Russian Economy at the Start of
1998.” U.S.-Russian Investment Symposium, Harvard
University, Cambridge, MA, 9 January 1998.
Flemming, Marcus. “Domestic Financial Policies Under
Fixed and Under Floating Exchange Rates.” IMF Staff
Papers, 9 November 1962.
Flood, Robert P. and Garber, Peter M. “Collapsing Exchange
Rate Regimes: Some Linear Examples.” Journal of
International Economics, August 1984, 17(1-2), pp 1-13.
___________ and Jeanne, Olivier. “An Interest Rate Defense
of a Fixed Exchange Rate?” Working Paper WP/00/159,
International Monetary Fund, October 2000.
Kharas, Homi; Pinto, Brian and Ulatov, Sergei. “An Analysis
of Russia’s 1998 Meltdown: Fundamentals and Market
Signals.” Brookings Papers on Economic Activity, 2001,
0(1), pp. 1-67.
FEDERAL RESERVE BANK OF ST. LOUIS
Chiodo and Owyang
Krugman, Paul. “A Model of Balance-of-Payment Crises.”
Journal of Money, Credit, and Banking, August 1979, 11(3),
pp. 311-25.
___________. “Balance Sheets, the Transfer Problem, and
Financial Crises.” International Tax and Public Finance,
November 1999, 6(4), pp. 459-72.
Malleret, Thierry; Orlova, Natalia and Romanov, Vladimir.
“What Loaded and Triggered the Russian Crisis?” PostSoviet Affairs, April-June 1999, 15(2), pp. 107-29.
Mudell, R.A. “Capital Mobility and Stabilization Policy Under
Fixed and Flexible Exchange Rates.” Canadian Journal of
Economics, November 1963.
Obstfeld, Maurice. “Rational and Self-Fulfilling Balance-ofPayments Crises.” American Economic Review, March 1986,
76(1), pp. 72-81.
___________. “The Logic of Currency Crises.” Cahiers
Economiques et Monetaires, Banque de France, 1994, 43,
pp. 189-213.
Popov, A. “Lessons of the Currency Crisis in Russia and in
Other Countries.” Problems of Economic Transition, May
2000, 43(1), pp. 45-73.
Russian Economic Trends. Various months.
Shleifer, Andre and Treisman, Daniel. Without A Map:
Political Tactics and Economic Reform in Russia. Cambridge,
MA: MIT Press, 2000.
Velasco, Andrés. “Financial Crises in Emerging Markets.”
National Bureau of Economic Research Reporter, Fall
1999, pp.17-19.
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REVIEW
Asset Mispricing,
Arbitrage, and Volatility
William R. Emmons and Frank A. Schmid
fter nearly four decades, academic economists continue to debate financial-market
efficiency as vigorously as ever.1 The original
theoretical arguments put forward in favor of efficient markets were based on the notion of stabilizing speculation in the form of arbitrage (Friedman,
1953). Simply put, arbitrage is “the simultaneous
purchase and sale of the same, or essentially similar,
security in two different markets for advantageously
different prices” (Sharpe and Alexander, 1990). In
theory, a perfectly hedged trading position of this
sort could be executed at no cost (as the short-sale
proceeds are used to finance the long position).
Vigilant traders on the look-out for just such arbitrage opportunities would ensure that no one could
consistently “beat the market”—the hallmark of
efficient markets theory.
The academics’ logical case for efficient markets
boils down to a pair of simple rhetorical questions:
Why would utility-maximizing traders leave unexploited any profitable opportunities (after adjusting
properly for risk)? And if no risk-adjusted “free
lunches” exist, how could market prices be predictable enough to make money? For several decades,
empirical evidence piled up both for and against
market efficiency. As of the early 1990s, neither
side could claim total vindication. As the 1990s
progressed, however, the weight of the evidence
seemed to tip toward those who claimed asset prices
were, at least to some extent, predictable (Campbell,
Lo, and MacKinlay, 1997, Chaps. 2 and 7).
The academic asset-pricing literature today is
dominated by attempts to explain why and to what
extent the price movements of financial assets are
predictable. One potential explanation of stockreturn predictability is that markets are efficient
(“no free lunch”) but expected returns are timevarying, perhaps being linked to the business cycle.
For example, expected returns may be highest when
economic risks are perceived to be high, such as at
or near the bottom of a business cycle. Conversely,
A
William R. Emmons is an economist and Frank A. Schmid is a senior
economist at the Federal Reserve Bank of St. Louis. William V. Bock
provided research assistance.
© 2002, The Federal Reserve Bank of St. Louis.
expected returns may be lowest when economic
risks are perceived to be low, at or near a businesscycle peak. Thus, the simple random-walk model
of stock returns may be false, but a relevant notion
of market efficiency survives because high returns
are earned only by taking large amounts of risk. A
different type of explanation of return predictability
rejects market efficiency and focuses on market
imperfections of various sorts, such as incomplete
stock-market participation by households, significant
transactions costs, changes in investor sentiment,
or limited wealth and liquidity resources to conduct
arbitrage (as in the current article).2
Whatever its economic explanation, mounting
evidence of return predictability leads Campbell, Lo,
and MacKinlay (1997, p. 24) to suggest that it is time
for financial economists to focus their attention
on the “relative efficiency” of a market instead of
continuing the all-or-nothing battle of attrition that
is characteristic of much of the earlier market efficiency literature.
As we now understand more clearly, the original
case for efficient markets probably leaned too heavily on the notion of risk-free, cost-free arbitrage to
eliminate all profitable trading strategies immediately. In real markets, arbitrage is neither as easy
nor as effective as economists once had assumed.
For one thing, financial markets are not complete
and frictionless, so arbitrage in general is risky and
costly. In addition, it is not realistic to assume that
the number of informed arbitrageurs or the supply
of financial resources they have to invest in arbitrage
strategies is limitless.
This article builds on an important and insightful recent model of arbitrage by professional traders
who need—but lack—wealth of their own to trade
(Shleifer and Vishny, 1997). Professional arbitrageurs
must convince wealthy but uninformed investors
to entrust them with investment capital in order to
exploit mispricing and push the market back toward
the ideal of efficiency. Unfortunately, arbitrageurs
cannot prove that they recognize the intrinsic (or
“fundamental”) values of the assets they claim are
mispriced. Even worse, it is possible the assets will
1
For early statements of the theory of efficient markets and the unpredictability of asset-price movements, see Fama (1965), Muth (1960),
or Samuelson (1965). For a recent summary of the evidence for return
predictability and its implications for efficient-markets theory, see
Campbell, Lo, and MacKinlay (1997, Chap. 2).
2
Ironically, Keynes (1936, Chap. 12) clearly foreshadowed the recent
interest in investor sentiment and liquidity for understanding stock
market behavior, but was forgotten for decades as the efficient-markets
hypothesis dominated the academic discussion.
N OV E M B E R / D E C E M B E R 2 0 0 2
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Emmons and Schmid
become even more mispriced before reverting
eventually to their intrinsic values. Having incurred
losses, the outside investors may demand their
money back at this point even though the expected
profit of staying invested actually has increased.
Thus, market efficiency may depend ultimately
on the successful resolution of a principal-agent
problem that exists between informed but wealthconstrained arbitrageurs and uninformed wealthy
investors. The resulting degree of market efficiency
may change over time and differ across markets,
and it could depend importantly on factors such as
the outside investors’ use of performance-based
(“feedback”) strategies when deciding on the possible termination of ongoing investment mandates.
After developing a simple model of wealthconstrained professional arbitrage that departs in
several important aspects from the canonical Shleifer
and Vishny (1997) model, we calibrate our model
to illustrate its qualitative features. We show that the
existence of professional arbitrageurs mitigates—
but cannot eliminate—mispricing in the market
relative to intrinsic values, regardless of how sensitive the outside investors are to arbitrageurs’ past
performance in deciding whether to remain invested
with them. We also show that arbitrage dampens
the unconditional volatility of asset returns, which
we measure as the expected value of squared returns.
Most importantly, the presence of arbitrageurs limits
both the degree of increased mispricing and level
of volatility during a financial crisis, which we define
as a period of heightened volatility and acute shortage of liquidity.3 This result points out that professional arbitrageurs tend to stabilize markets even
when they are wealth-constrained. Other papers
show that investors who use “positive feedback”
trading strategies—such as portfolio insurers—tend
to destabilize markets (Grossman and Zhou, 1996).
We analyze a three-date (two-period) model of
an aspiring professional arbitrageur (or “convergence
trader” in the language of Kyle and Xiong, 2001,
and Xiong, 2001) who must obtain financing from
investors less informed than he is about the intrinsic value of a financial asset—that is, its liquidation
value at the end of the second period. In addition to
these two types of individuals, there are noise traders
who have wealth to invest but who misperceive the
asset’s intrinsic value. It is the noise traders who
drive the asset’s price away from the intrinsic value.
The investors provide the arbitrageur with funds
to invest in an underpriced asset at the outset of the
model. The price is observed again at the end of the
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first period, at which time the investors may “roll
over” their funds with the arbitrageur or demand
their money back if they have lost confidence in his
ability. The asset will assume its intrinsic value at the
end of the second period with certainty, although
only the arbitrageur knows in advance what that
value is. Consequently, the two-period return on the
arbitrageur’s private information would be both positive and risk-free if he could be assured of financing.
Our set-up highlights the fact that a two-period
risk-free arbitrage nevertheless can be risky over a
one-period horizon in the presence of noise traders
and financial constraints on the arbitrageur. The
risk arises because the arbitrageur needs outside
investors, and these outside investors might revise
their beliefs about the arbitrageur’s talent at the
interim date, based on the return the arbitrageur
achieved in the first period. If the investors downwardly revise their beliefs about the arbitrageur’s
abilities because the fund lost money due to a deepening of the mispricing, they might withdraw their
money precisely when the expected return on the
arbitrage is at its maximum. One implication is that
the arbitrageur will invest “strategically”—that is,
he will not invest as much initially as he would in a
world without wealth constraints—in order to hedge
against the possibility of being unable to exploit
even greater mispricing should it occur one period
ahead. Of course, this is not a new finding; for papers
with similar results, see Grossman and Vila (1992),
Shleifer and Vishny (1997), or Gromb and Vayanos
(2001).4 Our paper’s contributions in this respect
3
Myron Scholes (2000) suggests that the global financial crisis of 199798 was characterized by an increase in volatility, especially in equity
markets, and a flight to liquidity (that is, a preference by many investors
for assets whose liquidity was expected to be good). The crisis was
accentuated by the “negotiated bankruptcy” of Long-Term Capital
Management (LTCM), a hedge fund in which Scholes himself was a
partner. According to Scholes, prior to the crisis, LTCM “was in the
business of supplying liquidity” and therefore its demise worsened
the crisis by eliminating the liquidity it had been supplying. A theoretical
analysis relevant to this episode is Xiong (2001).
4
The first rigorous investigations of the multi-period investment problem
were Merton (1971, 1973) and Breedon (1979). Merton concluded that
a trader should keep a constant fraction of his wealth invested in the
risky asset at all times. The fraction depends on the asset’s expected
return and risk and the investor’s degree of risk aversion. Grossman
and Vila (1992) added leverage and solvency constraints to the dynamic
trader’s problem. Their trader optimally commits more wealth to the
risky asset the shorter is the investment horizon and the further from
the leverage constraint (not just today but prospectively in the future)
the trader finds himself. Campbell and Viceira (1999) is a recent examination of the problem under the assumption that the investor is aware
that the probability distributions from which asset returns are drawn
change over time.
FEDERAL RESERVE BANK OF ST. LOUIS
Emmons and Schmid
Figure 1
Timeline of the Model
t1
t2
t3
Noise traders’
misperception, S1 ,
in place.
Noise traders’
misperception
might deepen to S 2 .
Noise traders’
misperception
corrects (S3 = 0).
Arbitrageur allocates
financial resources
to asset and cash.
If asset price reverts
to intrinsic value, V,
arbitrageur liquidates.
Hedge fund
winds down.
are a more realistic objective function for the arbitrageur and a set-up in which the arbitrageur’s trading significantly affects the asset’s price. Our model
generates interior solutions and we provide calibrated illustrations of the model’s results. While
Shleifer and Vishny (1997) assume that the arbitrageur maximizes assets under management, we
assume that he maximizes his income. The arbitrageur’s income is determined by an incentive
scheme that resembles real-world contracts of hedge
fund managers.
THE MODEL
There are three types of agents in the model.
Noise traders have wealth but misperceive the intrinsic value of a financial asset. Professional arbitrageurs
have no wealth or borrowing capacity but know the
intrinsic value of the financial asset. Investors have
wealth but no insight into the financial asset’s intrinsic value. Unlike noise traders, investors know that
they cannot recognize the asset’s intrinsic value.
All parties are risk-neutral.
The investors may provide the arbitrageur with
funds to invest in an underpriced asset at the outset
of the model (see Figure 1). We refer to this arrangement as a hedge fund. Noise traders misperceive
the intrinsic value of at least one financial asset in
the economy, which generates arbitrage opportunities that so-called “long-short” investment strategies
seek to exploit. Asset mispricing implies that there
are relatively overpriced and relatively underpriced
assets, which means that a portfolio that is long on
the relatively undervalued asset and short on the
relatively overvalued asset trades below intrinsic
value.
We treat a market-neutral long-short portfolio
as a single, complex financial asset. Arbitrage is the
process of acquiring a long-short portfolio and holding it until its price returns to the portfolio’s intrinsic
value. The long-short portfolio that any arbitrageur
might hold defines a market segment of a larger
arbitrage industry. We assume that arbitrageurs are
highly skilled people who pursue proprietary trading
strategies and therefore enjoy a monopoly in their
segment. For simplicity only, we make the assumption that the operating costs in the arbitrage industry
are zero.
The risk-free rate of return, and therefore the
opportunity cost of capital, is zero. For simplicity,
we assume that risky assets trading at fair value—
including the stock market index—also have an
expected return of zero. This implies that there are
no priced systematic risk factors in the economy,
that is, there is no equity risk premium.
The asset trades at three moments in time, t
(t=1,2,3). We capture the influence of the noise
traders’ misperceptions of the intrinsic value of the
asset at times t1 and t2 with the parameters S1 and
S2, respectively. There is no fundamental risk in the
model because the price of the asset will revert to
the intrinsic value at a known date (t3) with certainty
(so S3=0).
The supply of the financial asset is unity. Noise
traders’ demand for the financial asset at time t
(t=1,2,3) is expressed as
V − St
(1)
, 0 ≤ St<V,
QNt =
pt
where pt is the price of the financial asset and St is
the misperception of the noise traders about the
intrinsic value of the financial asset. Because the
financial asset in question is a long-short portfolio
whose value is underestimated by the noise traders,
the noise traders demand less than one unit of the
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Emmons and Schmid
financial asset. Without misperception (S=0), the
noise traders would be willing to absorb the unit
supply of the asset or, in other words, the asset would
trade at the intrinsic value ( pt=V ).
The arbitrageur is compensated in two ways in
accord with actual practice—via an up-front “management fee” and an after-the-fact performancebased “incentive fee.”5 At the beginning of each
period, he receives a fraction (α ) of the assets under
management, and at the end of the period he receives
a fraction ( β ) of any positive return on the portfolio.
This corresponds to compensation structures in
real-world hedge funds, where managers typically
collect α=1 percent or α=2 percent of the equity
capital, plus β=20 percent of any positive return
on the fund’s equity. We assume that the arbitrageur
invests his entire fee income in the fund. This is
because he recognizes the profitability of the fund’s
activities.
The variable Ft denotes the total financial
resources available to the arbitrageur at time t
(t=1,2,3). The value of F1 is exogenous, while the
quantities F2 and F3 are determined in the model.
The startup capital, F1, is provided solely by the
investors, while the arbitrageur acquires the share
α in F1 immediately as part of his compensation.
The arbitrageur acquires additional equity at t2 in
the amount of a fraction α of the outsiders’ share
in F2. Furthermore, the arbitrageur acquires equity
in the fund through capital gains on his equity
position and through his share β in the capital
gains on the outsiders’ equity. The quantity F3 is the
fund’s liquidation value. Note that the arbitrageur
is both the general equity partner of the fund and
its manager, receiving compensation from outside
investors (limited partners) according to the fee
schedule described above.
We assume that the fund raises equity capital
only at the outset—at t1. This assumption prevents
the arbitrageur from diluting initial investors’ equity
stakes later on. Remember that the arbitrageur’s
compensation depends not only on the return on
but also on the amount of the outsiders’ equity
capital under management. The arbitrageur therefore might have an incentive to raise fresh capital
at t2, particularly if he expects low returns in the
second period. This would dilute the fund’s existing
investors’ equity stakes. Thus, we assume (in keeping
with typical hedge-fund arrangements) that the fund
closes to new and existing investors after raising
the initial capital. Reinvested capital gains are conse22
N OV E M B E R / D E C E M B E R 2 0 0 2
quently the sole source of additional equity capital
in the second period.
At time t2, the price of the asset either reverts
to V or it does not. If the asset price is V at t2, the
arbitrageur liquidates the fund and holds cash until
t3. If the asset price does not equal V at t2, the arbitrageur invests aggressively—albeit not all of the
fund’s cash—in the underpriced asset. This portfolio
then generates a risk-free return because the asset
price rises to V at t3 with certainty.
The arbitrageur’s (that is, the hedge fund’s)
demand for the asset at the interim date, t2, is given
by
D
QA2 = 2 , 0 ≤ D2 ≤ F2 ,
(2)
p2
where D2 is the amount of the hedge fund’s demand
in dollars. The amount F2 – D2 ≥ 0 is held in cash.
Because total demand aggregated across noise
traders and the arbitrageur must equal the asset
supply of one unit (QN2+QA2=1), the price of the
financial asset at t2 is determined by combining (1)
and (2):
(3)
p2 = V − S2 + D2 , 0 ≤ D2 < S2 .
The condition D2<S2 implies that the asset still
trades at a discount to the intrinsic value at t2: p2<V.
This assumption recognizes the arbitrageur’s incentive not to bid up the price all the way to intrinsic
value immediately—an implication of the fact that
the arbitrageur will be compensated during the last
period for achieving a positive return on investment.
As shown by Grossman and Vila (1992), the
arbitrageur does not want to invest all of F1 in the
asset at t1, either. After all, the asset may become
even more underpriced at t2, in which event he will
want to increase his investment (“double up”). With
D1 denoting the amount the arbitrageur invests in
the asset at t1, we have
D
QA1 = 1 ,
(4)
p1
which implies the initial asset price will be
5
Amin and Kat (2001) report that hedge funds typically charge their
investors a fixed annual “management fee” of 1 or 2 percent of assets
under management plus an “incentive fee” of 15 to 25 percent of the
fund’s realized annual return. The incentive fee is waived if a particular
“hurdle rate” has not been achieved, which can be a fixed number or
a reference rate such as the T-bill rate plus or minus a spread. Most
funds also apply a “high-water mark” provision, which requires the
fund to make up any past losses before the incentive fee is paid. We
assume the hurdle rate is zero, and we exclude any high-water mark
for the sake of simplicity.
FEDERAL RESERVE BANK OF ST. LOUIS
(5)
p1 = V − S1 + D1, D1 < S1.
The condition D1<S1 implies p1<V, which again
captures the fact that the arbitrageur will not bid
the price all the way up to the asset’s intrinsic value
because of the incentives built into his compensation schedule.
The investors have prior beliefs about the arbitrageur’s talent in exploiting possible asset mispricing, but are not perfectly informed. Investors update
their beliefs about the arbitrageur’s talent using a
simple Bayesian learning rule, which is based solely
on the arbitrageur’s past performance. When past
returns are poor, investors don’t know for sure
whether the poor returns are due to a random error
(noise), a deepening of noise trader misperception
(bad luck), or truly inferior investment talent. Pulling
some of their money from the hedge fund after the
asset mispricing has deepened—that is, when the
expected return on the long-short portfolio is
highest—is the investor’s rational response to the
problem of inferring the arbitrageur’s (unobservable)
talent from data that are ambiguous (that is, observationally equivalent under more than one possible
economic structure).
The investor’s rule of updating his beliefs about
the arbitrageur’s talent implies that, if the hedge
fund loses money during the first period, the fund
faces withdrawals at the interim date, t2. Specifically,
we assume that the withdrawals at t2 are a multiple
of the hedge fund’s posted gross return (that is,
before management fees) at t2, denoted R2, should
this return be negative. Remember that, while
investors can withdraw capital, they cannot inject
additional funds. Thus, the supply of funds in the
second period is the following 6:
(6)
Emmons and Schmid
The arbitrageur knows that—despite a temporary
deepening of the mispricing—the price of the asset
will revert to intrinsic value at t3 for certain, so he
will keep his own money invested, come what may.
Our multiplicative feedback rule provides the
arbitrageurs with what may be a more realistic incentive structure than the linear feedback rule in Shleifer
and Vishny (1997). Our feedback rule does not penalize small negative returns quite as severely for a
high degree of responsiveness, γ, as is the case in
Shleifer and Vishny. For a responsiveness coefficient
of γ =5, for instance, a gross return in the first period,
R2, of –1 percent reduces the fund’s equity capital
by approximately 4 percentage points. A 5 percent
loss, on the other hand, leaves the fund with approximately 77 percent of its equity capital at the beginning of the next period. We provide more results
from the model below.
The gross return of the hedge fund in the first
period, R2, is given by
p
p − p1
( F1 − D1 ) + D1 ⋅ 2 − F1 D1 ⋅ 2
p1
p1
R2 =
=
.
(7)
F1
F1
The fund’s first-period return consists of its return
on the financial asset, normalized by the total funds
available for investment.
For simplicity, we assume a specific form of
uncertainty about noise trader sentiment at t2, S2.
With probability 1 – q (0<q<1), noise traders recognize the true value of the asset, which implies S2=0.
In this case, the arbitrageur liquidates at t2 and holds
cash until t3. Then the arbitrageur’s assets under
management at t3 would amount to
(8)
where
F ⋅ α ⋅ (1 + R ) + F ⋅ (1 − α ) ⋅ (1 + R )γ ,γ > 1, if − 1 ≤ R < 0
2
1
2
2
F2 = 1
⋅
1
+
,
if
0
,
F
R
R
>
2)
2
1 (
where γ is a parameter that determines the responsiveness of the investor to past performance. For
γ =1, poor first-period returns do not shake the
confidence of investors in the arbitrageur’s talent.
At the other extreme, responsiveness that becomes
unboundedly large implies that even a small firstperiod loss is multiplied into a huge withdrawal of
funds. Note that the outside investors may withdraw
only what is theirs. This means that, even if the outsiders pull all of their money, the arbitrageur’s equity
stake remains and the fund can stay in business.
F3S2 = 0 = F2S2 =0 ≡ F1 ⋅ (1 + R2S2 = 0 ),
R2S2 = 0 =
( F1 − D1 ) + D1 ⋅
F1
V
− F1
p1
.
On the other hand, noise trader misperception
deepens to S2 with probability q, S2=S>S1(>0). If
noise traders continue to misperceive the intrinsic
value of the asset, the hedge fund’s assets at t3 will
amount to the following:
6
Some hedge funds have “lock-up” periods of one to three years, while
others allow investors to withdraw money with only a few weeks’
notice. As a result of the poor quality of investors’ information about
the arbitrageur’s talent, the arbitrageur’s past performance often is a
major determinant of the resources he receives to manage, regardless
of the actual arbitrage opportunities available to him.
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Emmons and Schmid
F3S2 = S =
(9)
=
where
R2S2 = S
V
p2S2 = S
V
p2S2 = S
misperception deepen in the first period, while
MF2S2=0 is the fee income if the asset price reverts
to intrinsic value. The arbitrageur also captures capital gains on the equity he builds from the reinvested
management fees. The expected value of the capital
gains, CG, equals
⋅ D2 + ( F2S2 = S − D2 )
⋅ D2 + F1 ⋅ (1 + R2S2 = S )γ − D2 ,
(14)
p S2 = S
− F1
( F1 − D1 ) + D1 ⋅ 2
p1
=
.
F1
CG = q ⋅ ( R2S2 = S ⋅ MF1 ⋅ [1 + R3S2 = S ] + R3S2 = S ⋅ MF2S2 = S )
+ (1 − q ) ⋅ R2S2 = 0 ⋅ MF1 .
THE ARBITRAGEUR’S OPTIMIZATION
PROGRAM
The arbitrageur’s total income consists of
management fees and capital gains on reinvested
management fees. The expected value of the management fees, MF, equals the sum of the expected
values of the management fees collected at t1(MF1),
at t2(MF2), and at t3(MF3). The expected value of the
capital gains is CG. The arbitrageur’s maximization
problem therefore is
Max {MF1 + MF2 + MF3 + CG},
(10)
D1 , D2
where the management fees are
MF1 = α ⋅ F1,
(11)
MF2 = MF2S2 = S + MF2S2 = 0, and
(12)
(13)
MF3 = β ⋅ q ⋅ R3S2 = S
⋅( F2S2 = S − (1 + R2S2 = S ) ⋅ MF1 − MF2S2 = S )
and where
MF2S2 = S = α ⋅ q ⋅ ( F2S2 = S − α ⋅ [1 + R2S2 = S ] ⋅ F1
− β ⋅ max{0, R2S2 = S} ⋅ (1 − α ) ⋅ F1 )
+ β ⋅ q ⋅ max{0, R2S2 = S} ⋅ (1 − α ) ⋅ F1 ,
MF2S2 = 0 = α ⋅ (1 − q ) ⋅ ( F2S2 = 0 − α ⋅ [1 + R2S2 = 0 ] ⋅ F1
− β ⋅ R2S2 = 0 ⋅ (1 − α ) ⋅ F1 )
+ β ⋅ (1 − q ) ⋅ R2S2 = 0 ⋅ (1 − α ) ⋅ F1 , and
R3S2 = S =
( F2S2 = S − D2S2 = S ) + D2S2 = S ⋅
F2S2 = S
V
p2S2 = S
− F2S2 = S
.
The quantity MF2S2=S represents the income the
arbitrageur collects at t2 should the noise traders’
24
N OV E M B E R / D E C E M B E R 2 0 0 2
The arbitrageur’s choice variables are D1( ≤ F1 )
and D2( ≤ F2S2=S ), which are the amounts the arbitrageur invests in the asset at t1 and t2, respectively.
Unless the asset reverts to intrinsic value at t2( p2=V ),
the t2 price of the asset given in equation (3) is a
function of the t2 choice variable, D2. Similarly, the
t1 price of the asset given in equation (5) is a function
of the choice variable, D1.
SOLUTION TO THE MAXIMIZATION
PROBLEM
We solve the maximization problem numerically. We hold constant all of the following: V=1;
F1=S1=0.2; S2=0.4; q=1– q=0.5; α=0.02; and
β=0.2. Note that F1=S1=0.2 means that the arbitrageur has sufficient buying power to eliminate the
t1 mispricing entirely if so desired. Also, note that
0.4=S2>S1=0.2 means that noise trader misperception may deepen between t1 to t2—that is, the asset
may become even more mispriced. For the values
chosen for S1, S2, and q, noise trader misperception,
S, is as likely to double as it is to vanish. Thus, the
expected value of noise trader misperception in the
second period, q·S2, equals the noise trader misperception observed in the first period, S1.
We vary γ , the responsiveness to past performance of fund withdrawals, from γ=1 (no responsiveness by the investors to past investment performance,
that is, no withdrawals) to γ =20 (extreme responsiveness) with a step length of unity. We use a grid
search method to solve the maximization problem.
This involves varying D1 and D2 independently in
very small increments within their bounds, 0 ≤ Di ≤
Fi ( i=1,2), to find the maximum of the objective
function.
The findings of the grid search are displayed
in Figures 2 through 5. The first important point to
make concerns the extent to which the presence
of the hedge fund affects asset mispricing. Figure 2
shows that the mispricing is less pronounced in each
period than it would be without the hedge fund.
FEDERAL RESERVE BANK OF ST. LOUIS
Emmons and Schmid
Figure 2
Figure 3
Effect of Investor Responsiveness on
Asset Price Volatility
0.90
0.090
0.88
0.085
Unconditional Volatility
Asset Prices p1, E(p2)
Effect of Investor Responsiveness on
Asset Prices
0.86
0.84
p1
0.82
E(p2)
0.080
0.075
0.070
0.065
0.80
0.060
0.78
0
2
4
6
8
10
12
14
16
18
20
Responsiveness of Cash Flows (γ )
Remember that, without arbitrage, the first-period
price, p1, and the expected value of the second-period
price, E[p2], both would equal 0.8 (shown as a dashed
line). On the other hand, without noise traders, the
asset would trade at unit value in both periods (not
shown). The hedge fund almost halves the difference
between the expected value of the second-period
price, E[ p2] (shown as solid circles), and the asset’s
intrinsic, unit value. In fact, the degree of investor
responsiveness, γ, has little bearing on E[ p2], which
approaches the value of approximately 0.8873
(shown as a solid horizontal line) as γ approaches
infinity. By comparison, the degree of responsiveness
has a strong impact on the first-period price, p1
(shown as open boxes). This is because the arbitrageur treads even more cautiously when putting on
this trade in the first period when he knows that the
investors penalize negative returns with sizeable
withdrawals. In fact, the higher is γ, the more cash
the arbitrageur holds in the first period, and therefore,
the lower is p1. As the degree of investor responsiveness, γ, goes to infinity, the amount the arbitrageur
invests in the first period goes to zero and, consequently, the first-period price, p1, converges to 0.8—
the value the asset would adopt if there were no
hedge fund in the market (shown as a dashed line).
Thus we conclude that the hedge fund pushes the
price of the asset (or its respective expected value)
toward the intrinsic, unit value in both periods. This
is our first main finding.
0
2
4
6
8
10
12
14
16
18
20
Responsiveness of Cash Flows (γ )
Figure 3 shows the unconditional volatility of
the asset’s returns for various degrees of investor
responsiveness, γ. The unconditional volatility is
calculated as the expected value of the squared
returns over the two periods. For low values of
investor responsiveness, volatility increases as γ
increases. For high values of responsiveness, a further increase in γ reduces volatility monotonically.
As γ goes to infinity, volatility approaches a level
(as shown by the solid line) that is lower than the
volatility level at γ =1 (as indicated by the leftmost
symbol), which is the benchmark case of unwavering investor confidence in the hedge fund manager.
The reason for this “volatility hump” lies in the existence of two opposite effects. All else equal, the
higher γ is, the bigger is the drop in the asset’s price
from t1 to t2 should the noise traders’ misperception
deepen. On the other hand, the higher γ is, the lower
is the price of the asset at t1 because the arbitrageur
puts less money to work. For low values of investor
responsiveness, the volatility-increasing effect dominates. For increasingly higher values of γ, this effect
becomes progressively weaker until it vanishes for
an infinitely large degree of investor responsiveness.
It is important to note that the hedge fund
greatly reduces asset price volatility, regardless of
the degree of investor responsiveness. The unconditional volatility without the hedge fund runs at
0.5694 (not shown), which is a multiple of the volatility that we observe even at the degree of responsiveN OV E M B E R / D E C E M B E R 2 0 0 2
25
REVIEW
Emmons and Schmid
Figure 4
Figure 5
Effect of Investor Responsiveness on
Asset Return When Misperception
Deepens
Effect of Investor Responsiveness on
Arbitrageur’s Profit
0.0142
Arbitrageur’s Expected Profit
First-Period Asset Return for S=S2
–0.025
–0.050
–0.075
–0.100
0.0140
0.0138
0.0136
0.0134
0.0132
0.0130
0
–0.125
0
2
4
6
8
10
12
14
16
18
20
2
6
4
8
10
12
14
16
18
20
Responsiveness of Cash Flows (γ )
Responsiveness of Cash Flows (γ )
ness that generates the highest level of volatility.
Thus, we conclude that the hedge fund unambiguously reduces unconditional volatility. This is our
second main finding.
Another way to look at the impact of arbitrage
on volatility is to ask how the market behaves when
asset mispricing deepens. Such an event—if severe—
might cause, or occur alongside, a financial crisis.
Figure 4 shows, for the case of a deepening noise
trader misperception of the asset’s intrinsic value,
the first-period asset return as a function of investor
responsiveness. The absolute value of the percentage
decline of the asset price increases with investor
responsiveness, γ. For an infinitely high value of γ,
the arbitrageur holds cash in the first period and
then invests aggressively at t2, although he does not
invest all the cash available. The horizontal line in
Figure 4 signifies the first-period return for this
borderline case of an infinite degree of responsiveness. Note that, without a hedge fund, the first-period
return would amount to a negative 25 percent (not
shown), which is more than twice as much (in absolute value) as what is observed even with a degree
of responsiveness of zero (that is, γ equal to one).
Hence, we conclude that the presence of a hedge
fund dampens volatility in the event of a deepening
of noise trader misperception, as might occur in a
financial panic. This is our third main finding.
Finally, we are interested in the question of how
investor responsiveness affects the arbitrageur’s
26
N OV E M B E R / D E C E M B E R 2 0 0 2
profit, that is, his incentive to set up a hedge fund
and engage in arbitrage. Figure 5 shows the arbitrageur’s profit as a function of γ. Not surprisingly,
the profit of the arbitrageur decreases monotonically
with increased investor responsiveness to past performance. The monotonic decline in the profitability
of arbitrage with increasing investor responsiveness
to past performance is a manifestation of the fact
that liquidating a hedge portfolio when the expected
return from arbitrage is highest is counterproductive—that is, it runs against “the nature of the trade.”
CONCLUSION
Even financially constrained professional
arbitrageurs may be able to exploit asset mispricing
if they can link up with rational but uninformed
investors. To achieve this goal, the two parties must
overcome—at least to a degree—the problem of
asymmetric information about the arbitrageur’s
talent. The result of such an endeavor is a hedge
fund that goes long on (comparatively) underpriced
assets and short on (comparatively) overpriced assets.
As a byproduct, the impacts of noise trader misperceptions on asset prices and volatility are reduced.
This holds for any degree of responsiveness to past
performance (“feedback”) of the investors’ confidence in the arbitrageur’s talent.
This article builds on the dynamic-investment
literature that reaches back at least to Merton (1971).
FEDERAL RESERVE BANK OF ST. LOUIS
Shleifer and Vishny (1997) provided an insightful
model of wealth-constrained arbitrageurs that can
be, and has been, extended in several directions.
We add several realistic features to the professional
arbitrageur’s problem in the canonical model, including the ability to build an equity stake in his hedge
fund over time, and a potentially more realistic multiplicative (rather than linear) investor feedback rule.
Like Shleifer and Vishny, we assume that the hedge
fund can influence the market price. Hedge funds
do, in fact, sometimes move market prices because
they operate in specialized market segments that
have limited liquidity. It is also true, however, that
hedge funds alone cannot prevent asset-price volatility or occasional mispricing—which might deepen
before it eventually corrects.
Emmons and Schmid
Working paper, London Business School and Massachusetts
Institute of Technology, October 2001.
Grossman, Sanford J. and Vila, Jean-Luc. “Optimal Dynamic
Trading with Leverage Constraints.” Journal of Financial
and Quantitative Analysis, June 1992, 27(2), pp. 151-68.
___________ and Zhou, Zhongquan. “Equilibrium Analysis
of Portfolio Insurance.” Journal of Finance, September
1996, 51(4), pp. 1379-1403.
Keynes, John Maynard. The General Theory of Employment,
Interest, and Money. New York: Harcourt, Brace & World,
1936.
Kyle, Albert S. and Xiong, Wei. “Contagion as a Wealth
Effect.” Journal of Finance, August 2001, 56(4), pp. 1401-40.
REFERENCES
Amin, Guarav S. and Kat, Harry M. “Hedge Fund Performance
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Breedon, Douglas T. “An Intertemporal Asset Pricing Model
with Stochastic Consumption and Investment Opportunities.” Journal of Financial Economics, September 1979,
7(3), pp. 265-96.
Campbell, John Y.; Lo, Andrew and MacKinlay, A. Craig.
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Merton, Robert C. “Optimal Consumption and Portfolio
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Muth, J. “Optimal Properties of Exponentially Weighted
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Samuelson, Paul. “Proof That Properly Anticipated Prices
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___________ and Viceira, Luis M. “Consumption and
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Varying.” Quarterly Journal of Economics, May 1999, 114(2),
pp. 433-95.
Scholes, Myron S. “Crisis and Risk Management.” American
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pp. 17-21.
Fama, Eugene F. “The Behavior of Stock Market Prices.”
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Sharpe, William P. and Alexander, Gordon. Investments.
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Friedman, Milton. “The Case for Flexible Exchange Rates,”
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Chicago Press, 1953.
Shleifer, Andrei and Vishny, Robert W. “The Limits of
Arbitrage.” Journal of Finance, March 1997, 52(1), pp. 35-55.
Gromb, Denis and Vayanos, Dimitri. “Equilibrium and Welfare
in Markets with Financially Constrained Arbitrageurs.”
Xiong, Wei. “Convergence Trading with Wealth Effects: An
Amplification Mechanism in Financial Markets.” Journal
of Financial Economics, November 2001, 62(2), pp. 247-92.
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Emmons and Schmid
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REVIEW
Regime-Dependent
Recession Forecasts
and the 2001 Recession
Michael J. Dueker
usiness recessions, as a major source of
nondiversifiable risk, impose high costs on
society. Since firms cannot obtain “recession
insurance,” they try to foresee recessions and reduce
their exposure ahead of time. Consequently, forecasting business cycle turning points has remained
an important endeavor. Of course, the difficulty is
deriving reliable methods to forecast business cycle
turning points. Previous studies found that accurate
recession forecasts remain elusive (Filardo, 1999;
Del Negro, 2001; Chin, Geweke, and Miller, 2000).
Forecasts of economic output are not a good substitute for forecasts of business cycle turning points
because less than 20 percent of all months pertain
to recessions. Hence, empirical models of output
growth focus largely on explaining variation in
output growth during economic expansions, since
this variation accounts for the lion’s share of the
sample variance.
Throughout the 1990s, recession forecasting
models relied exclusively on the 1990-91 recession
for out-of-sample confirmation (Estrella and Mishkin,
1998; Birchenhall et al., 1999; Friedman and Kuttner,
1998). Out-of-sample confirmation is particularly
important for recession forecasting because recessions are infrequent, making it tempting to overfit
specific episodes in sample. In general, recession
forecasting models failed to predict the 1990-91
recession out of sample. The occurrence of the 2001
recession raises the question: Was the 1990-91 recession uniquely difficult to predict or is recession forecasting a failed enterprise? If recession forecasting
models were to repeat in 2001 their dismal performance from the 1990-91 recession, then doubts
about such models would mount with justification.
In this article, I examine the out-of-sample forecasts
from recession forecasting models with three levels
of sophistication. All three models concur with the
previous finding that the 1990-91 recession was
B
Michael J. Dueker is a research officer at the Federal Reserve Bank of
St. Louis. Mrinalini Lhila and John Zhu provided research assistance.
© 2002, The Federal Reserve Bank of St. Louis.
hard to predict. The simplest of the three models
largely misses the 2001 recession, but two regimeswitching models come quite close to predicting
the onset date of the recession six months ahead
of time. One innovation to recession forecasting
introduced here is to allow the critical probability
level for a recession to be predicted to depend on
the current state of a Markov switching process—
hence, regime-dependent recession forecasts.
In this way, the forecasts presented here respond
to the criticism that economists equivocate too much
when it comes to their recession forecasts. When
recession forecasts are expressed as probability
statements, it is tempting to claim ex post that the
ex ante probability of recession from the forecasting
model was “close enough” to either one or zero to be
considered a correct forecast. For example, if the
model suggested that a recession would occur with
a probability of 35 percent, then after the fact the
model builder could try to justify either outcome:
If a recession ensued, the model builder could cite
the jump in probability from zero to 35 percent as
evidence that a large shift toward recession was
detected; if no recession ensued, the model builder
could say that the 35 percent probability was far from
100 percent and did not indicate recession. To avoid
such ambiguity, economists are often asked to make
specific calls as to whether the economy will or will
not be in recession six months from now. A yes/no
recession signal comes from comparing the forecasted probability of recession with a critical value
determined prior to the out-of-sample forecasting.
The dependent variable I use to separate business
recessions from expansions is based on the business
cycle turning points defined by the National Bureau
of Economic Research (NBER). As in Birchenhall et al.
(1999), I use the composite index of leading indicators (CLI) from the Conference Board as the explanatory variable in the probit forecasting models. The
CLI receives much attention as a harbinger of future
business cycle conditions. It has ten components:
manufacturing hours, consumer expectations, stock
prices, initial unemployment claims, building permits,
the money supply, the spread between short- and
long-term interest rates on government securities,
vendor performance, manufacturing orders for
consumer goods, and manufacturing orders for
capital goods. Figure 1 shows the upward trend in
the CLI and its three-month percentage changes.
The decreased volatility in the three-month change
since the early 1980s is symptomatic of decreased
volatility in the business cycle.
N OV E M B E R / D E C E M B E R 2 0 0 2
29
REVIEW
Dueker
Figure 1
THE SIMPLE PROBIT MODEL
Index of Leading Indicators
I study three probit forecasting methods. One is
the simple probit model and the other two are based
on a Markov switching probit from Dueker (1997).
A probit model can be used to predict a qualitative
variable such as a recession indicator, Rt, where
Index
120
3-Month Change in Index
20
100
15
80
10
60
5
40
0
20
–5
0
1959
–10
1965
1971
1977
1983
1989
1995
2001
The 1990-91 and 2001 recessions can be used
to evaluate the out-of-sample performance of the
model and the leading indicators. I find that the
1990-91 recession is the anomaly in that the recession signal emanating from the leading indicators
largely misses it. The 2001 recession, in contrast,
was largely predictable from the leading indicators
six months ahead.
The probit model takes the monthly movements
in the leading indicators and translates them into
precise probability statements regarding the likelihood of recession. When dealing with qualitative
events such as recessions, however, it is often desirable to define a specific recession yes/no signal from
the probit probabilities. That way, the forecasting
method either correctly “calls” the recession or it
does not. Birchenhall et al. (1999) use this approach
to say that a recession is signaled if the logit probability of recession exceeds a critical value. If one
chooses the critical value to maximize the in-sample
fit, then out-of-sample confirmation of recession
forecasting models becomes particulary important,
given Robert Lucas’s dictum: Beware of econometricians bearing free parameters. The critical value that
defines a recession signal is an example of what
Lucas calls a free parameter because—although it
is not an inherent part of the econometric model—
it combines with the model estimates to suggest that
the model fits the data well. Out-of-sample confirmation helps ensure that the free parameters are not
simply overfitting the in-sample data.
30
N OV E M B E R / D E C E M B E R 2 0 0 2
Rt=1 if the economy is in NBER recession in period t
=0 otherwise.
One way to think of a probit model is to assume that
a normally distributed latent variable, R*, lies behind
the recession indicator:
(1)
Rt* = − c0 + − c1 Xt − k + ut ,
where u is a normally distributed error team and X
is the leading indicator explanatory variable lagged
k periods—the forecasting horizon. A probability
of recession is associated with each possible value
of the latent variable, where the latent variable is
assumed to be negative during expansions and positive during recessions. In this case, the forecasted
probability of recession is
(2)
Prob ( Rt =1) = 1 − Φ (c0 + c1 Xt − k ) ,
where Φ(.) is the cumulative standard normal density
function.
The log-likelihood function for a simple probit
model is
(3)
(
L = ∑ Rt lnProb Rt=1 Xt − k
t
(
)
)
+ (1 − Rt ) ln Prob Rt=0 Xt − k .
COEFFICIENT VARIATION VIA MARKOV
SWITCHING IN THE PROBIT MODEL
The log-likelihood function in equation (3) highlights the assumption in the probit model that the
recession outcomes conditional on available information are independently distributed from month
to month. This assumption is questionable unless
the econometric model allows for considerable
serial correlation in the recession probabilities. As
in Dueker (1997), one way to achieve this degree of
serial correlation is to introduce serial correlation
in the model’s coefficients by making them subject
to Markov switching.
The simplest interpretation of Markov switching
coefficients in a probit model is that they capture
time variation in the variance of the error term u
from equation (1). In the low-variance regime the
variance would still be normalized to one, but in
FEDERAL RESERVE BANK OF ST. LOUIS
Dueker
(
the high-variance regime the variance would be
greater than one:
Prob ( Rt =1| High Variance )
Prob St = 0 Rt −1 , Xt −2
= 1 − Φ (c0 / σ + c1 / σ Xt − k ), σ > 1 .
St equals 0 or 1
Prob (St=0|St–1=0)=p
Prob (St=1|St–1=1)=q.
(4)
In this way, the coefficients take on either of two
values and thereby change the magnitude of the
shock needed to induce a recession:
(5)
Rt=1 if ut >c0 ( St ) + c1( St ) + c1( St ) Xt − k
(6)
(
)
Prob ( S = 0 R , X ) Prob ( R = 0 S = 0, X )
∑1 Prob ( S = s R , X ) Prob ( R = 0 S = s, X )
Prob St = 0 Rt = 0, Xt −1 =
t −1
s=0
t
t −2
t −1
t
t −2
t −1
t
t
t
t −1
)
The probability in equation (7) is called the oneperiod-ahead prior probability because it is not conditional on the recession outcome at time t. For a
forecast horizon of several months, we need to use
the transition probabilities to derive a k-period-ahead
probability of the state variable:
(8)
(St = 0 R
Prob
Prob
(
)
′
Xt − k ,
=
St = 1 Rt − k , Xt − k
t −k ,
(
(
)
)
)
Prob S = 0 R , X
′
t −k
t −k
t −k ,
,
G
Prob S = 1 R , X
t −k
t −k
t −k
k
where G is the transition matrix of the Markov state
variable.
For forecasting k periods ahead, one finds the
best-fitting model by maximizing the corresponding
likelihood function:
(9)
(
1
∑ Prob St=s Rt − k , Xt − k
∑ Rt ln s=0
t=1
Prob R = 1 St = s, Xt − k
t
(
The transition probabilities, p and q, indicate
the persistence of the states and determine the
unconditional probability of the state St=0 to be
(1 – q )/(2 – p – q ). Since the state is unobserved and
must be inferred as a probability, allowance for two
states means that the expected values of the coefficients can lie anywhere between the high and low
values corresponding to the two states. In the estimation, Bayes’ rule is used to obtain filtered probabilities of the states in order to sum over possible
values of the unobserved states and evaluate the
likelihood function, as in Hamilton (1990):
t
(
+ (1 − q ) Prob St −1 = 1 Rt −1, Xt −2 .
T
=0 if ut ≤ c0 ( St ) + c1( St ) Xt − k .
)
= p Prob St −1 = 0 Rt −1 , Xt −2
(7)
Variance switching implies that the coefficients are
restricted to change by the same percentage between
regimes. I do not impose this condition because I
do not want to restrict the signs of the coefficients,
for example, to be the same in both regimes. Nevertheless, conditional heteroskedasticity helps motivate
why the coefficients might be subject to regime
switching, since volatility is one aspect of the economy that does vary across the business cycle. Because
it is not the only aspect of the economy that varies
across the business cycle, however, we keep the
model more general by not restricting the regime
switching to variance switching.
In a Markov switching model, the parameters
change values according to an unobserved binary
state variable, St, which follows a Markov process:
(
)
)
(
)
1
∑ Prob St=s Rt − k , Xt − k
+(1− Rt ) ln s=0
Prob Rt = 0 St = s, Xt − k
(
) .
)
In this forecasting exercise, the forecaster is
assumed to know whether the economy is currently
in recession when forecasting whether the economy
will be in recession six months from now. This
assumption is somewhat problematic when forecasting from the early stages of a recession before
the NBER has officially declared that the economy
entered a recession. For example, when forecasting whether the economy would be in recession in
October 2001, it was probably not clear that the
economy was in recession in April 2001. The NBER
did not announce that the recession had started in
March 2001 until November 26, 2001. On the other
hand, forecasts of the onsets of recessions are not
likely to be clouded by this assumption. In forecasting whether the economy would be in recession in
N OV E M B E R / D E C E M B E R 2 0 0 2
31
REVIEW
Dueker
Figure 2
Figure 3
Probability of Recession Conditional on
Regime S=0
Six-Month-Ahead Probability of Regime S=0
Probability
Probability
In Sample
1
1
Out of Sample
0.9
0.8
0.8
0.7
0.6
0.6
0.5
0.4
0.4
0.3
0.2
0.2
0.1
0
1962
1968
1974
1980
1986
1992
1998
NOTE: Shaded bars indicate recessions.
0
1962
1968
1974
1980
1986
1992
1998
NOTE: Shaded bars indicate recessions.
March or April 2001, no one believed in September
or October 2000 that the economy was already in
recession. There was no confusion about the current
state of the economy. Similarly, in January 1990
everyone knew that the economy was still in an
expansion when forecasting whether a recession
would start by July 1990. For this reason, one might
pay special attention to how the model predicts the
onset dates of recessions.
The explanatory variable, X, is the three-month
percentage change in the leading indicators index
shown in Figure 1. The minimum value of the change
in the leading indicators index is about –5. If we plug
this minimum value and the coefficient estimates
from Table 1 into equation (5), we see that a recession
is essentially never predicted in the state where S=1.
Given the values of c0(S=1) and c1(S=1), a standard
normal shock, u, greater than 2.7 would have to
occur at the minimum value of the leading indicators
for a recession to occur in that state. In contrast,
recessions are often implied in the regime where
S=0, as shown in Figure 2. (Note that in this and
the following charts, the coefficient estimates are
also applied to the out-of-sample data from January
1990 to December 2001.) The unconditional probability of the regime S=0, however, is only 0.25 and
it is forecasted less often than regime S=1, as seen
in Figure 3. Combining Figures 2 and 3, we see that
six-month-ahead forecasts of a high probability of
S=0 amount to a forecast of recession. Figure 4 combines the two explicitly by plotting the probability
of recession after summing across the two states:
(10)
FORECAST RESULTS
Prob Rt = 1 Xt − k
Table 1
Coefficients from the Markov Switching Probit
Equation
Coefficient value
c 0 (S=0)
0.140 (0.233)
c 1 (S=0)
1.415 (0.336)
c 0 (S=1)
2.397 (0.730)
c 1 (S=1)
–0.062 (0.351)
p
0.950 (0.012)
q
0.984 (0.010)
NOTE: Standard errors are in parentheses.
The Markov switching probit model was estimated with data from May 1960 to December 1989.
32
N OV E M B E R / D E C E M B E R 2 0 0 2
(
1
(
)
)
(
)
= ∑ Prob St=s Rt − k , Xt − k Prob Rt = 1 St = s, Xt − k .
s=0
FEDERAL RESERVE BANK OF ST. LOUIS
Dueker
A standard approach—which I call model 1—
to deriving explicit recession signals from the forecasted probability of recession, Prob (Rt=1|Xt –k ),
is to choose a critical value, m, such that a recession
is signaled if
(
)
Prob Rt = 1 Xt − k − m >0 .
(11)
(
)
(Prob(R = 1 S = 0, X ) − m )
+ Prob ( S = 1 R , X )
(Prob (R =1 S =1, X ) − m ) >0.
Prob St = 0 Rt − k , Xt − k
t
t −k
t
t −k
t −k
t
t
t
(
)
Out of Sample
0.8
0.6
0
t −k
0.2
0
1962
1
(
+ Prob ( S =1 R
)
)m .
Prob Rt =1 Xt − k >Prob St = 0 Rt − k , Xt − k m0
t
In Sample
0.4
Alternatively, one can rewrite this recession
signal as
(13)
Probability of Recession from
Six-Month-Ahead Forecasts
1
A key innovation in this paper is to recognize
that one can derive an alternative recession signal—
called model 2—from regime-specific critical values,
m0 and m1, such that a recession is signaled if
(12)
Figure 4
t − k , Xt − k
1
Either way, two critical values are used, where the
weight given to each depends on the regime probabilities. As shown in Figure 2, the probability of recession is relatively high on average in the regime where
S=0, with an average probability of 0.34. In contrast,
the average probability of recession in the regime
where S=1 is not much above zero. Given the difference between the average probabilities of recession
in the two regimes, it seems desirable to have separate critical probability levels for each regime, as in
equation (12).
I chose critical probability levels based on the
in-sample period through 1989 and examined how
well they work in the out-of-sample period. The
criterion I used was the greatest number of correct
signals, where one point was given to a correct signal
during a recession and half a point to a correct signal
during an expansion. This point scheme puts greater
emphasis on not missing recessions versus supplying false recession signals during expansions. The
impetus for this asymmetry in the point scheme is
the belief that most firms would be more willing to
pay for recession insurance than for a contract that
would indemnify them in the case where the economy performed above expectations when a recession
was forecast.
1968
1974
1980
1986
1992
1998
NOTE: Shaded bars indicate recessions.
For the in-sample period through 1989, I found
that values of m=0.28 (for model 1) and m0=0.43
and m1=0.135 (for model 2) gave the greatest number of correct signals. It makes sense that the optimal
value of m would lie between optimal m0 and m1,
since it is trying to fill both roles. The critical probability level m0 lies above the average probability of
recession conditional on S=0 (0.34), so that one
predicts a recession less than half of the time that
S=0.
Figure 5 shows the fit of the recession-signaling
model, where the signal is based on model 2 with
the two regime-dependent critical values. With forecasts from model 2, recessions are generally not
missed and the only notable false signal occurred
in the 1966 slowdown. Figure 6, in turn, shows the
fit of model 1—the signaling procedure that uses
only one critical value, as in equation (11). Here, some
of the recessions are projected to start earlier and
end later than they did and there are many more
false recession signals during expansions.
Similarly, Figure 7 shows the fit of the signal
from the simple probit model from equation (2). The
optimal critical value, m, for the 1960-89 period is
0.24. This approach, model 3, generated even more
and longer-lasting false recession signals than the
Markov switching model with one critical value
(model 1). Based on these results, we do not look
N OV E M B E R / D E C E M B E R 2 0 0 2
33
REVIEW
Dueker
Figure 5
Figure 7
Fit of Recession-Signaling Model
Fit of Recession Signal from Simple Probit
Model (Model 3)
(Model 2: Two Critical Values)
Out of Sample
In Sample
1962
1968
1974
1980
1986
1992
1998
Out of Sample
In Sample
1962
1968
1974
1980
1986
1992
1998
NOTE: Actual recessions (top) and six-month-ahead recession
signals (bottom).
NOTE: Actual recessions (top) and six-month-ahead recession
signals (bottom).
Figure 6
Figure 8
Fit of Recession-Signaling Model
1990-91 Recession and Signal
(Model 1: One Critical Value)
(Signals from Models 1 and 2 Coincide: One or Two
Critical Values)
Out of Sample
In Sample
1962
1968
1974
1980
1986
1992
1998
NOTE: Actual recessions (top) and six-month-ahead recession
signals (bottom).
further at the predictions from the simple probit
model.
In comparing the two signals from the Markov
switching models, a closer look at the two out-ofsample recessions will help determine whether the
34
N OV E M B E R / D E C E M B E R 2 0 0 2
Jan 1990
Jul 1990
Jan 1991
Jul 1991
NOTE: Actual recession (top) and six-month-ahead recession
signal (bottom).
use of two critical values in model 2 as free parameters to fit the in-sample data resulted in overfitting.
Figure 8 zooms in on the 1990 recession and shows
that the recession signals from models 1 and 2 are
identical and they both miss the 1990 recession in
FEDERAL RESERVE BANK OF ST. LOUIS
Dueker
Figure 9
Figure 10
2001 Recession and Signal
2001 Recession and Signal
(Model 1: One Critical Value)
(Model 2: Two Critical Values)
Jan 2000
Jul 2000
Jan 2001
Jul 2001
NOTE: Actual recession (top) and six-month-ahead recession
signal (bottom).
the sense that the six-month-ahead signal does not
kick in until at least six months too late. This result
confirms previous findings that the 1990 recession
was difficult to predict out of sample.
Fortunately, the performance of both signal
approaches is better in the 2001 recession. Figure 9
shows that the signal from model 1 with one critical
value predicted a recession onset in April 2001 using
information through October 2000. Thus, this signal
did not miss the actual onset date of March 2001
by much. The approach with two critical values—
model 2—does slightly worse during the 2001 recession. Figure 10 shows that this signal needed data
through November 2000 to predict a recession onset
date of May 2001. In addition, it incorrectly projected
August 2001 as an expansion month. Nevertheless,
one has to keep Figures 5 and 6 in mind before concluding that the signal derived from one critical value
is better out of sample than the signal derived from
two critical values. Model 2 gave fewer false recession signals than model 1 during the long economic
expansion of the 1990s, as seen by comparing
Figures 5 and 6.
Looking out from the December 2001 data,
both signaling approaches based on the Markov
switching model—with either one or two critical
values—predict that the recession would have ended
by January 2002. Later, the NBER will officially date
the end of the recession and then the accuracy of
Jan 2000
Jul 2000
Jan 2001
Jul 2001
NOTE: Actual recession (top) and six-month-ahead recession
signal (bottom).
the model’s trough prediction will be known.
SUMMARY AND CONCLUSIONS
This article looks at forecasting the 1990 and
2001 recessions out of sample and shows that 1990
appears to be an anamoly in terms of being difficult
to predict. Thus, one should not conclude based on
the 1990 recession that recession forecasting is a
failed enterprise. This article also responds to the
exhortation economists receive to provide unequivocal predications about whether or not the economy
will be in recession in six months. To translate from
a probability of recession to a yes/no recession signal,
one compares the probability with a critical value.
One innovation in recession signaling that I pursue
here is to have regime-specific critical values when
the recession probability comes from a regimeswitching model. This method of deriving a recession
signal reduces the number of false recession signals
outside of recession, without impairing the ability
to signal the recessions that occur.
REFERENCES
Birchenhall, Chris R.; Jessen, Hans; Osborn, Denise R. and
Simpson, Paul. “Predicting U.S. Business-Cycle Regimes.”
Journal of Business and Economic Statistics, July 1999,
17(3), pp. 313-23.
Chin, Dan M.; Geweke, John F. and Miller, Preston J. “Predicting
N OV E M B E R / D E C E M B E R 2 0 0 2
35
Dueker
Turning Points.” Federal Reserve Bank of Minneapolis
Staff Report No. 267, June 2000.
Del Negro, Marco. “Turn, Turn, Turn: Predicting Turning
Points in Economic Activity.” Federal Reserve Bank of
Atlanta Economic Review, Second Quarter 2001, 86(2),
pp. 1-12.
Dueker, Michael. “Strengthening the Case for the Yield Curve
as a Predictor of U.S. Recessions.” Federal Reserve Bank
of St. Louis Review, March/April 1997, 79(2), pp. 41-51.
Estrella, Arturo and Mishkin, Frederic S. “Predicting U.S.
Recessions: Financial Variables as Leading Indicators.”
Review of Economics and Statistics, February 1998, 80(1),
pp. 45-61.
Filardo, Andrew J. “How Reliable Are Recession Prediction
Models?” Federal Reserve Bank of Kansas City Economic
Review, Second Quarter 1999, 84(2), pp. 35-55.
Friedman, Benjamin M. and Kuttner, Kenneth N. “Indicator
Properties of the Paper-Bill Spread: Lessons from Recent
Experience.” Review of Economics and Statistics,
February 1998, 80(1), pp. 34-44.
Hamilton, James D. “Analysis of Time Series Subject to
Changes in Regime.” Journal of Econometrics, July/August
1990, 45(1/2), pp. 39-70.
36
N OV E M B E R / D E C E M B E R 2 0 0 2
REVIEW
Investment-Specific
Technology Growth:
Concepts and Recent
Estimates
Michael R. Pakko
T
he rapid pace of productivity growth since the
mid-1990s has been attributed to improvements in technology, particularly in the areas
of information processing and communications.
From e-mail and cell phones to inventory management and robotic manufacturing techniques, new
ways of doing business—facilitated by the use of
new types of capital equipment—have transformed
the workplace.
However, traditional growth theory and growth
accounting techniques—which emphasize the role
of disembodied, neutral technological progress—are
deficient in explaining the phenomenon of productivity growth driven by technology that is embodied
in new types of capital equipment. Consequently,
models of “investment specific” technological
progress have gained prominence as a framework
for evaluating the role of capital-embodied growth.
This article outlines a general model of investment-specific technological change, presents some
new estimates, and examines the role that this type
of technological progress has in explaining and
predicting recent and prospective productivity
growth trends.
GROWTH THEORY WITH INVESTMENTSPECIFIC TECHNOLOGY
The idea that technology can be manifested in
new, more efficient types of capital equipment has
a long history in economics, dating at least to the
“embodiment controversy” of Solow and Jorgenson
in the 1960s.1 The rapid advancement of informationprocessing and communications technologies has
renewed interest in the issue, inspiring the development of general equilibrium models that include
investment-specific technological progress.
Michael R. Pakko is a senior economist at the Federal Reserve Bank
of St Louis. Rachel Mandal, Mrinalini Lhila, and Athena Theodorou
provided research assistance.
© 2002, The Federal Reserve Bank of St. Louis.
In this section, I describe a simple neoclassical
growth framework—based on the model of
Greenwood, Hercowitz, and Krussell (1997)—that
incorporates this idea. In addition to balanced,
neutral technological progress, the model includes
a source of technological change that is associated
with improvement in the quality of investment goods
that becomes embodied in the productive capital
stock. The model differs slightly from Greenwood,
Hercowitz, and Krussell in two respects: First, the
model in this paper treats equipment and nonresidential structures as two components of a single,
composite capital good. In addition, the model
described below includes a convex production
possibilities frontier.
Our interest is in explaining economic growth—
a sustained increase in economic activity per capita.
Hence, attention will focus on “steady state” growth
paths in which all variables increase at constant
(though possibly differing) rates.
A Growth Model with Two Types of
Technological Change
A simple model that incorporates both types of
technological change can be described as follows:
The household sector is modeled as a representative
agent who directly controls the production technology and owns the capital stock. Households supply
labor inelastically to the production sector and make
consumption-saving decisions by maximizing a
stream of discounted utility over consumption:
(1)
∞
t
∑ β u (ct ) ,
t =0
where β<1 is a constant discount factor and ct is
(per capita) consumption. The momentary utility
function is assumed to be of the constant relative
risk aversion (CRRA) form u(ct )=ct 1–σ/1– σ.
Technology is typically incorporated directly
into the production function: Output is produced
using capital, labor, and the current state of technology. The production function is Cobb-Douglas and
technology is specified in labor-augmenting form2:
(2)
Yt = Ktα ( z t Lt )1− α .
1
See, for example, Solow (1960) and Jorgenson (1966). Hercowitz (1998)
describes the 1960s controversy in the context of contemporary
models of investment-specific technology like the one described here.
2
Note that with a simple transformation of variables, z̆=z1– α, the production function can be written in the alternative form Y=z̆·F(K,L),
where z̆ is an index of total factor productivity.
N OV E M B E R / D E C E M B E R 2 0 0 2
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REVIEW
Pakko
Figure 1
Production Possibilities Frontier
Investment
x/c
A
Consumption
Here, z t is the technology index that directly
enhances the productivity of labor, Lt, and indirectly
that of capital, Kt, in the production of output, Yt.
Note that equation (2) can be written in terms of
labor productivity as
(2′)
yt = ktα z t1− α ,
where the ratio of capital and output to labor are
represented by lower case variables; that is, k=K/L
is the capital/labor ratio and y=Y/L is labor productivity.
Writing equation (2) in terms of log-differences,
productivity growth can be expressed as
(3)
g y = (1 − α ) gz + α gk ,
where gi , for example, denotes the growth rate of
variable i. The “growth accounting” equation (3)
shows that productivity growth can be decomposed
into components representing “total factor productivity,” (1–α )gz, and “capital deepening,” α gz .3
Investment-specific technology enters the model
through the capital accumulation equation,
(4)
(5)
N OV E M B E R / D E C E M B E R 2 0 0 2
k tα z t1− α = H (ct , xt ) ,
and to the capital accumulation equation (4).
3
Using the notation from the previous footnote, the growth accounting
equation (3) can be written explicitly in terms of the total factor productivity variable, gy=gz̆ +α gk.
4
The accumulation equation is often written so that there is a one-period
time to build; that is, capital at time t depends on investment at time
t–1. The specification in this paper simplifies the exposition of capital
growth and emphasizes the flow concept of investment.
5
Formally, the H(·) function is assumed to be homothetic. The nonlinear
PPF can be thought of as shorthand for a more detailed model in which
consumption goods and investment goods are produced in separate
sectors, with costly transfer of factors between sectors.
k t = (1 − δ )kt −1 + qt xt ,
which states that the current productive capital stock
consists of undepreciated capital from the previous
period plus net investment, qt x t.4 In equation (4)
physical investment measured in consumption units,
38
x t, is enhanced by an index of the quality of newly
produced capital goods, qt . The product qt x t represents investment as measured in efficiency units.
The improvement in the quality of capital goods
reflected in increasing values of qt is the driving force
behind investment-specific technological change.
In the subsequent analysis of the growth properties of these two types of technology, we will assume
that the economy’s opportunities for producing
consumption goods and investment goods is characterized by a nonlinear production possibilities frontier, H(ct , x t ), that is concave and invariant to scale.5
Figure 1 illustrates the tradeoff summarized by H(≅).
For a given level of technology and existing capital,
the economy is capable of producing any combination of consumption and investment lying on or
below the production possibilities frontier (PPF).
Points that lie outside the frontier are not feasible
given the current state of technology, while points
inside the frontier imply inefficient underutilization
of resources. The optimal production combination
will therefore lie on the frontier itself. The slope of
the PPF at any given point shows the trade-off
between consumption goods and investment goods—
that is, their relative price.
The durability of capital goods means that
investment produces a stream of consumption goods
into the future. Hence, the location of the optimal
point on the PPF will depend on household preferences for substituting consumption between the
present and the future (which, given the separable
CRRA form of utility assumed, is time invariant in
this model).
This combination of consumption and investment can be found from the representative agent’s
problem of maximizing utility (1) subject to the overall resource contraint,
FEDERAL RESERVE BANK OF ST. LOUIS
Pakko
For a given level of technology, the representative
household’s maximization problem yields an optimal investment/consumption ratio, implying a
specific equilibrium such as that shown as point A
in Figure 1. The slope of the dotted line shows the
price of consumption goods relative to investment
goods implied by this equilibrium.
Figure 2
Balanced Growth
Investment
Case 1: Neutral Technological Change
and Balanced Growth
Suppose that the sole source of technology
growth is zt, the index of labor-augmenting technological progress. For given quantities of labor and
preexisting capital, an increase in zt shifts the production possibilities frontier outward, as shown in
Figure 2.
Because the expansion takes the form of a
radial outward shift, both consumption and investment expand at the same rate as total output; that
is, gc=gx=gy.6 Moreover, with q constant, the capital
accumulation equation (4) implies that capital grows
at the same rate as investment, gk=gx . Hence, this
type of growth is often referred to as “balanced,”
based on “neutral” technological progress. With
investment and consumption growing at the same
rate, the economy’s growth path will be characterized
by a constant x/c ratio, as shown by the growth path
running through points A and B in Figure 2. Along
this growth path, the slope of the PPF, representing
the relative price of consumption and investment
goods, is also constant.
From the growth accounting relationship (3),
the shift in the PPF includes the direct effect of the
increase in zt (represented in Figure 2 as movement
point A′ ) as well as a component associated with
capital growth (accounting for the remaining shift
to point B in Figure 2). However, the role of capital
deepening for this type of technological expansion
is distinctly secondary. The direct effect of technology growth is an expansion of investment, which
gives rise to a commensurate growth rate of capital.
Indeed, substituting the relationship gk=gy into the
growth accounting equation (3), we find that the
rate of output growth (as well as of consumption,
investment, and capital growth) is equal to the rate
of labor-augmenting technical progress. Although
the growth accounting decomposition shows a role
for capital deepening, there is no sense in which
technological progress is “embodied” in capital
growth. Rather, the capital component represents a
passive response to “disembodied” technological
x/c
B
A
A'
Consumption
progress and does not comprise a truly independent
source of economic expansion.7
Case 2: Investment-Specific
Technological Change and CapitalEmbodied Growth
Growth associated with investment-specific
technological progress differs from neutral technology growth in several respects. First, note that qt does
not appear directly in the economy’s resource constraint, (5). Instead, the investment-specific technology index appears in the capital-accumulation
equation and therefore operates through the capitaldeepening component of the growth accounting
equation.
Investment-specific technological progress can
be illustrated using a modified PPF framework, as
shown in Figure 3. The vertical axis now measures
“effective” investment, qt x t, incorporating the notion
of improvement in the quality of investment goods.
In Figure 3, the direct effect of an increase in qt is
6
This outcome is ensured by the scale-invariance property that is
implied by the assumed homotheticity of utility and the PPF function.
7
Capital deepening does play an important role in the adjustment
dynamics of the model. That is, when the economy is not on its steadystate growth path (King and Rebelo, 1993) or is in the transition
between steady-state paths (Pakko, 2002b), capital deepening is the
mechanism that moves the economy toward long-run equilibrium.
N OV E M B E R / D E C E M B E R 2 0 0 2
39
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Pakko
in qt has the effect of increasing the effective capital
stock. In fact, when improvement in the quality of
capital goods is accounted for, the growth rate of
the capital stock will be the sum of the growth rates
of physical investment and quality improvement,
Figure 3
Investment-Specific Growth
Effective Investment
(6)
q' . x/c
A
q . x/c
B
A
Consumption
shown by the rotation of the PPF to the dashed line
passing through point A′ . This twist in the PPF represents a change in the tradeoff between consumption
and capital accumulation. The movement from
point A to point A′ represents no change in c or x
(or their ratio), but is simply a measure of the growth
of “effective” capital that is made possible by the
increase in q.
For this reason, the selection of an appropriate
numeraire is important. If output were to be measured in terms of constant prices, the shift in the
PPF attributable to the increase in q would imply
that output had risen for fixed inputs of labor and
capital. Hence, growth accounting would incorrectly
attribute part of the change to an increase in neutral
technology, z. This mismeasurement would be even
more severe if total output were measured in units
of investment goods.
When the consumption good is taken as numeraire, total real income—as measured in consumption
units along the horizontal axis—is left unchanged
by the direct effect of growth in qt. Appropriate
measurement of investment-specific versus neutral
technology growth therefore requires that the data
be expressed in consumption units. In practice, this
means that for growth accounting in the presence
of investment-specific technical progress, nominal
output and investment data should be deflated by a
consumption price index.8
From the accumulation equation, an increase
40
N OV E M B E R / D E C E M B E R 2 0 0 2
gk = gx + gq .
Hence, the indirect impact of investment-specific
technology growth will be reflected in effective
capital stock growth that shifts the PPF in Figure 3
outward. As was the case for neutral technological
progress, the growth component of investmentspecific technological progress will be represented
by a radial outward shift of the PPF that is characterized by a constant xt /ct ratio and a common growth
trend for output, consumption, and physical
investment.
Substituting equation (6) and the relationship
gy=gx into (3), we obtain a relationship between
productivity growth and the two sources of technology growth:
α
g y = gz +
gq .
(7)
1− α
In the presence of investment-specific technological progress, total economic growth will be equal
to the rate of labor-augmenting technical change
plus a component reflecting improvement in the
quality of capital goods. Hence, investment-specific
growth represents a channel through which technological progress is manifested through “embodiment”
in productive capital.
Two features of the growth path passing through
points A and B in Figure 3 are important for evaluating the role of investment-specific technology in the
data. First, investment—when properly measured
to include improvements in the quality of new
capital goods—is predicted to grow faster than consumption along a steady-state growth path. In addition, the nature of the change in the tradeoff between
consumption and investment, represented by the
twist in the PPF, implies that the relative price of
investment goods should be falling over time relative
to consumption goods.
Figure 4 shows that these trends are, in fact, a
characteristic of the data in the National Income and
Product Accounts (NIPA).9 The ratio of investment
8
Greenwood, Hercowitz, and Krusell (1997) emphasize this point.
9
In Figure 4, “investment” corresponds to total nonresidential fixed
investment and “consumption” is measured as nondurables plus services less housing services.
FEDERAL RESERVE BANK OF ST. LOUIS
to consumption has risen persistently over the past
half-century and has appeared to accelerate sharply
in the past decade. Simultaneously, the price of
investment relative to consumption has followed a
clear downward trend since at least the late 1950s,
with the rate of decline increasing since the 1980s.
Pakko
Figure 4
NIPA Investment and Consumption:
Relative Prices and Quantities
Indices (1996=100)
180
ESTIMATES OF INVESTMENT-SPECIFIC
TECHOLOGICAL CHANGE
The data presented in Figure 4 suggest that
investment-specific technology growth has been
an important feature of post-WWII trends in productivity growth. In order to quantitatively evaluate the
role of investment-specific technology, however, it
is important to carefully examine the issue of quality
improvement for investment goods.
The measurement of quality change has always
been important in the construction of the NIPA data.
Quality characteristics of newly introduced goods
are routinely incorporated into the data using socalled “matching models” that compare the attributes
of new and existing products. In recent years, the
BEA has implemented several revisions to its methodologies in order to account for the rapid rate of innovation in information processing, communications,
and other high-tech sectors. In particular, so-called
“hedonic regression techniques” have been applied
to construct quantity and price indices that adjust
for changes in quality over time. Among the more
important applications of this approach, the BEA
incorporates hedonic indices for computer equipment and purchased software, telephone switching
equipment, cellular services, and video players,
among others.10 Moreover, the BEA has even changed
its aggregation methodology to more accurately
measure the contribution of quality change to GDP
growth: the adoption in 1996 of a chain-weighting
methodology was intended to allow aggregates to
track quality improvement better over time.
Nevertheless, some economists contend that a
significant amount of quality change goes unmeasured in the official statistics, particularly in cases
where quality improvement is more incremental.
In a seminal 1990 study, The Measurement of Durable
Goods Prices, Robert Gordon undertook to quantify
the extent of this unmeasured quality change. Drawing data from a variety of sources, including special
industry studies, Consumer Reports, and the Sears
catalog, Gordon compiled a data set of more than
25,000 price observations. He constructed qualityadjusted price indexes for 105 different product
categories, then aggregated the data to correspond
160
Price
140
120
100
80
Quantity
60
40
1947 1953 1959 1965 1971 1977 1983 1989 1995 2001
to the individual components of the BEA’s measure
of spending on producers’ durable equipment. For
each of 22 major categories of investment, Gordon
calculated “drift ratios” representing the cumulative
deviation of his adjusted price measures from the
official data. The adjusted price components were
then used to deflate nominal series, with the resulting real series aggregated to create a new qualityadjusted series for investment in durable equipment.
The bottom line of Gordon’s study was that the
official NIPA data (as constructed at the time) understated the true growth rate of real investment spending by nearly 3 percentage points per year over the
period 1947-83. This quality adjustment for real
investment spending is mirrored in the price deflator:
the finding that quality-adjusted real investment
spending is undermeasured implies that increases
in the price of investment goods have been overstated. Unfortunately, Gordon’s data set extends
only through 1983.
Quality Improvement for Equipment
and Software Investment
Previous estimates of investment-specific technology growth have been based on extrapolation of
10
Landefeld and Grimm (2000) report that 18 percent of GDP is estimated
using hedonic methods.
N OV E M B E R / D E C E M B E R 2 0 0 2
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Pakko
Figure 5
Growth Rates for Equipment
and Software Investment
25
20
15
10
5
0
–5
–10
–15
1948
1954
BEA
1960
1966
1972
Pakko
1978
1984
1990
1996
Cummins-Violante
Gordon’s aggregate data for series producers’ durable
equipment. For example, Greenwood, Hercowitz,
and Krusell extended the Gordon data through 1990
by adding 1.5 percent to the growth rates of real
investment spending for all categories except computers. Hornstein (1999) invoked a similar procedure
to extend the estimate through 1997.
As BEA definitions and methodologies are
updated and as relative shares of the components
of equipment investment change over time, however,
the simple extrapolation of Gordon’s aggregate data
becomes less satisfactory. Ideally, one would like to
have extended data series at the disaggregated level
of Gordon’s original study. A less ambitious alternative is to extrapolate the drift ratios for each of
Gordon’s 22 major investment categories independently—accounting for changes in BEA definitions
and methodology—then aggregate the extrapolated
data to calculate a new, extended series.11
Two recent studies have followed variants of
this procedure. Cummins and Violante (2002) estimate a simple time-series model that relates Gordon’s
quality-adjusted estimates and official BEA time
series data for each of the individual investment
categories.12 After estimating the coefficients of
the model, Cummins and Violante extrapolate outof-sample estimates of quality-adjusted price levels
for the period 1984-2000.13 Pakko (2002a,b) uses a
simpler extrapolation technique: recognizing that
the measurement bias documented by Gordon is
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N OV E M B E R / D E C E M B E R 2 0 0 2
larger in the earlier years of the sample period than
the latter period, the Pakko estimates are based on
a linear extrapolation of Gordon’s drift ratios for the
period 1973-83. The drift ratios were then applied
to the official BEA price data to create extended
quality-adjusted series.
Both sets of estimates were then aggregated to
create a quality-adjusted measure of equipment
investment for the period 1947-2000. Recent changes
in BEA definitions and methodology complicate this
procedure. One important innovation made in 1996
was the inclusion of software as an investment
component. Gordon’s data set did not include software, so both Pakko and Cummins and Violante
used the official BEA measure for this component.
Similarly, the BEA has devoted considerable effort
to accurately measuring quality change for computers and peripheral equipment; hence, both studies
assume that the bias found by Gordon in the vintage
data has been eliminated in contemporary time
series estimates for that component.
Figure 5 shows annual growth rates of these
quality-adjusted series for aggregate equipment and
software investment, along with the corresponding
BEA measure. The two adjusted series track each
other closely during the 1947-83 period, since both
are based on Gordon’s original data.14 The main
source of divergence between the estimates over
this period is the difference in aggregation methodologies: Cummins and Violante use the Törnqvist
index approach advocated by Gordon, while Pakko
uses the Fisher-ideal chain-weighting approach
that has subsequently been adopted by the BEA.15
During the post-1983 period, the CumminsViolante series displays more rapid growth than the
11
A disaggregated approach is preferable to a simple extrapolation of
the aggregate trend for two reasons: First, several changes in the BEA’s
definitions and methodology have, for some components, eliminated
or at least mitigated the measurement problems suggested by Gordon’s
study. In addition, the procedure of re-aggregating the quality-adjusted
components using a chain-weighting methodology allows the role of
changing expenditure shares over time to be appropriately accounted
for.
12
The model posits that the adjusted price index is a function of a constant, a time trend, current and lagged values of the BEA time series,
a cyclical indicator (lagged GDP growth), and an error term.
13
Giovanni Violante was kind enough to provide the data from Cummins
and Violante (2002).
14
The growth rates of both adjusted measures exceed the official BEA
growth rate by an average of about 2.75 percent per year over this
period.
15
The measures also differ in that the Pakko aggregate includes net
sales of scrap equipment (excluding autos), as measured by the BEA.
FEDERAL RESERVE BANK OF ST. LOUIS
Pakko
Table 1
Growth Rates and Contributions to Growth of Nonresidential Fixed Investment
Nonresidential
Source of
fixed investment
Equipment and software
Nonresidential structures
equipment
and software data 1950-2001 1950-1975 1976-2001 1950-2001 1950-1975 1976-2001 1950-2001 1950-1975 1976-2001
BEA
5.17 (100) 4.59 (100)
5.75 (100) 6.26 (80.3) 5.30 (70.9) 7.23 (87.8) 2.96 (19.7) 3.48 (29.1) 2.44 (12.2)
Adjusted 1
6.85 (100) 6.65 (100)
7.05 (100) 8.35 (80.0) 8.02 (74.0) 8.68 (85.7) 3.95 (20.0) 4.48 (26.0) 3.42 (14.3)
Adjusted 2
7.28 (100) 6.61 (100)
7.95 (100) 8.97 (81.2) 7.95 (73.8) 9.98 (87.3) 3.95 (18.8) 4.48 (26.2) 3.42 (12.7)
NOTE: Numbers in parentheses refer to percent contributions to NFI growth.
Pakko series—due largely to assumptions regarding
quality change in communications equipment. In
1997, the BEA introduced a quality-adjusted price
index for telephone switching equipment and carried
back these revisions to 1985 in the 1999 comprehensive revision of the national accounts.16 Because
this component (the largest single component in
the communications equipment category) was the
predominant source of quality bias in Gordon’s study,
Pakko considers that the updated BEA data accurately
measure quality change in that sector. On the other
hand, Cummins and Violante note that the quality
of other types of telecommunications equipment
has been improving rapidly, so they opt to use their
extrapolated estimate of quality bias from the Gordon
data set (amounting to a drift ratio of nearly 7 percent). The two studies also differ somewhat in their
treatment of automobiles, instruments and photocopy equipment, and office equipment other than
computers.17 The effect of these differences in
assumptions and methodology is that, for the 19842000 period, the Cummins-Violante series displays
an average annual growth rate that is 2.7 percent
higher than the official BEA data, while the growth
rate of the Pakko series exceeds the BEA measure
by only 1.1 percent per year.18
Incorporating Quality Change for
Nonresidential Structures
In addition to equipment and software, another
important component of the capital stock is the
structures component—accounting for approximately 35 percent of nominal nonresidential
fixed investment in the period 1948-2001. Gort,
Greenwood, and Rupert (1999) examined the measurement of quality improvement in nonresidential
structures and estimated that the official NIPA data
understates real, quality-adjusted growth by approximately 1 percent per year.
To account for this source of investment-specific
technology growth, I construct an adjusted measure
of nonresidential structures by adding 1 percentage
point to each year’s growth rate in real nonresidential
structures over the sample period of 1947-2001
(deducting 1 percent growth annually from its price
index). The resulting real investment series and price
index are then aggregated by chain-weighting with
the adjusted measures of equipment and software
spending to produce quality-adjusted decompositions
for total private nonresidential fixed investment (NFI).
Table 1 shows the growth rates for these estimates of quality-adjusted NFI, along with the contribution of equipment and software and nonresidential
structures to total growth.19 Two measures of qualityadjusted data are included: The first corresponds to
the equipment and software data from Pakko. The
second measure uses the Cummins-Violante data
series. Both measures incorporate the quality
improvement in structures suggested by Gort,
Greenwood, and Rupert.
For the period 1950-2001, equipment and software spending accounted for more than 80 percent
of the growth in total nonresidential investment.
The relative contributions to growth have not been
constant over time, however. During the first half
16
Moulten and Seskin (1999).
17
For more detail, see the appendix to Pakko (2002a).
18
These growth spreads are used to extrapolate each of the adjusted
series for the final growth observation from 2000 to 2001 (which was
not included in either of the original series).
19
The contributions to growth in Table 1 are calculated using the BEA’s
current methodology, as described in Moulten and Seskin (1999).
N OV E M B E R / D E C E M B E R 2 0 0 2
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Pakko
Figure 6
Investment-Specific Technology (q)
Log Indices (Base= 1950)
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
–0.2
1950
1960
BEA
1970
1980
Adjusted 1
1990
2000
Adjusted 2
of the sample period, equipment and software
investment accounted for less than 75 percent of
total NFI growth, but accounted for 85 to 90 percent
during the second half of the sample.
In previous literature, estimates of investmentspecific technology growth have treated the equipment and structures components separately. The
estimates in this article use chain-weighted aggregates of both components, allowing flexibility to
account for the shifting growth-shares, suggested
by the pattern of growth contributions shown in
Table 1.
Growth Accounting with InvestmentSpecific Technical Progress
The data for quality-adjusted investment and
associated price indices form the basis for estimating
the contribution of investment-specific technology
to productivity growth. The first step is to calculate
the index of investment-specific technology, q, as
the price of consumption goods relative to (qualityadjusted) investment goods:
(8)
qt = Pc / ˜Pi ,
∼
where Pi is a quality-adjusted price index for investment and Pc is a consumption price index. Following
the practice common in previous literature, the
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N OV E M B E R / D E C E M B E R 2 0 0 2
consumption price index used for this calculation
covers nondurables and non-housing services.20
Durable goods are excluded from the consumption
measure so as to avoid issues of quality improvement
in that component.
Figure 6 shows this measure of q for each of the
three measures of investment prices constructed
in the previous section. The data are indexed to a
base year of 1950 in order to show their cumulative
growth. The two quality-adjusted measures track
each other closely through 1983, exceeding the
growth rate of the unadjusted NIPA relative price by
an average of 1.9 percent. For the period 1984-2001,
the two adjusted series exceed the NIPA-based series
by 1.0 percent (estimate 1, Pakko) and 2.0 percent
(estimate 2, Cummins and Violante) per year.
The estimates of q, along with associated data
for real investment, x, can be used to construct
adjusted measures of the capital stock that account
for embodied technological progress. The model
suggests that real physical investment corresponds
to nominal investment deflated by the consumption
price index, Pi I/Pc. Effective investment, qx, is there∼
∼
fore given by Pi I/Pi . In the NIPA data, with Pi =Pi , this
is simply the real investment series, so the BEA’s data
for private nonresidential fixed assets is an appropriate measure of the capital stock. For each of the
adjusted investment series, qx is the quality-adjusted
real component from which a quality-adjusted
measure of the capital stock can be derived.
The procedure used to construct quality-adjusted
capital stock measures is as follows: First, I use the
accumulation equation (4) and the NIPA series for
investment and capital to back out a series of implied
depreciation factors, (1– δt ).21 These factors are then
used to construct synthetic capital-stock series using
a perpetual-inventory method—that is, by reconstructing the capital stock using equation (4) with
the quality-adjusted investment data. Starting values
for capital stocks in the base year used for these
calculations, 1950, are initialized using the accumu20
The non-housing services data are constructed by chain-weighting
PCE services with the additive inverse of the housing services component. The resulting series is then chain-weighted with nondurables
consumption.
21
The BEA constructs measures of net stocks for individual components,
then uses chain-weighted aggregation to build aggregates. The use of
these annual depreciation factors approximately adjusts for changes
in the composition of the capital stock and total depreciation that arise
from this procedure. For more information about the construction of
the BEA’s fixed-assets series, see Katz and Herman (1997).
FEDERAL RESERVE BANK OF ST. LOUIS
Pakko
Figure 7
Figure 8
Capital Stock Growth Rates
Neutral Technology (z)
Percent
9
Log Index (Base=1950)
1
8
0.9
7
0.8
6
0.7
5
0.6
4
0.5
3
0.4
2
0.3
1
0.2
0
1950
1960
BEA
1970
1980
Adjusted 1
1990
2000
0.1
0
1950
Adjusted 2
1960
BEA
lation equation (4) to relate investment/capital ratios
to the BEA data.22 The growth rates for these adjusted
capital stock series, shown in Figure 7, exceed the
official BEA measure by about 2.2 percent (Adjusted
1) and 2.5 percent (Adjusted 2) per year on average
over the entire sample period.
Completion of the growth accounting exercise
requires data for output and labor. In order for the
data to correspond to a broad measure of labor
productivity, output is taken to be gross domestic
business product.23 Business sector hours—from
the BLS labor productivity accounts—is used to
measure labor input. These data series, along with
the series for capital growth, can be used to back
out measures of labor-augmenting technological
change from the growth accounting equation (3).
Figure 8 shows measures of “neutral” technology that are derived from this procedure, where the
series are expressed in log levels relative to a 1950
base in order to illustrate cumulative growth. Each
of the series displays a clear decelleration beginning
in the early 1970s, corresponding to the widely cited
“productivity slowdown” that has prevailed for much
of the subsequent period. For the two measures of
z derived from quality-adjusted data, the slowdown
is particularly distinctive. After growth associated
with investment-specific technology has been
accounted for, the indexes of neutral technological
progress have been nearly flat since 1970.
1970
1980
Adjusted 1
1990
2000
Adjusted 2
Estimates of Neutral and InvestmentSpecific Technology
Table 2 provides a summary of the two sources
of growth, reporting the contributions to total potential growth provided by neutral and investmentspecific technological change as in equation (7).
For comparability with previous studies, the data
coverage for this decomposition begins with 1954.
Over the entire period from 1954 to 2001, the qualityadjusted measures show that the role of investmentspecific technological change has been considerable,
accounting for 60 to 68 percent of total potential
growth. Even the unadjusted NIPA data show a contribution of investment-specific technology that is 25
percent of the implied total.
The relative contributions of the two types of
technology growth have not been constant over
22
In particular, the accumulation equation implies that qx/k=
(1– δ )/(1+gk ). The properties of the adjusted investment series and
growth rates of investment-specific technology can therefore be used
to relate the initial adjusted capital stock levels to the BEA data. This
calculation yields initial values for the adjusted capital series of about
one-third the level of the official data. Results are not very sensitive
to small changes in the assumptions generating this relationship,
however.
23
In keeping with the model’s implications for price measurement,
real output is calculated by deflating nominal business sector GDP
using the consumption price deflator.
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Pakko
Table 2
Sources of Technological Progress, 1954-2001
1954-2001 1954-1977 1978-2001
BEA
Neutral
Investment-specific
Total
1.65
0.55
2.21
2.46
0.10
2.56
0.83
1.01
1.85
Adjusted 1
Neutral
Investment-specific
Total
0.69
1.20
1.89
1.29
0.91
2.20
0.09
1.50
1.59
Adjusted 2
Neutral
Investment-specific
Total
0.57
1.39
1.97
1.33
0.93
2.26
–0.18
1.86
1.67
1.76
2.52
1.00
Actual productivity
growth
the entire sample period, however. In the first half
of the sample, 1954-1977, the quality-adjusted
measures show that investment-specific technology
contributes only about 38 percent to total potential.
For the NIPA numbers, the measured contribution
of investment-specific technology during this period
is negligible. During the second half of the sample
period, investment-specific technology overwhelmingly predominates. The second of these two adjusted
measures (derived from Cummins and Violante)
shows a negative contribution for neutral technology
growth, while the first measure (based on Pakko)
measures the contribution of neutral technology at
only about 6 percent.
Implications for Potential Productivity
Growth
The final line in Table 2 shows the actual growth
rate of output per worker for the relevant sample
periods. Over the entire period from 1954 to 2001,
all three measures of technology change overpredict
actual growth. As demonstrated in the breakdown
between the first half and the second half of the
sample, however, the overprediction is attributable
to the more recent span of years. For the period
1954-77, the two adjusted measures slightly underpredict actual productivity growth. For the period
1978-2001, all three overpredict actual growth.
Of course, the measures of potential growth
derived from the estimated technology series are
approximated measures of long-run relationships,
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so it is not surprising that they do not precisely
replicate actual growth over any given finite sample.
During the period from the mid-1970s to the present,
however, the magnitude and prevalence of the
discrepancy suggest more than measurement or
approximation error.
Recent research on the economic effects of
introducing new technologies help to explain the
apparent gap between measures of technology
growth and productivity growth. The data suggest
a rather dramatic change in the pattern of technology trends: the period of slow productivity growth
in the 1970s and 1980s is associated with a change
in the composition of technological progress from
neutral to investment-specific technology.
Many economists have suggested that changes
in trend technology growth— particularly for capitalembodied technologies—are associated with long
transition periods during which productivity lags the
rate of technological advance. Indeed, both Cummins
and Violante (2002) and Pakko (2002b) focus on the
adjustment of productivity growth to technological
innovations. Cummins and Violante calculate that
the “technology gap”—the gap between the productivity of the best technology and average productivity—rose from 15 percent in 1975 to 40 percent
in 2000. This finding is in the spirit of “technology
diffusion” models (e.g., Hornstein and Krusell, 1996;
Jovanovic and MacDonald, 1994; Greenwood and
Yorukoglu, 1997; Andolfatto and MacDonald, 1998;
Hornstein, 1999), which posit that learning about
the full potential of new technologies can generate
long implementation lags as resources are channeled
into the process of adapting new technologies into
existing production structures.24 Pakko (2002b)
shows that even in the absence of explicit diffusion
lags, the adjustment of the capital stock to changes
in technology growth trends give rise to long lags
between technology and productivity—particularly
when technology growth is investment-specific.
These findings can be interpreted as suggesting that
a great deal of the potential productivity improvement has yet to be fully incorporated into measured
actual productivity growth.
CONCLUSIONS
A great deal of attention has recently been paid
to the notion that rapid technological innovation
24
Another class of general growth models addressing the adaptation of
“general purpose technologies” (e.g., Helpman, 1998) suggests similar
lags.
FEDERAL RESERVE BANK OF ST. LOUIS
has been the driving force behind recent gains in
U.S. productivity growth. However, the nature of
these technology advances—being embodied in
entirely new types of high-tech capital equipment—
is not well explained by classical growth theory.
This paper has reviewed a class of economic models
featuring “investment specific” growth that explicitly
describe a process in which new technologies are
capital-embodied.
Recent estimates of the magnitude of this type
of technology growth reported in this article suggest
that over 60 percent of potential productivity growth
over the past half-century can be attributed to
investment-specific technology. Since at least the
mid-1970s, the estimates suggest that the importance
of investment-specific technology has increased
sharply, accounting for practically all of the implied
potential productivity gains.
However, measured productivity growth has
fallen short of these estimates of potential. Recent
research on the process of adapting new technologies
to existing production frameworks gives reason for
optimism about this finding. To the extent that rapid
growth of investment-specific technological innovation has yet to be fully exploited, as the data suggest,
technology-related gains in productivity should be
expected to continue well into the future.
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