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An Introduction to Two-Rate Taxation of
Land and Buildings
Jeffrey P. Cohen and Cletus C. Coughlin
When taxing real property at the local level in the United States, land and improvements to the
land, such as buildings, are generally taxed at the same rate. Two-rate (or split-rate) taxation departs
from this practice by taxing land at a higher rate than structures. This paper begins with an elementary discussion of taxation and the economic rationale for two-rate taxation. In theory, moving to
a two-rate tax reduces the deadweight losses associated with distortionary taxation and generates
additional economic activity. The paper also provides a history of two-rate taxation in the United
States and a summary of studies attempting to quantify its economic effects. Discussions of the
practical and political challenges of implementing two-rate taxation complete the paper.
Federal Reserve Bank of St. Louis Review, May/June 2005, 87(3), pp. 359-74.
“In my opinion, the least bad tax is the property
tax on the unimproved value of land, the Henry
George argument of many, many years ago.”
—Milton Friedman,
as quoted in Mankiw (2004),
1976 Nobel Prize laureate in economics.
“The property tax is, economically speaking, a
combination of one of the worst taxes—the part
that is assessed on real estate improvements…
and one of the best taxes—the tax on land or
site value.”
—William Vickrey (1999),
1996 Nobel Prize laureate in economics.
R
evenues from the taxation of real
property play a key, and frequently
controversial, role in the funding of
elementary and secondary education
as well as many other publicly provided services.
Our focus is on one suggested improvement of
property taxation known as “two-rate” or “splitrate” taxation. When taxing a specific parcel of
real property in the United States, the same rate
is usually applied to the land as well as to the
improvements to the land, such as buildings.
The opinions expressed by Nobel Prize winners
Milton Friedman and William Vickrey are at the
root of proposals to differentiate the taxing of
land from the buildings on that land. Such proposals have attracted increasing attention from
researchers and policymakers in Connecticut,
Massachusetts, Virginia, and Pennsylvania in
recent years.1
The two-rate proposal is a modification of
the extreme case in which the only tax levied is
on the value of land. Taxes on the value of buildings, as well as all other taxes, would be zero.
Thus, the owners of buildings would no longer
pay a property tax; only the owners of land would
be taxed. Such a pure land tax approach was
advocated by Henry George in a book published
in 1879, Progress and Poverty. He argued that
land should be taxed at 100 percent of its “rental
value.”2 George reasoned that the land value tax
1
Craig (2003) notes that over 700 cities worldwide use two-rate
taxation of property.
2
O’Sullivan (2003, p. 154) defines land rent as “the annual payment
in exchange for the right to use the land.”
Jeffrey P. Cohen is an assistant professor of economics at the Barney School of Business, University of Hartford; he acknowledges the support
of the Lincoln Foundation. Cletus C. Coughlin is deputy director of research and a vice president at the Federal Reserve Bank of St. Louis.
Jason Higbee provided research assistance. The views expressed are those of the authors and do not necessarily reflect official positions of
the Federal Reserve System or the Lincoln Foundation.
© 2005, The Federal Reserve Bank of St. Louis.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
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Cohen and Coughlin
would increase efficiency (and the wealth of
society) by allowing governments to abolish taxes
on improvements to land, as well as eliminate
all other forms of taxation. He also cited equity
reasons for the “single tax” on land.3 Namely,
increases in land value (exclusive of improvements) in the early 1900s were due primarily to
an entire community’s private-sector and publicsector economic activities rather than the actions
of the specific land owner. Therefore, George
argued, land owners should not benefit disproportionately from city growth, and the tax on
land would allow for the redistribution of these
unearned gains.4
A pure land tax, however, is not without some
faults. First, it is not easy to measure the value of
land net of improvements, and this would make it
difficult for government to determine the amount
of the land tax. This shortcoming of the pure land
tax would also be present with the two-rate tax.
Second, if a pure land tax were to capture all
current and future rent from the landowners, the
market value of the land would become zero. This
would be equivalent to the government taking the
land from landowners. Thus, people would have
no incentive to hold land, leading to abandonment of the land, and likely resulting in governmental decisions about how the land should be
used and by whom. Third, the change to a pure
land tax would likely have significant redistributional effects, with large landowners likely incurring substantial adverse wealth effects. This effect,
however, might be viewed by some as a virtue
rather than a fault.
Compared with the pure land tax, the two-rate
tax on land and buildings is a more general and,
perhaps, more practical alternative. Instead of
taxing land and structures at the same rate, as is
the case with the conventional property tax, the
two-rate tax would tax land at a higher rate than
3
4
George used the term “single tax” because he thought that a tax
on unimproved land could yield sufficient revenues to finance all
government spending. While his thinking was appropriate for the
late nineteenth century, the revenue potential of land taxation is
far less than the size of public spending today.
A discussion of the ethical arguments involving land taxation
(i.e., Is such a tax just?) can be found in Fischel (1998) and Bromley
(1998).
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the structures on the land. This form of the tax
would encourage improvements on relatively
small lots of land because such improvements
would be taxed at a lower rate than the land itself.
The increased incentive for improving structures
would lead to increased economic development.
In the context of urban economic development,
such a tax policy might reverse the trend of economic decay experienced by some cities. Moreover, because the tax rate on land using a two-rate
tax would be less than the tax rate using a pure
land tax, the potentially large changes in land
prices would be mitigated somewhat. Thus, the
size of adverse wealth effects would be reduced,
which might help in reaching a political agreement
to support a two-rate system.
In the next section, we provide an introduction
to taxation. This general introduction provides
the foundation for a discussion of land taxation
and the two-rate tax. A history of two-rate taxation
in the United States follows this discussion. Tworate taxation has been used in Pennsylvania, most
notably in Pittsburgh. Next, we review a number
of studies attempting to quantify the effects of tworate taxation. These studies include a case study
of Pittsburgh as well as studies attempting to identify the potential effects of various tax-change
proposals. This discussion is followed by an elaboration of the practical problems of implementing two-rate taxation. A summary of the political
economy issues involved in land value taxation
completes the body of our paper.
THE WELFARE EFFECTS OF
TAXATION USING DEMAND AND
SUPPLY CURVES5
Demand and supply curves can be used to
illustrate how taxes affect the behavior and the
economic well-being of consumers and producers.
The effect of taxation is one of the topics in what
economists refer to as welfare economics. Before
5
Readers familiar with this material might want to proceed directly
to the next section on land taxation. For readers desiring an elaboration of the material in this section, see Chapters 6 through 8 in
Mankiw (2004).
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
Cohen and Coughlin
Figure 1
Figure 2
Demand and Consumer Surplus
Supply and Producer Surplus
Price
Price
Supply
A
Consumer Surplus
Producer Surplus
P1
B
P2
C
Demand
D
O
Q1
Quantity
analyzing the effects of a specific tax, we must
first introduce the concepts of consumer surplus,
producer surplus, and efficiency.
O
Quantity
Q2
what they actually pay (i.e., consumer surplus)
is represented by the triangular area P1AB.
Producer Surplus
Consumer Surplus
We begin by using a demand curve to measure consumer surplus. Consumer surplus is the
amount that buyers are willing to pay for a good
minus the amount they actually pay for it.
Figure 1 shows a hypothetical demand curve.
Assuming a price per unit of P1, buyers would
purchase Q1 units of this good. Thus, the total
expenditure by consumers on this good would be
P1 times Q1 or, in terms of an area, the rectangle
OP1BQ1.
The demand curve reveals how much consumers are willing to pay for the Q1 units. Moving
rightward on the quantity axis from the origin,
the value that consumers are willing to pay is
reflected by the height of the demand curve. This
reflects the assumption that the first unit is valued
the most by consumers, the second unit somewhat
less, and so on as one moves down the demand
curve. Thus, the total amount that consumers are
willing to pay for the Q1 units is equal to the area
of the four-sided figure OABQ1. The difference
between what consumers are willing to pay and
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
Turning to the supply side of this market, the
concept of producer surplus can be illustrated
using a supply curve. Producer surplus is the
difference between actual compensation received
by sellers for a given quantity of output (i.e., total
revenue) and the minimum compensation sellers
would require to provide that given quantity.
Figure 2 shows a hypothetical supply curve.
The positive slope of the supply curve reflects
the assumption that the compensation to induce
additional units of production increases as output
increases. Assuming a price per unit of P2, producers would supply Q2 units of this good. Thus,
the total revenue would be P2 times Q2 or the area
of the rectangle OP2CQ2.
The minimum compensation necessary to
induce producers to supply Q2 is revealed by the
supply curve. Moving rightward on the quantity
axis from the origin, the minimum compensation
is reflected by the height of the supply curve.
Thus, the minimum compensation for Q2 units
is equal to the four-sided area ODCQ2. The difference between the total revenue of producers and
the minimum they must receive to produce (i.e.,
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Cohen and Coughlin
Figure 3
Figure 4
Market Equilibrium: Consumer and Producer
Surplus
Effects of a Tax Levied on Consumers
Price
Price
Supply
Consumer Surplus
Supply
Pc
P0
Pp
E
Pe
Demand0
Producer
Surplus
Demand1
Demand
Q1
Qe
Effects of Taxes
Now let’s examine the effect of taxes on this
market. Taxes impose a wedge between what
consumers pay and what producers receive.
Assume a tax of $1 per unit is levied on buyers
of a particular good. Such a tax can be illustrated
by shifting the demand curve downward by the
size of the tax because consumers only care about
their out-of-pocket expense in determining a
desired quantity. This is shown in Figure 4 by
M AY / J U N E
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Quantity
Quantity
producer surplus) is represented by the triangular
area DP2C.
In equilibrium, the quantity consumers are
willing to buy equals the quantity producers are
willing to supply. The competitive equilibrium
shown in Figure 3 reflects what economists term
“economic efficiency.” One key implication of
economic efficiency is that total economic surplus,
which is the sum of consumer and producer surplus, cannot be increased by either increasing or
decreasing the output of this good. Increased output would cause the additional cost incurred by
sellers to exceed the additional value to buyers,
while decreased output would cause the additional value to buyers to exceed the additional
cost incurred by sellers.
362
Q0
the shift in demand from Demand0 to Demand1.
The new equilibrium quantity is Q1, which is less
than the original equilibrium of quantity of output.
At Q1, the price per unit received by producers
is Pp and the price paid by consumers is Pc. The
difference in these two prices is $1, which is the
amount per unit received by the taxing authority.6
Note that, despite the fact that the tax is levied
on consumers, both consumers and producers
bear the burden of the tax. Consumers incur a
reduction in consumer surplus because they are
now paying a higher price per unit for a reduced
quantity. Meanwhile, producers incur a reduction
in producer surplus because they are now receiving a lower price per unit and producing less.
Does it matter in this case if producers had
been taxed $1 per unit of output rather than taxing
consumers $1 for every unit they purchased? The
answer is no. This possibly surprising result is
shown in Figure 5. Because the tax increases production costs by $1 per unit, the supply curve is
shifted upward by the size of the tax. Once again,
the difference between the price paid by consumers, Pc, and the net price received by producers, Pp , is $1. This tax wedge is identical to
6
To distinguish between the two prices, the price paid by consumers
can be called the gross-of-tax price, while the price received by
producers can be called the net-of-tax price.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
Cohen and Coughlin
Figure 5
Figure 6
Effects of a Tax Levied on Producers
Deadweight Loss of a Tax
Price
Price
Supply1
Supply0
Supply0
Pc
Pc
P0
P0
Pp
Pp
Demand0
A
Deadweight
Loss
E
B
Demand0
Q1
Q0
the tax wedge shown in Figure 4. Consequently,
the equilibrium quantity, Q1, in Figure 5 is the
same quantity as in Figure 4. Given the identical
price faced by consumers and the identical quantity, consumers bear the same burden, regardless
of upon whom the tax is levied. An identical comment can be made concerning the tax burden of
producers.
Taxes and Welfare
Next, let’s examine the welfare consequences
in more detail. Because Figures 4 and 5 generate
identical results, we can simplify the analysis by
not showing the curve that shifts. Figure 6 shows
the same information as Figures 4 and 5. The $1
tax per unit drives a $1 wedge between what consumers pay and producers receive. This $1 per
unit is received by the government as tax revenue.
In Figure 6, tax revenue is represented by the
rectangle PpPcAB (or (Pc – Pp) × Q1). Meanwhile,
the tax imposes burdens on consumers and producers. The cost of taxation for consumers and
producers reflects not only the amount paid to
the taxing authority, but also the cost associated
with transactions that no longer occur because the
tax has made them “uneconomic.” This latter
point is due to the fact that, in nearly all cases,
taxation causes consumers and producers to
change their behavior.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
Q1
Quantity
Quantity
Q0
The tax burden for consumers is the reduction
in consumer surplus. Due to the higher price and
the reduced consumption, this loss is the foursided area P0PcAE. The tax burden for producers
is the reduction in producer surplus. Due to the
lower price and the reduced production, this
loss for producers is the four-sided area PpP0EB.
Note that some of the losses incurred by both
consumers and producers reflect a transfer to the
government.7 Overall, the net decline in national
well-being is the triangle BAE, which is termed
the deadweight loss (DWL) caused by the tax. This
loss reflects the fact that taxation prevents some
mutually beneficial exchanges between consumers
and producers from occurring.
For a given tax, the distribution of the effects
on economic well-being and the size of the DWL
depend on how much quantity demanded and
quantity supplied respond to the change in price
stemming from the tax. A summary measure of
this responsiveness is the price elasticity of
demand (supply). The price elasticity of demand
is the absolute value of the percentage change in
7
To simplify the analysis, we have assumed that the government
programs funded by the tax revenues yield benefits that are equal
to the losses incurred by consumers and producers associated with
the tax payments.
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Cohen and Coughlin
quantity demanded divided by the percentage
change in price. Larger values of the price elasticity of demand are associated with flatter slopes
of the demand curve; conversely, smaller values
of the price elasticity of demand are associated
with steeper slopes of the demand curve.8,9 The
same terminology and implications for slope are
used for the price elasticity of supply, for which
larger (smaller) values of the price elasticity of
supply are associated with flatter (steeper) slopes
of the supply curve.
The price elasticities of demand and supply
affect the tax burdens imposed on consumers
and producers. Exactly how is straightforward.
Begin by envisioning a clockwise rotation of the
demand curve around point E in Figure 6. In this
case, the price elasticity of demand is becoming
less elastic (more inelastic). With an unchanged
supply curve, as the demand curve becomes less
elastic, the price that consumers pay will rise as
will the price that producers receive. Note that the
tax wedge must remain constant. The end result
is that the tax burden imposed on consumers rises
relative to that of producers. In other words, holding all other things constant, as the price elasticity
of demand decreases, the tax burden of consumers
rises relative to that of producers.
Similar results occur when the price elasticity
of supply becomes less elastic. With the demand
curve unchanged, as the supply curve becomes
less elastic, the price that producers will receive
falls as will the price that consumers pay. Thus,
the tax burden imposed on producers rises relative to that of consumers. In summary, as the price
elasticity of demand (supply) decreases, the larger
the relative tax burden of consumers (producers).
The economic intuition underlying this result
is straightforward. In terms of their consumption,
the less responsive consumers are to the higher
8
The price elasticity of demand at a specific point on a demand
curve, for instance (P0 ,Q0), is equal to the absolute value of P0 /Q0
times ∆Q/∆P. The latter term is the inverse of the slope of the
demand curve. If a demand curve were to become flatter (steeper),
the value of ∆Q/∆P would increase (decrease). Thus, the price
elasticity of demand increases (decreases).
9
Economists refer to increasing values of the price elasticity of
demand (supply) as being “more elastic” or “less inelastic” and
decreasing values as being “less elastic” or “more inelastic.”
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M AY / J U N E
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price they pay as a result of a tax, the higher their
relative tax burden. In other words, the tax burden
of consumers is relatively more the less they
change their behavior in response to higher prices.
Similar reasoning pertains to producers. In terms
of their production, the less responsive producers
are to the lower (net) price they receive as a result
of a tax, the higher their relative tax burden.
In addition to being related to the tax burdens
of consumers and producers, the price elasticities
of demand and supply affect the DWL of the tax.
A tax creates a DWL because it causes buyers and
sellers to change their consumption and production behavior. For a given tax, the larger the price
elasticities of demand and supply, the larger are
the changes in consumption and production.
Thus, larger price elasticities of demand and
supply are associated with larger DWLs.
THE THEORY OF LAND TAXATION
“Tax something, there will be less of it—
except land.” (Harriss, 2003)
Land is different from most other goods.
Namely, proponents of land taxation note that the
supply of (unimproved) land, which is provided
by nature, is fixed. In other words, the supply is
perfectly inelastic. This implies that the supply
curve for land is vertical, as shown in Figure 7.
Recall that a tax on consumers of land (as well as
a tax on consumers of any good, as outlined in the
previous section) will shift the demand curve
downward. Figure 7A shows a decline in demand
from Demand0 to Demand1. Because the supply
curve is vertical, shifting the demand curve downward implies that the new demand curve will
intersect the supply curve at the same quantity
of land as before the land tax (i.e., Q0). As a result,
the intersection of the new demand curve and
supply curve will occur at a lower net-of-tax
equilibrium price than before the land tax (i.e.,
P1 rather than P0)—with no change in the equilibrium quantity of land. Further, note that the
gross-of-tax price, P0, is identical to the price in
the absence of the tax. The land tax has no effect
on the allocation of productive resources. The
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
Cohen and Coughlin
result is that land owners bear the entire burden
of the tax and there is no DWL with this land tax.10
A property tax on buildings, however, alters
or distorts behavior away from that which would
take place in a competitive economy without
taxes. As seen in Figure 7B, because higher prices
encourage producers to supply additional buildings, the supply curve for buildings slopes upward. The demand curve slopes downward for
the same reason that the demand curve for land
slopes downward—higher prices result in a
decrease in the quantity of buildings demanded.
A tax on consumers of buildings causes the
demand curve to shift down by the amount of the
tax. The end result is that some of the burden of
the tax is borne by individuals who produce buildings (in the form of lower building prices) and
fewer buildings are consumed in equilibrium.
Thus, relative to the land tax case, the tax on buildings distorts behavior, leading to a DWL: The loss
of consumer and producer surplus is greater than
the revenue transferred to the government through
the tax.
Moving from a traditional property tax
(where land and buildings are taxed at one rate)
to a two-rate tax (where land is taxed at a relatively
higher rate) lowers DWL. If a goal is to keep total
tax revenues unchanged, the tax on buildings can
be lowered and the tax on land raised to achieve
a revenue-neutral alternative. As a result, the
distortionary (building) tax is decreased (i.e., in
Figure 7B, the demand curve shifts upward
from Demand1), while the neutral (land) tax is
increased. The overall effect is to lower the DWL.
One way to think of this reduction in DWL is that
a change to a more efficient tax system is equivalent to a tax cut. A given amount of public services
can be provided with a lower local tax burden.
Despite the fact that tax revenues are unchanged,
the tax burden is effectively lowered because of
the decline in DWL.
A reduction of the DWL associated with the
current system of property taxation, however, is
not the only economic argument that can be
10
O’Sullivan (2003, pp. 526-28) presents a somewhat different
exposition of the market effects of land taxation but arrives at the
same outcome that the equilibrium price of land falls by the amount
of the tax, with the quantity of land in equilibrium unchanged.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
Figure 7
Taxing Land versus Taxing Buildings
A
Price of
Land
Supply0
P0
P1
Demand0
Demand1
Quantity of Land
Q0
B
Price of
Buildings
Supply0
P0
P1
Demand0
Demand1
Q1 Q0
Quantity of Buildings
made to support increased tax rates on land and
decreased tax rates on improvements. Mills (1998)
has provided an analysis of the spatial equilibrium effects of single taxation. Specifically, Mills
showed how productive activity throughout a
hypothetical metropolitan area would be changed
by a revenue-neutral switch from a conventional
property tax (i.e., one that applies to both buildings [capital] and land) to a tax on land only.
The switch causes capital and labor to be substituted for land. The more intensive use of capital
and labor increases the productivity of each land
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Cohen and Coughlin
Table 1
Mill Rates: Kauai County, Hawaii, Fiscal Year 2004 (July 2003–June 2004)
Homestead
Single
family
Apartment
Hotel/
resort
Commercial
Industrial
Agricultural Conservation
Buildings
3.64
4.5
8.15
8.15
8.15
8.15
4.5
4.5
Land
4.35
5.49
8.55
8.55
8.55
8.55
7.95
8.45
SOURCE: Tax Foundation of Hawaii; www.tfhawaii.org/taxes/property.html.
parcel, which tends to increase gross-of-tax land
prices.11 With agricultural land remaining untaxed, the city expands. Due to the increased use
of capital and labor on each land parcel, output
in the metropolitan area expands—in fact, output
increases at every location within the metropolitan
area. Thus, as shown by Brueckner (2001), such
a tax change would lead to denser patterns of land
development and, therefore, inhibit metropolitan
sprawl. Since land in many inner cities is currently underutilized, such denser land development would be desirable.
In a subsequent section of our paper, we take
a closer look at the possible magnitudes of the
economic effects of using two-rate taxation. A
caveat mentioned by Mills is that the adjustment
period associated with such a tax change might
well be very long and require very large, albeit
justified, investments.
TWO-RATE TAXATION IN THE
UNITED STATES
Because real property taxes in the United
States are generally levied by local taxing authorities, most examples of two-rate taxation are at
the local level. The most frequently mentioned
example involves the state of Pennsylvania and,
specifically, the city of Pittsburgh. In 1979-80,
Pittsburgh revamped its property tax system by
raising tax rates on land to more than five times
the rate on structures. From 1913 to 1979-80,
Pittsburgh had a two-rate tax in place, with the
tax rate on buildings being twice the rate on land
11
Technically speaking, the equilibrium gross-of-tax rent-distance
function rises, while the net-of-tax rent-distance likely falls.
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(Hartzok, 1997).12 According to the state’s Taxation
Manual (Pennsylvania Department of Community
and Economic Development, 2002), Scranton is
the other city in Pennsylvania that is authorized
to charge lower tax rates on buildings than on
land.13
Although recent state legislation authorized
two local governments in Virginia to implement
a two-rate tax, neither has adopted it (Brunori,
2004). The cities of Fairfax and Roanoke have
the authority to tax property on land at a lower
rate than the corresponding land; however, one
stipulation of the legislation is that the tax on
property may not be zero, thus precluding a pure
land tax.14
A final example involves Hawaii, whose state
legislature passed a two-rate tax in 1963. A major
difference between the Hawaii legislation and
the Pittsburgh legislation, however, is that in
Hawaii the two-rate tax applied to all jurisdictions
(Rybeck, 2000). Legislation in 1978 granted counties the authority to set their own local property
tax rates. As of fiscal year 2004, though, Kauai
was the only one of Hawaii’s four counties to set
12
The Taxation Manual for Pennsylvania (2002) notes that all property
owners in the state pay property taxes to the municipality, the
corresponding county, and school district. Oates and Schwab (1997)
also note that for the city of Pittsburgh, the presence of these school
district and county property taxes that levy a “conventional property
tax” imply that the net tax rate for land is greater than twice the
rate for structures.
13
Other governmental entities in Pennsylvania, such as third-class
cities, boroughs, and third-class school districts coterminous with
third-class cities, may also use two-rate taxation. For a discussion
of the structure of different local levels of Pennsylvania government,
see section 6 of volume 116 of the Pennsylvania Manual (2003):
www.dgs.state.pa.us/pamanual/lib/pamanual/sec6/section6a.pdf.
14
For a reproduction of the detailed Virginia legislation, see
www.progress.org/cg/roan03.htm.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
Cohen and Coughlin
higher tax rates for land than for buildings.15 As
can be seen in Table 1, the differences in tax rates
for many property classes for Kauai are small.
Table 2
EFFECTS OF TWO-RATE
TAXATION
City
A number of recent quantitative studies have
examined the effects of implementing two-rate
taxation. Quantitative studies are important for
providing policymakers with estimates of the
potential gains from shifting toward land as a tax
base and some sense of the size of the distributional issues of such a change. To date, only one
comprehensive study, focused on the consequences for Pittsburgh, has attempted to identify
the actual effects of two-rate taxation. Generally
speaking, existing quantitative studies have
attempted to gauge the hypothetical effects of tworate taxation. Some of these latter studies have
focused on the short-run initial effects, while
others have attempted to identify the likely effects
given the economic decisions that would ensue
under the changed tax regime. In other words, the
former studies consider only the initial redistribution of the property tax burden and, as a result,
do not identify how differential rates on land and
improvements are likely to induce more intensive
use of land.
The Pittsburgh Experience
After Pittsburgh further increased the difference between the tax rate for land and the tax rate
for buildings in 1979-80, the city experienced a
substantial increase in building activity. Oates
and Schwab (1997) provided suggestive evidence
that Pittsburgh’s change in tax rates played a major
role in stimulating the building boom.16 They
noted that this finding is surprising, however,
because public finance theory suggests that
increasing the land tax while leaving the buildings
15
For the details of property tax rates for all four counties in Hawaii,
see www.tfhawaii.org/taxes/property.html.
16
Oates and Schwab also point out, however, that there was a major
Pittsburgh revitalization effort (Renaissance II) underway in the
late 1970s in an attempt to counteract the demise of the city’s
steel industry.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
Percent Change in Average Annual Value of
Building Permits Between 1960-79 and
1980-89
Percent change
Akron
–34.4
Allentown
–40.2
Buffalo
–11.5
Canton
–39.7
Cincinnati
–27.2
Cleveland
–31.8
Columbus
15.4
Dayton
–14.4
Detroit
–24.7
Erie
–52.9
Pittsburgh
70.4
Rochester
–30.6
Syracuse
–43.2
Toledo
–32.4
Youngstown
–67.0
SOURCE: Oates and Schwab (1997, Table 3).
tax unchanged should have no effect on building activity. It is also worth noting, however,
that according to Oates and Schwab, the city of
Pittsburgh granted tax cuts for new building construction. These tax cuts essentially indirectly
lowered the tax rate on new (but not on existing)
buildings.
Suggestive evidence concerning the impact
of Pittsburgh’s change in tax rates is presented in
Table 2, which shows the percentage change in
average annual value of building permits for 15
cities between the two periods 1960-79 and 198089. Excluding Pittsburgh, which had a greater
than 70 percent increase in average annual building permits between these two periods, and
Columbus, which had a 15 percent increase, all
13 other cities experienced a decrease in building
permits between these two periods.
To generate stronger evidence, Oates and
Schwab also used an econometric model to test
the impact of structural change that may have
occurred in 1979-80 when the city of Pittsburgh
M AY / J U N E
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Cohen and Coughlin
increased the land/buildings tax differential. For
each of the 15 cities listed in Table 2, Oates and
Schwab ran regressions with the real value of
building permits against a constant and a dummy
variable. This dummy variable took a value of
zero for years prior to 1980 and a value of 1 for
1980 and later. They found that the coefficient
on the dummy variable was both positive and
statistically significant only in the regression for
the city of Pittsburgh.17
To present further evidence on the impact of
increasing the land/buildings tax rate differential,
Oates and Schwab looked at U.S. Census Bureau
data of the metropolitan statistical areas (MSAs)
of these 15 cities over the years 1974-89. With
these data, they made a distinction between cities
and suburbs and between the real values of residential and nonresidential building permits. They
ran regressions with these Census data using the
same specifications as for the Dun and Bradstreet
data, with distinct regressions for residential, nonresidential, and office building permits for each
city and its respective suburbs. For the city of
Pittsburgh, the post-1979 dummy was significant
in the regressions for both the nonresidential and
office building permits, but insignificant for the
residential regression.18 For the Pittsburgh suburb
regressions, the post-1979 dummy in the residential permit regression was significant but negative;
this dummy was significant but positive in the
Pittsburgh suburban office regression, and insignificant in the Pittsburgh suburban nonresidential
regression.19
These findings reveal a correlation between
the 1979-80 tax reforms in Pittsburgh and the
subsequent increases in building permits. As mentioned above, however, these findings are far from
definitive in light of public finance theory and the
specifics of the tax reform in Pittsburgh (that is,
the fact that the tax on buildings was unchanged
when the tax on land was raised).20
17
The limited use of two-rate taxation has motivated a number of informative simulation studies
Oates and Schwab also looked at a slight variation of the aforementioned model, which included a time trend in addition to the
other variables. They found that the coefficient on the post-1979
dummy variable was positive and statistically significant only in
the Pittsburgh and Buffalo regressions.
18
The signs and significance of these variables are the same for the
similar specifications that include time trends.
19
Once again, the signs and significance of these variables are robust
to the inclusion of a time trend in these regressions.
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M AY / J U N E
2005
Short-Run Initial Effects
Because Virginia is a state whose citizens
have shown much interest in two-rate taxation,
Bowman and Bell (2004) used data on individual
property parcels from three Virginia locations to
estimate property tax liabilities using a tax in
which only the unimproved land is taxed. Consequently, Bowman and Bell were able to identify
the initial change in the real property tax liabilities of taxpayers resulting from a shift to a pure
land tax, a limiting case of two-rate taxation, from
the current uniform tax on land and improvements. The three areas examined vary substantially from each other. Roanoke, a city of roughly
100,000 residents, has been slowly losing population, yet has experienced job growth. Chesterfield
County, a bedroom county in the Richmond area
with over 250,000 residents, has grown both in
terms of population and jobs. Highland County,
a small rural county of less than 2,500 residents,
has experienced declines in both population and
jobs.
Regardless of the area, Bowman and Bell
found that owners of properties with high landto-improvements ratios will tend to experience
an increase in their tax liabilities with the move
to two-rate taxation, while owners of properties
with low land-to-improvements ratios will tend
to experience a decrease in their tax liabilities.
Generally speaking, owners of residential property,
especially owners of multi-unit housing properties, would tend to benefit. In addition, the
researchers found that, even within a specific
classification of land use, substantial differences
in distributional effects were likely.
Simulation Studies
20
The Pittsburgh City Council removed the two-rate system in
2000. Craig (2003) reports that construction spending in the city
was higher in the two years prior to rescission than the two years
after. Construction activity in the city was also lower than in the
surrounding suburbs and in the United States as a whole after the
rescission.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
Cohen and Coughlin
to generate information about its potential effects.
It is important to stress, similar to Kodrzycki
(1998), some important caveats about simulation
studies. Computable general equilibrium models,
which provide the foundation for simulation
studies, provide a range of answers to policy
questions because the appropriate structure of
the underlying model and the choice of parameter
values are subject to much uncertainty.21 Here
we focus on three studies. These studies provide
insights into the economic consequences of
land value and two-rate taxation in a variety of
situations.
Nechyba (2001) has explored the economic
impacts of land tax reforms for each U.S. state as
well as for an average state. Numerous revenueneutral reforms were examined; in other words,
the increase in revenues from increased taxes on
unimproved land exactly matches the decrease in
tax revenues from reducing some distortionary
tax on capital or labor. Generally speaking, based
on the likely change in land prices, Nechyba
found that reforms eliminating entire classes of
taxes are feasible in nearly all states. The political
prospects for passing a specific reform are better
in states with high per capita taxes and low per
capita incomes and when the reform is targeted
to lowering taxes on capital rather than labor. In
addition, reforms targeted to lowering taxes on
capital cause either increases in land prices or
modest declines, while reforms targeted to lowering taxes on labor tend to cause large declines in
land prices.
The second study we examine was done by
England (2003). He undertook a simulation study
using county-level data that examined a revenueneutral shift for New Hampshire from a uniform
property tax to a land value tax. The shift of the
tax burden from capital to land reduces the disposable income of owners of land, some of which is
21
For example, Kodrzycki (1998) highlights the importance of the
elasticity of substitution between land and capital, which is the
optimal response of the capital/land ratio to a change in the relative
prices of these inputs. When this elasticity equals 0.25, Nechyba
(1998) finds that the substitution of land taxes for capital taxes leads
to an increase of 43 percent in the capital/land ratio and 32 percent
in national output. Meanwhile, a higher value of this elasticity, 0.5,
is associated with a more than doubling of the capital/land ratio
and an 89 percent increase in national output.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
likely borne by nonresidents. The reduction in
disposable income leads to reduced consumer
spending on items other than housing services.
These impacts, however, are more than offset by
the changes set in motion by the decline in the
cost of owning residential buildings as well as
commercial and industrial capital. As a result,
residential construction and business investment
spending are boosted. Overall, employment and
gross state product increase in New Hampshire,
both immediately and after ten years. Moreover,
each of New Hampshire’s ten counties is projected
to have higher output, income, employment, and
population a decade after the tax change. While
all counties benefit, the economic changes for the
county that benefits the most are roughly double
those of the county benefiting the least.
The final study we examine was done by
Haughwout (2004), who estimates the consequences for New York City of replacing its current
tax system with a land tax. Two situations are
examined. In one case all taxes are eliminated
with the exception of the land tax, which is maintained at its current rate. In the other case, the key
difference is that the tax rate on land is increased
so that total tax revenue is maintained.
In the first case, the distortions caused by
taxes are eliminated and overall tax burdens are
reduced. At the same time, tax revenues decline,
so the provision of public goods falls correspondingly. Overall, New York City experiences substantial increases in private output, private capital
stock, employment, land values, and population
and a substantial reduction in public good provision and per capita tax revenues.
In the second case, the tax rate on land is
increased substantially so that tax revenues are
maintained. Contrary to the first case, land prices
fall, due in part to the substantially higher land
tax rate. Public goods provision is maintained.
Similar to the first case, private output, private
capital stock, employment, and population rise
sharply.
The two cases examined by Haughwout produce a clear message. The potential gains from
eliminating the distortions stemming from the
taxation of capital and labor, especially in a city
in which existing tax rates are relatively high,
M AY / J U N E
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Cohen and Coughlin
are quite large. Such a conclusion leads quite
naturally to the issue of why two-rate taxation is
rarely used.
IMPLEMENTING TWO-RATE
TAXATION: SOME PRACTICAL
PROBLEMS
In opposition to the theory and evidence of
the potential gains from using two-rate taxation,
a number of practical problems face a region that
decides to implement two-rate taxation. These
problems include valuing land accurately, determining the revenue potential of land value taxation, and providing sufficient public infrastructure
to support the increased economic activity.
To impose different tax rates on improvements
to land and raw land, one must have estimates of
the value of the improvements and the value of
raw land. Netzer (1998), using an in-depth examination of land value data, concluded that nonagricultural land values could not be trusted.
Moreover, the data were incomplete with respect
to timing and coverage. Therefore, practically
speaking, useful land value data for two-rate
taxation purposes do not exist.
As Mills (1998) has stressed, to preclude distortions, a land tax must be applied to the value
of land prior to any improvements. Defining
exactly what raw land is presents problems. When
a parcel of land is ready to be developed, it has
already been improved substantially. Preparing
land for development generally requires a number
of costly activities, such as clearing and leveling
the land, conducting environmental tests, surveying, obtaining the required permits, and installing
underground infrastructure. Furthermore, the
value of raw land hinges on the state of technology
as well as on the state of urban and rural development. For example, agricultural inventions have
affected the value of rural land, while construction innovations have affected the value of urban
land. It remains to be seen how developments in
information technology will affect land values.
The bottom line is that estimating the value of
raw land, which is likely to change over time, is
very challenging.
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Even more challenging is the assessment of
land values of developed properties. With respect
to commercial property, Mills (1998) notes the
sites and the structures are owned by different
groups. The separate ownership is frequently
driven by tax considerations, with the site owned
by an untaxed organization and the structure
owned by a business in a high tax bracket that can
utilize the benefits of depreciation. In theory,
separate estimates of site and structure values of
developed properties could be generated using
an approach known as hedonic pricing. Such an
approach is commonly used to explain, in a statistical sense, housing prices. The sales price of a
house is related to the characteristics of the house
(i.e., living space, number of bathrooms, age, etc.),
lot size, the neighborhood, and the community.
Applying hedonic pricing to commercial
properties is problematic. Difficulties would arise
because of a lack of agreement as to which characteristics should be included, the paucity of transactions, and the fact that many transactions are
not arms-length exchanges. Consequently, generating accurate estimates of raw land values, an
essential component of land taxation, is difficult;
uniform taxation may be preferred because it is
less costly to use than two-rate taxation.22 However, whether the additional administrative cost
is large or small is unclear. Netzer (1998) has noted
that, despite the fact that each parcel of land is
unique, the difference in value for adjacent parcels
is minimal, a fact that should ease the administrative burden.
The absence of accurate land value data makes
it difficult to answer the question of whether land
value taxation would generate sufficient revenues
to be an important replacement for revenues from
conventional property taxes. Despite the lack of
land value data, Netzer (1998) and McGuire (1998)
find that Pittsburgh’s experience with two-rate
taxation suggests that land value taxation can
generate an adequate level of tax revenue. On the
other hand, Mills (1998) is doubtful. His reasoning is straightforward: Annual real estate taxes
are 1.5 to 2.0 percent of the market value of tax22
One way to overcome this problem, suggested by Anas (1998), is
to have the city purchase and demolish some buildings and then
sell the land.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
Cohen and Coughlin
able property and site values are estimated to be,
at most, 10 percent of property values. If site and
structure rents are capitalized at the same rate,
gross-of-tax site rents are, at most, 1 percent of
property values. Consequently, a 100 percent
land rent tax would not generate sufficient revenue to replace the revenue from existing real
estate taxes.
A land tax rate of 100 percent of the land rent
is equivalent to land confiscation without assuming the liabilities of ownership. Mills (1998) has
noted that courts have consistently ruled that
similar regulations or taxes require, based on the
Fifth Amendment, that owners be compensated
for their losses. Such a court decision would
negate the value of using the land tax. While it
is unlikely that proponents of two-rate taxation
would argue for a tax rate of 100 percent on land,
there remains a question as to what percentage
of land rent could be taxed away without substantially affecting an owner’s incentive to seek
the best use for the land. At some tax rate, major
misallocations of land use would result.
Another potential problem occurs as a result
of the increased economic activity that takes place,
assuming the successful implementation of land
taxation. The resulting increase in the building/
land and employment/land ratios would necessitate increased infrastructure provided by government, such as transportation facilities and schools.
Without transportation infrastructure, increased
traffic congestion could negate the potential benefits of land taxation. The unanswered question is
whether the political process would be responsive
to the changed environment in the private sector.
In light of the increased activity, many would
downplay this situation as a problem, but rather
view it as an opportunity.
THE POLITICAL ECONOMY OF
TWO-RATE TAXATION
A strong case exists that two-rate taxation is
more efficient than, and thus preferable to, uniform taxation. A reasonable question is why
uniform taxation remains the norm. In addition
to the practical problems discussed in the precedF E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
ing section, a number of explanations have been
proposed. These explanations fall into either of
two general categories—one stressing that the
efficiency gains are likely to be elusive and another
stressing that opposition from those likely to be
harmed by the change to a two-rate system prevents such a change.
Efficiency
We begin with a discussion of the arguments
based on efficiency. Lee (2003) has shown that
uniform taxation of land and capital may be more
efficient than the taxation of land only. This possibility arises when some land in a taxing jurisdiction is owned by nonresidents. In terms of public
policy, a specific jurisdiction is assumed to structure its fiscal policies in the interests of its residents. Thus, one might argue that tax policies are
made with minimal consideration for the wellbeing of absentee owners because nonresidents
do not vote in the jurisdiction. One consequence
is that the jurisdiction taxes land excessively to
exploit absentee owners and the resulting funds
are used to overprovide public goods.23 One way
to mitigate the inefficiency of overtaxing land is
for a higher-level government to require jurisdictions to tax land and capital at a uniform rate.
This is what occurs in the United States because
most state governments do not allow lower-level
governments to deviate from uniform taxation.
Another argument suggesting the desirability
of uniform taxation has been made by Wildasin
and Wilson (1998). They start with the observation
that the returns to land are risky under production
uncertainty. This feature of the economy provides
an incentive for individuals to diversify their risk
by owning land in multiple jurisdictions. However, if each jurisdiction eliminates the rent on
owning land with 100 percent tax rates on land,
the benefits of diversification are eliminated.
23
Public goods, according to Rosen (1995, p. 61), are goods characterized by “non-rival consumption.” Nonrival consumption exists
when one person’s consumption of the good does not reduce its
availability to anyone else. Common examples are national defense,
lighthouses, roads, and parks. Note that for roads and parks, at
some point, as more and more individuals attempt to enjoy the
services of roads and parks congestion costs arise; when this occurs,
consumption is no longer nonrival.
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Cohen and Coughlin
Therefore, uniform taxation allows for benefits
from diversification and may be superior to the
pure land tax.
Opposition
The argument that political opposition would
mount against the change from uniform taxation
to two-rate taxation is straightforward. The change
in taxation will create winners and losers. Owners
of properties with high land-to-improvements
ratios (e.g., car dealerships) will tend to experience
an increase in their tax liabilities with the move
to two-rate taxation, while owners of properties
with low land-to-improvements ratios (e.g., highrise office buildings) will tend to experience a
decrease in their tax liabilities. The owners of substantial amounts of land are likely to be wealthy
and may have a disproportionate voice in the
political process and, thus, prevent a change that
would harm them.
The preceding discussion suggests that communities with heterogeneous consumer preferences and incomes might be unlikely candidates
to adopt a land tax. On the other hand, more
homogeneous areas, such as a suburban community, are more likely candidates for adoption.
However, as Hamilton (1976) and Fischel (1998)
have noted, these more homogeneous communities are also likely to be less afflicted by distortionary taxes.
A fundamental question concerns how tworate taxation can be introduced so as to reduce the
political opposition. England (2004) runs simulations using tax parcel data and shows that the
opposition to tax reform will likely be reduced if,
as part of the introduction of two-rate taxation,
uniform property tax credits are also introduced.
Before completing our discussion concerning
opposition to two-rate taxation, a few points about
the knowledge of policymakers are warranted. A
lack of understanding of two-rate taxation on the
part of political leaders likely is not a reason for
the limited use of the two-rate tax in states and
localities in the United States. Brunori (2004) conducted a survey of state, county, and city officials
and received about 1200 responses. The results
indicate that between 65 and 70 percent of the
respondents were “very or somewhat familiar”
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M AY / J U N E
2005
with land value taxation, and about 65 to 67 percent of these political leaders responded the same
for the two-rate tax. About 76 percent of city and
county government officials and over 62 percent
of state lawmakers thought that a two-rate tax
would enhance economic development. According to Brunori, over 40 percent of political leaders
who responded held a common “misperception”
that the two-rate tax system would lead to greater
sprawl, due to additional building on undeveloped
suburban land stemming from the reduction in
the tax rate on structures.
CONCLUSION
Proponents of two-rate taxation stress that
the taxation of real property involves two taxes.
One falls on man-made capital, such as buildings,
while the other falls on land, which is provided
by nature. The taxation of capital tends to deter its
formation. The higher the tax rate is in a specific
location, the larger the incentive for investors to
direct their capital elsewhere. The taxation of
land, however, does not deter either the formation
of land or encourage its relocation because land is
essentially fixed in quantity and immobile. Therefore, the taxation of land does not generate the
changes in behavior that one sees with the taxation of capital. This differential effect of taxation
provides a justification for real property taxation
that taxes buildings and land at different rates.
The theoretical gains associated with a
revenue-neutral movement from single-rate taxation of real property to two-rate taxation are subject to little controversy. Gains arise in the form
of declines in the deadweight losses associated
with taxation and increases in overall economic
activity. Parcels of land within a city would tend
to be used more productively. However, the size
of the gains associated with specific two-rate proposals is subject to much uncertainty. For example,
the study of Pittsburgh’s experience with two-rate
taxation by Oates and Schwab (1997) and a number of simulation studies have suggested that the
gains can be substantial. On the other hand, the
paucity of experience with two-rate taxation, the
sensitivity of the results of simulation studies to
the underlying model’s structure and the choice
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
Cohen and Coughlin
of parameter values, and concerns about administrative feasibility raise questions about the size
of the gains that could be realized.
The majority of legislators are familiar with
the theoretical consequences of two-rate taxation.
However, the fact that few regions use two-rate
taxation reflects the existence of significant obstacles. First, the practical implementation of tworate taxation complicates the assessment process
because the value of land must be separated from
the value of improvements. Second, significant
political opposition to two-rate taxation arises
because the change to two-rate taxation causes
some individuals to suffer adverse distributional
consequences; generally speaking, owners of
property with high land-to-improvement ratios
tend to be harmed, while owners of property with
low land-to-improvement ratios tend to benefit.
In light of these consequences, policies that mitigate the adverse effects, yet allow for the capture
of the economic gains, are required to reduce the
opposition to two-rate taxation and increase the
prospects for adoption.
Given the current system of taxation in the
United States, pressures for using two-rate taxation
will likely continue to emerge at the local level.
It remains to be seen, however, whether the opinions of Nobel Prize winners Milton Friedman
and William Vickrey concerning land taxation
will become widely held by legislators and voters.
Brueckner, Jan K. “Property Taxation and Urban
Sprawl,” in Wallace E. Oates, ed., Property Taxation
and Local Government Finance: Essays in Honor of
C. Lowell Harriss. Cambridge, MA: Lincoln Institute
of Land Policy, 2001, pp. 153-72.
Brunori, David. “What Politicians Know About Land
Taxation.” Land Lines, October 2004, 16(4);
www.lincolninst.edu/pubs/pub-detail.asp?id=972.
Craig, Eleanor D. “Land Value Taxes and Wilmington,
Delaware: A Case Study,” Proceedings of the
National Tax Association’s 96th Annual Conference
on Taxation, November 14, 2003, pp. 275-78;
www.buec.udel.edu/craige/nta-lvt.htm.
England, Richard W. “State and Local Impacts of a
Revenue-Neutral Shift from a Uniform Property to
a Land Value Tax: Results of a Simulation Study.”
Land Economics, February 2003, 79(1), pp. 38-43.
England, Richard W. “An Essay on the Political
Economy of Two-Rate Property Taxation.” Working
Paper WP04RE1, Lincoln Institute of Land Policy,
2004.
Fischel, William A. “The Ethics of Land Value
Taxation Revisited: Has the Millennium Arrived
Without Anyone Noticing?” in Dick Netzer, ed.,
Land Value Taxation: Can It and Will It Work Today?
Cambridge, MA: Lincoln Institute of Land Policy,
1998, pp. 1-23.
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F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
Evidence on Wage Inequality, Worker Education,
and Technology
Christopher H. Wheeler
The rise in U.S. wage inequality over the past two decades is commonly associated with an increase
in the use of “skill-biased” technologies (e.g., computer equipment) in the workplace, yet relatively
few studies have attempted to measure the direct link between the two. This paper explores the
relationship among inequality, worker education levels, and workplace computer usage using a
sample of 230 U.S. industries between 1983 and 2002. The results generate two primary conclusions:
First, this rising inequality in the United States has been caused predominantly by increasing wage
dispersion within industries rather than between industries. Second, within-industry inequality
is strongly tied to both the frequency of computer usage among workers and the fraction of total
employment with a college degree. Both results lend support to the idea that skill-biased technological change has been an important element in the rise of U.S. wage inequality.
Federal Reserve Bank of St. Louis Review, May/June 2005, 87(3), pp. 375-93.
T
he rapid rise of U.S. wage inequality in
recent decades has produced a sizable
literature both documenting the empirical trends and theorizing about their
1
causes. The main empirical findings can be summarized by three basic patterns. First, the overall
distribution of hourly and weekly earnings across
all workers in the economy has grown wider.
Second, consistent with this rise, the wage gaps
between workers with different levels of education, especially between college graduates and
workers with no more than a high school diploma, have also increased. This rise in “betweeneducation-group” earnings disparity, however,
accounts for only a modest fraction of the rise
in overall wage dispersion because of the third
pattern: The variance of wages among workers
with the same level of education has also grown.2
1
See Levy and Murnane (1992) and Acemoglu (2002) for surveys.
2
These basic patterns have also been observed for a number of
Organisation for Economic Co-operation and Development (OECD)
countries, although wage inequality in the United States remains
higher than that of most other developed economies. See Blau and
Kahn (1996).
To explain these patterns, a variety of theories
have been advanced, including those stressing the
growth of international trade, changes in institutions (e.g., declining unionization and real minimum wage), rising immigration, and technological
change. Growing levels of imports into the United
States, for instance, may have hit workers in tradesensitive industries (e.g., textiles and apparel)
particularly hard as domestic labor demand and,
consequently, wages have dropped.3 Rising immigration since the 1960s may also have contributed
to these trends by increasing the supply of lessskilled workers in the U.S. labor market (Borjas,
Freeman, and Katz, 1997). In addition, because
unionization is often associated with wage compression (Fortin and Lemieux, 1997), declining
rates of union membership in the United States
may have contributed to rising earnings disparity.4
3
The Bureau of Labor Statistics produces the Occupational Outlook
Handbook, which offers predictions about job and wage growth in
various sectors, including Textiles and Apparel, given (among other
things) trends in international trade. The most recent edition can
be found at www.bls.gov/oco/home.htm.
4
In addition to Fortin and Lemieux (1997), Topel (1997) and Johnson
(1997) offer surveys of several prominent theories of wage inequality.
Christopher H. Wheeler is an economist at the Federal Reserve Bank of St. Louis. Elizabeth La Jeunesse provided research assistance.
© 2005, The Federal Reserve Bank of St. Louis.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
M AY / J U N E
2005
375
Wheeler
While there remains some disagreement as to
the significance of each of these mechanisms, a
general consensus has formed around one particular theory: skill-biased technological change
(SBTC).5 The hypothesis is quite simple. Over the
past several decades, the supply of highly educated workers in total employment has grown. In
1950, for example, 17 percent of U.S. workers had
some education at the college level. By 1990, 57
percent did.6 As a result of this increase, the return
to investing in technologies that complement the
skills of these highly educated workers—the most
commonly cited example of which is information
technology—also rose because the search costs
involved in finding and hiring “skilled” labor
declined.7 Accordingly, recent technological
change has served to boost the wages of skilled
workers while depressing the employment opportunities and earnings of the less-skilled. As noted
by Acemoglu (1999), if “skills” are positively but
imperfectly associated with educational attainment, this mechanism can lead to larger betweeneducation-group gaps as well as greater inequality
within education groups.
Although there has been a host of evidence
documented on the general topic of technological
change, skill distributions, and inequality, there
are (at least) two issues that remain unresolved.
First, to what extent is rising inequality a withinor between-sector phenomenon? That is, does the
SBTC argument imply that inequality is driven by
growing differentials across workers in different
sectors or by growing gaps within the same sector?
Caselli (1999), for example, reports that, between
1975 and 1991, the variance of (equipment) capitallabor ratios across 450 four-digit manufacturing
sectors rose sharply in the United States. Because
capital-labor ratios tend to correlate positively
with both wages and the fraction of highly skilled
workers in total employment, Caselli interprets
this trend as evidence that SBTC has been highly
5
As noted by Card and DiNardo (2002), the SBTC explanation is
far from complete. Nonetheless, as suggested by Johnson (1997),
there is wide agreement that it has been an important determinant
of rising inequality.
6
These statistics are reported by Wheeler (2004).
7
See Autor, Levy, and Frank (2003) for an empirical analysis of
why computers are considered skill-biased.
376
M AY / J U N E
2005
variable across sectors: Some industries have
adopted advanced technologies and hired educated workers; others have chosen to utilize skillunbiased technologies and less-educated workers.
This result suggests that SBTC has driven inequality higher through a between-industry channel.
A qualitatively similar result is reported by
Acemoglu (1999), who finds that the fraction of
workers in the United States holding jobs (defined
by 174 industry-occupation cells) in the bottom
and top tails of the distribution of average hourly
pay increased between 1983 and 1993. This finding, he concludes, indicates that workers have
increasingly been sorted into “good” and “bad”
jobs, which further suggests that rising inequality
has been the product of growing between-sector
dispersion.
On the other hand, many studies of inequality
(e.g., Katz and Murphy, 1992; Juhn, Murphy, and
Pierce, 1993; Card and DiNardo, 2002) suggest
that, even after accounting for observable differences across workers (including their industries
of employment), the dispersion in their wage earnings has risen markedly. Such evidence suggests
that within-sector differences must also be an
important aspect of rising dispersion. However,
it remains unclear just how important these two
elements have been in explaining the overall
increase in earnings disparity.
Second, much of the evidence on technological change and wage dispersion tends to be indirect. That is, in spite of the popularity of the SBTC
hypothesis, surprisingly little research has directly
examined the association between inequality and
the extent to which computer equipment (or any
other “advanced” technology) is used in production.8 Most studies have either connected average
wage earnings to the use of computers and other
sophisticated technologies (Krueger, 1993; Doms,
Dunne, and Troske, 1997) or explored the relationship between the adoption of information technology and the distribution of worker skill (Berman,
Bound, and Griliches, 1994; Doms, Dunne, and
Troske, 1997; Autor, Katz, and Krueger, 1998).
8
Dunne, Foster, and Troske (2004) is a notable exception. However,
the focus of that paper is the U.S. manufacturing sector rather than
the entire private U.S. economy, which I examine here.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
Wheeler
This paper seeks to address both of these
issues. To this end, I perform two exercises. In the
first, I use annual data from the Current Population
Survey (CPS) over the period 1983-2002 to evaluate the degree to which rising wage dispersion
in the entire private U.S. economy can be attributed to growing dispersion within industries as
opposed to between them. In the second, I look
at the relationship between, on the one hand, a
variety of inequality measures within individual
industries and, on the other, the distribution of
educational attainment and the extent of computer
usage among workers employed in those industries. Computer usage, I assume, provides a direct
measure of SBTC; educational attainment provides
an indirect measure.9
To summarize briefly, the results indicate that
the rising U.S. wage inequality has been driven
primarily by growing dispersion among workers
within the same industry rather than between
industries. In each year, more than 75 percent of
the variance of hourly earnings can be attributed
to within-industry variation. More importantly,
this fraction has grown steadily over time, suggesting that the majority of the rise in overall wage
variance is due to increasing wage disparity among
workers within the same industry. When I turn to
the analysis of inequality within industries, I find
that wage dispersion—measured in a variety of
ways—is positively associated with both the fraction of college-educated workers and the extent
of computer usage. These results, I conclude, offer
some support for the skill-biased technological
change argument.
DATA
Sources
The majority of the worker-level data used in
this paper are derived from the Merged Outgoing
Rotation Group (MORG) files of the CPS for each
year between 1983 and 2002. These files are constructed by combining the individuals from each
month’s CPS who are in their final month (i.e.,
fourth or eighth) of interview and are, conse9
If SBTC is indeed a function of the distribution of skill, the fraction
of highly educated workers should capture (at least to a significant
degree) the extent of SBTC within an industry.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
quently, asked about their labor earnings. In an
effort to focus on individuals of prime working
age, I limit the sample to workers between the ages
of 18 and 65.
I perform two sets of calculations from the
MORG files. First, I compute educational attainment distributions and union membership rates for
a collection of more than 200 industries, which
correspond to an approximately three-digit
(Standard Industrial Classification [SIC]) level of
aggregation. To maximize the number of observations used for these computations, I use all individuals for whom an industry is identified and
who report positive weekly earnings. Doing so
produces a sample of 2,693,370 observations
across the 20 years.
The second set of calculations involves a
variety of earnings inequality measures based on
hourly wages. Here, I further limit the sample to
white males who report working at least 30 hours
per week so that the sample consists entirely of
workers with a strong attachment to the labor
force (i.e., their primary activity is work). Doing
so eliminates the need to account for the influence
of race and gender on earnings and, thus, the attendant inequality. It also reduces the effects of parttime workers whose presence in the workforce
from one year to the next may be heavily influenced by the business cycle. I further confine the
sample to hourly wages between $2.60 and $150
(in year-2000 dollars) to remove any remaining
outlier observations. These sample selection criteria are reasonably standard in the wage inequality literature (e.g., Katz and Murphy, 1992; Juhn,
Murphy, and Pierce, 1993; Card and DiNardo,
2002). In all, 1,156,715 observations are used in
the inequality calculations.
The industry coverage includes the entire
private sector. As noted, industries are mostly
defined at a three-digit (SIC) level of aggregation,
although some two-digit sectors and combinations of either three- or four-digit sectors are also
represented.10 For example, Coal Mining (CPS
10
A major (one-digit) sector is also included, Construction. To provide some sense of the differences between two-, three-, and fourdigit industries, Pharmaceutical Preparations and Medicinals and
Botanicals are four-digit sectors that belong to the three-digit sector
Drugs, which, in turn, is included in the two-digit sector Chemicals
and Allied Products.
M AY / J U N E
2005
377
Wheeler
industry code 41) and Air Transportation (code
421) are two-digit sectors; Hardware Stores (code
581), Drugs (181), and Advertising (code 721) are
three-digit sectors; Glass and Glass Products (code
250) is a combination of three-digit sectors; and
Primary Aluminum (code 272) is a collection of
four-digit sectors. A total of 230 industries are
identified over the 20-year period.
To quantify computer usage rates within each
industry, I use the October supplements to the
CPS for the years 1984, 1989, 1993, and 1997. In
these supplements, individuals were asked about
their computer use at work, including (for some
of the years) the types of tasks performed using
this equipment. Computer usage rates are calculated as frequencies of positive responses to the
question: “Do you directly use a computer at
work?” Note that these are the same data used by
Krueger (1993) in his study of the effect of information technology on wages and by Autor, Katz,
and Krueger (1998) in their analysis of computer
usage and skill distributions. Here, too, to maximize the number of observations used to estimate
computer usage within detailed sectors, the calculations incorporate all workers for whom an industry of employment can be identified. Additional
details about the construction of the final data set
appear in the appendix.
Although there have been years in which the variance has decreased, the general trend has clearly
been upward, rising 19 percent between 1983
and 2002.
Between-education-group gaps also exhibit
an upward trend. High school graduates in the
sample, for instance, earned roughly 16 percent
more than high school dropouts in 1983.12 In 2002,
they earned 27 percent more. What is even more
striking, however, is the gap at the top end of the
educational attainment distribution. Figure 2 plots
the evolution of the wage premium earned by
college graduates relative to workers with only
a high school diploma. This wage differential
increased from an average of 54 percent in 1983
to 73 percent in 2002.13
To see that earnings differentials among
workers with the same levels of education have
also grown over this period, consider Figure 3,
which plots the variance of the residuals following
a regression of log hourly wages on education
and experience.14 Based on the calculations, the
variance of these “residual earnings”—which is
often interpreted as the degree of spread in the
earnings distribution of workers with the same
observable levels of skill—rose by nearly 20 percent over this 20-year period.
Some Trends
BETWEEN-INDUSTRY VERSUS
WITHIN-INDUSTRY INEQUALITY
As noted in the introduction, three broad features characterize the evolution of the U.S. wage
distribution in recent decades: rising overall dispersion, widening gaps between workers with
different levels of education, and increasing dispersion among workers with the same levels of
education. All three are evident in the CPS data
examined here.
In 1983, for example, the 90th percentile of
the overall hourly wage distribution was roughly
1.9 times as large as the median. By 2002, it was
2.2 times as large. Figure 1 shows a similar result
using an alternative measure of overall wage
dispersion, the variance of log hourly wages.11
11
Wages are usually expressed in logarithms in studies of labor earnings. Doing so facilitates both the computation and interpretation
of the results (see Card, 1999).
378
M AY / J U N E
2005
Overall Wages
To assess the degree to which rising U.S. earnings dispersion has been a between- or withinindustry phenomenon, I consider the following
straightforward decomposition. Given a sample
12
These figures are based on the coefficients from year-specific
regressions of log hourly wages on four educational attainment
dummies (no high school, some high school, high school, some
college, college); a quartic polynomial in potential experience;
and indicators for marital status, union membership, metropolitan
status, and Census division of residence.
13
Figure 2 plots “log point” differences (i.e., the difference between
the log wages of one group and the log wages of another). To derive
percentages, simply calculate (exp(x) – 1), where x is the log point
difference.
14
More precisely, these residuals are derived from the same regression
as that described in footnote 12.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
Wheeler
Figure 1
Overall Wage Variance of Log Hourly Wages
0.35
0.34
0.33
0.32
0.31
0.3
0.29
0.28
19
83
19
84
19
85
19
86
19
87
19
88
19
89
19
90
19
91
19
92
19
93
19
94
19
95
19
96
19
97
19
98
19
99
20
00
20
01
20
02
0.27
Year
Figure 2
College Graduates Relative to High School Graduates
0.6
0.55
0.5
0.45
0.4
19
83
19
84
19
85
19
86
19
87
19
88
19
89
19
90
19
91
19
92
19
93
19
94
19
95
19
96
19
97
19
98
19
99
20
00
20
01
20
02
0.35
Year
Figure 3
Residual Wage Variance of Log Hourly Wages
0.23
0.22
0.21
0.2
0.19
0.18
84
19
85
19
86
19
87
19
88
19
89
19
90
19
91
19
92
19
93
19
94
19
95
19
96
19
97
19
98
19
99
20
00
20
01
20
02
19
19
8
3
0.17
Year
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
M AY / J U N E
2005
379
Wheeler
Table 1
Overall Inequality Decomposition
Year
Total wage variance
Within-industry component
Between-industry component
1983
0.288
0.222 (77.1)
0.066 (22.9)
1984
0.293
0.228 (77.9)
0.065 (22.1)
1985
0.3
0.23 (76.8)
0.069 (23.2)
1986
0.31
0.237 (76.6)
0.073 (23.4)
1987
0.313
0.24 (76.6)
0.073 (23.4)
1988
0.316
0.242 (76.8)
0.073 (23.2)
1989
0.304
0.233 (76.8)
0.07 (23.2)
1990
0.308
0.237 (76.9)
0.071 (23.1)
1991
0.308
0.235 (76.5)
0.072 (23.5)
1992
0.312
0.237 (76.1)
0.075 (23.9)
1993
0.313
0.24 (76.7)
0.073 (23.3)
1994
0.327
0.259 (79.3)
0.068 (20.7)
1995
0.324
0.259 (79.9)
0.065 (20.1)
1996
0.323
0.256 (79.2)
0.067 (20.8)
1997
0.324
0.258 (79.8)
0.066 (20.2)
1998
0.327
0.261 (79.7)
0.066 (20.3)
1999
0.327
0.262 (80)
0.065 (20)
2000
0.337
0.266 (79)
0.071 (21)
2001
0.335
0.267 (79.7)
0.068 (20.3)
2002
0.343
0.275 (80.2)
0.068 (19.8)
NOTE: Between- and within-industry components of total variance in log hourly wages as defined by equation (3). Percentages of
total variance accounted for by each component are reported in parentheses. The final column is calculated by dividing the annual
changes in the within-industry component by the corresponding changes in total variance.
of workers, the variance of the hourly wage distribution in year t, Vt , can be estimated as
Vt =
(1)
1
Nt
I t N i ,t
Vt =
1
Nt
i =1 j =1
I t N i ,t
∑ ∑ (w j ,i,t − w i,t + w i,t − w t )2 ,
i =1 j =1
– denotes the mean wage among workers
where w
i,t
of industry i, the variance of the wage distribution
can be expressed as the sum of two terms15:
380
M AY / J U N E
Vt =
∑ ∑ (w j ,i,t − w t )2 ,
where wj,i,t is the wage of worker j of industry i,
– is the overall mean wage, N is the number of
w
t
i,t
workers in industry i, It is the number of industries, and Nt is the total number of workers, Σi Ni,t ,
all for the year t. If we rewrite this expression as
(2)
(3)
2005
1
Nt
I t N i ,t
1
I t N i ,t
∑ ∑ (w j ,i,t − w i,t )2 + N ∑ ∑ (w i,t − w t )2 .
i =1 j =1
t i =1 j =1
The first, given by the sum of squared deviations
of individual wages from their industry means,
can be interpreted as a “within-industry” component of wage dispersion. The second, which is
constructed from the sum of squared deviations
of the industry means from the overall mean, can
be viewed as a “between-industry” component.
By calculating these two pieces, we can gain some
insight into the extent to which rising wage
inequality in the United States over the past two
15
The derivation of (3) is sketched in the appendix.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
Wheeler
Table 2
Residual Inequality Decomposition
Year
Total wage variance
Within-industry component
Between-industry component
1983
0.186
0.159 (85.7)
0.026 (14.3)
1984
0.187
0.162 (86.7)
0.025 (13.3)
1985
0.191
0.165 (86.2)
0.026 (13.8)
1986
0.195
0.167 (85.8)
0.028 (14.2)
1987
0.197
0.17 (86.4)
0.027 (13.6)
1988
0.199
0.171 (86.3)
0.027 (13.7)
1989
0.193
0.168 (87)
0.025 (13)
1990
0.192
0.168 (87.3)
0.024 (12.7)
1991
0.192
0.169 (87.7)
0.024 (12.3)
1992
0.19
0.167 (87.7)
0.023 (12.3)
1993
0.193
0.17 (88.3)
0.022 (11.7)
1994
0.205
0.184 (90)
0.021 (10)
1995
0.203
0.183 (90.2)
0.02 (9.8)
1996
0.203
0.184 (90.2)
0.02 (9.8)
1997
0.202
0.183 (90.7)
0.019 (9.3)
1998
0.206
0.187 (90.9)
0.019 (9.1)
1999
0.205
0.187 (91.5)
0.017 (8.5)
2000
0.216
0.196 (90.8)
0.02 (9.2)
2001
0.216
0.197 (91.4)
0.019 (8.6)
2002
0.222
0.204 (92)
0.018 (8)
NOTE: Between- and within-industry components of total variance in residual log hourly wages (after a regression on education and
experience) as defined by equation (3). Percentages of total variance accounted for by each component are reported in parentheses.
The final column is calculated by dividing the annual changes in the within-industry component by the corresponding changes in
total variance.
decades has been a between- or within-industry
phenomenon.
The resulting components using overall (i.e.,
unconditional) log hourly wages are listed in
Table 1. Most obviously, they show that the vast
majority of the wage dispersion observed each year
is due to earnings variation within industries. This
particular result can be seen from the fractions of
total variation accounted for by each component,
which are reported in parentheses. In all years,
the fraction of total wage variance accounted for
by within-industry variation is between 75 and
80 percent. More importantly, there seems to have
been a gradual rise in this fraction over time. At the
beginning of the sample time frame, the withinindustry component averaged approximately 77
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
percent of the total. By 2002, it was closer to 80
percent.
In all, the variance of log hourly wages rose
from 0.29 to 0.34 between 1983 and 2002. While
both the within- and between-industry components
also rose over this time frame, the within-industry
part accounted for nearly all—approximately
96.4 percent—of the increase in total variance.
Residual Wages
As noted previously, one of the basic features
of the rise in U.S. wage inequality is the growing
degree of dispersion in the wage earnings of workers with similar levels of skill (i.e., education and
experience). That is, the degree of variation among,
M AY / J U N E
2005
381
Wheeler
Figure 4
Computer Usage and College Completion Rates
19
83
19
84
19
85
19
86
19
87
19
88
19
89
19
90
19
91
19
92
19
93
19
94
19
95
19
96
19
97
19
98
19
99
20
00
20
01
20
02
0.55
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
Year
Computer Use
say, college graduates with 10 years of work experience has grown larger in recent decades. Has this
rise in residual inequality also been primarily a
within-industry phenomenon?
To consider this question, I begin by regressing
log hourly wages on a vector of personal covariates, including years of education; four educational attainment indicators (no high school, some
high school, high school, some college, college
or more); interactions of years of education with
these indicators; a quartic polynomial in potential
work experience; and dummies for marital status,
union membership, residence in a metropolitan
area, and Census division.16 I then collect the
residuals and use them in place of actual wages,
wj,i,t , when calculating the within- and betweenindustry pieces in (3).
Table 2 shows the results. Qualitatively, they
show precisely the same result as with overall
wages. In each year, the within-industry component is by far the larger piece of overall variation,
averaging between, roughly, 85 and 90 percent of
the total. Additionally, there has been a gradual
rise in this fraction over time—from 86 percent
in 1983 to approximately 92 percent in 2002—
16
These regressions are performed separately for each year. Again,
the logarithmic transformation of wage earnings is standard in the
labor literature as is the specification of the wage-experience profile by means of a fourth-order polynomial (e.g., Autor, Katz, and
Krueger, 1998). In terms of years of schooling completed, the educational attainment categories correspond to 0-8 (no high school),
9-11 (some high school), 12 (high school), 13-15 (some college),
16+ (college).
382
M AY / J U N E
2005
College Share
suggesting that the within-industry component
has become more important over time.
On the whole, between 1983 and 2002, the
change in within-industry residual wage variation
actually exceeded the increase in total residual
wage variation. To be specific, increases in withinindustry residual wage variation accounted for
123.9 percent of the change in total residual variation. Hence, there was actually a net decrease in
the extent of inequality across workers possessing
similar characteristics but employed in different
industries over these years. Evidently, whatever
has driven the rise of inequality across workers—
either with similar levels of education or not—
has done so primarily within individual
industries.
INEQUALITY, EDUCATION, AND
COMPUTER USE
Baseline Results
Given that the majority of rising wage dispersion has been the result of growing differentials
among workers within the same industry, I now
turn to the analysis of within-industry inequality
trends. Specifically, this section examines the
role of skill distributions (i.e., fractions of highly
educated workers in total employment) and
information technology in explaining industryspecific earnings inequality.
As shown in Figure 4, the fraction of total
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
Wheeler
Table 3
Education and Computer Usage Changes by Major Sector
Industry
College employment
fraction change 1983-2002
Agriculture, forestry, fisheries
Computer usage change 1984-97
0.02
0.17
Mining
–0.06
0.07
Construction
–0.001
0.13
Nondurable manufacturing
0.09
0.23
Durable manufacturing
0.05
0.15
Transportation
0.055
0.19
Wholesale trade
0.04
0.18
Retail trade
0.013
0.21
Finance, insurance, real estate
0.11
0.24
Business and repair services
0.11
0.29
Personal services
0.04
0.19
Entertainment and recreation services
0.05
0.26
Professional and related services
0.05
0.32
NOTE: Changes in proportions of employees with a bachelor’s degree and using a computer at work.
employment accounted for by college graduates
and the fraction of workers who use a computer
at work have both increased in the past two
decades. In 1983, the fraction of workers with at
least a bachelor’s degree stood at 19 percent. By
2002, it had grown to 25 percent. Similarly,
between 1984 and 1997, the fraction of workers
reporting use of a computer at work increased
from 30 percent to approximately 53 percent.
Table 3 shows that both of these qualitative
patterns were reasonably widespread, at least in
the sense that they occurred in nearly every major
industrial sector. In fact, of the 13 sectors listed
in the table, only 2—Mining and Construction—
saw their college employment fractions decrease
over the sample period. All, as it happens, witnessed increasing computer usage. Among the
228 (of 230) more detailed industry groups identified in both the beginning and ending years of
the sample, the results are similar. A total of 175
increased their fraction of college graduates in
total employment between 1983 and 2002, while
225 saw increases in their computer usage rates
between 1984 and 1997.17
To what extent do these trends account for
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
industry-specific levels of wage inequality? I
attempt to draw inferences about the answer using
the following statistical characterization of
inequality in industry i in year t, Ineqi,t :
(4)
Ineqi ,t = α + δt + β X i ,t + ε i ,t ,
where α is an overall constant; δ t represents a time
dummy added to capture the temporal variation
in inequality evident from Figures 1, 2, and 318;
Xi,t is a vector of time-varying industry characteristics; and εi,t is a residual. Three quantities are
included in Xi,t: the fraction of workers with a
bachelor’s degree,19 the fraction using a computer
17
The mean (standard deviation) change in the college employment
fraction is 0.04 (0.08); the change in the computer usage rate is 0.25
(0.16).
18
I reestimated specification I of equation (4) further adding industryspecific time trends to capture differences in the temporal behavior
of inequality across industries. The resulting estimates did not differ substantially from those reported here. All of the college-share
coefficients were significantly positive; all but one of the union
rate coefficients were significantly negative.
19
I also considered the share of total work hours accounted for by
college-educated workers instead of the college employment fraction.
Since the correlation between these two variables exceeds 0.99, the
results did not differ substantially from what is reported here.
M AY / J U N E
2005
383
Wheeler
at work, and the fraction who are members of a
union. As suggested previously, computer usage
is intended as a direct measure of SBTC, whereas
the college share is used as an indirect measure.
Both interpretations seem justifiable in light of the
research surveyed here connecting technological
adoption and the distribution of education/skill.
The unionization rate is included to capture the
influence of an institutional characteristic that has
likely contributed to changes in industry-level
inequality. Since these independent variables are
calculated from the CPS micro samples, I restrict
estimation to those industry-years for which at
least 10 observations were available, in an effort
to reduce the sampling noise inherent in each.
Because the computer usage data are available
for only 4 of the 20 years, I consider three different
specifications of this equation. In the first, I limit
Xi,t to the college and unionization fractions so
that I am able to use all 20 years of data. Direct
evidence correlating inequality with technology
is then given in the second specification, which
drops the college fraction but adds the computer
usage rate. The third specification considers both
direct and indirect measures of SBTC simultaneously by adding the college employment fraction
to this second specification.
To keep the analysis as broad as possible, I
examine three different categories of inequality
measures: (i) overall, (ii) between-education-group,
and (iii) residual. The overall measures include
the variance of log hourly wages and the differences between the 90th, 50th, and 10th percentiles
of the log hourly wage distribution. The betweeneducation-group gaps are given by differences
between the average log wages of college graduates
and those in each of the following four categories:
some college, high school, some high school, no
high school. Residual inequality is given by the
same statistics considered for overall inequality,
where the calculations are done using the residuals
following the regressions described in the subsection “Residual Wages.”
In all cases, estimation proceeds by generalized least squares in which the industry-year
observations are weighted by the number of CPS
observations used to calculate the inequality variables. An inequality figure based on 10 observa384
M AY / J U N E
2005
tions, after all, ought to involve greater sampling
error than one based on 1,000. This weighting
procedure helps to account for the differential
degree of noise across observations.
Results appear in Table 4. On the whole, they
show that inequality tends to be significantly
associated with each of the three regressors—the
college employment fraction, the computer usage
rate, and the extent of union membership. The
unionization rate, as expected, enters negatively
in 34 (of 36) instances (significantly in 30), suggesting that decreasing unionization is an important
piece of the rise in nearly every wage gap considered. Such a result, of course, reinforces the general view established in the inequality literature
that the decline in union activity in the United
States has been a major element in the rise of
earnings disparity.20
The two measures of SBTC, by contrast, both
enter positively in nearly every case. Indeed, none
of the college fraction coefficients and only one
of the estimated computer usage coefficients are
negative (albeit statistically insignificant). What
is more, of the 24 coefficients for each of these two
quantities, a large number are statistically important: 20 of the college fraction coefficients and 16
of the computer usage coefficients. The majority
of the insignificant coefficients, incidentally,
emerge from specification III in which both of
these regressors appear. Quite possibly, the lack
of significance in these cases derives from the
strong correlation between these two variables.21
Are the estimated associations economically
important? Just focusing on the overall 90-10 wage
difference, the point estimates suggest that a 1standard-deviation increase in either the college
employment fraction or the computer usage rate
is accompanied by a 4- to 7-percentage-point
increase in this differential.22 When evaluated at
20
Blau and Kahn (1996), for instance, find that differences in labor
market institutions (e.g., unionization) account for a large part of
the difference between inequality in the United States and that of
nine other OECD countries.
21
The correlation between the college employment fraction and the
frequency of computer usage is 0.61, which is consistent with the
findings of Autor, Katz, and Krueger (1998).
22
Summary statistics for the variables used in the inequality regressions are reported in Table A1 of the appendix.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
Wheeler
Table 4
Baseline Inequality Regressions
Dependent variable
Specification
College fraction
Overall variance
Overall 90-10 difference
Overall 90-50 difference
Overall 50-10 difference
College–no high school
College–some high school
College–high school
College–some college
Residual variance
Residual 90-10 difference
Residual 90-50 difference
Residual 50-10 difference
Computer rate
R2
Union rate
I
0.18* (0.01)
—
–0.17* (0.008)
0.38
II
—
0.11* (0.01)
–0.23* (0.02)
0.27
III
0.1* (0.03)
0.06* (0.02)
–0.22* (0.02)
0.31
I
0.53* (0.03)
—
–0.52* (0.03)
0.35
II
—
0.31* (0.05)
–0.66* (0.07)
0.24
III
0.31* (0.1)
0.17* (0.07)
–0.63* (0.07)
0.29
I
0.1* (0.02)
—
–0.55* (0.02)
0.33
II
—
0.002 (0.03)
–0.62* (0.04)
0.25
III
0.02 (0.06)
–0.006 (0.04)
–0.64* (0.05)
0.26
I
0.43* (0.02)
—
0.03 (0.02)
0.26
II
—
0.31* (0.04)
–0.04 (0.06)
0.2
III
0.29* (0.05)
0.18* (0.04)
I
0.58* (0.05)
—
–0.002 (0.04)
0.19
II
—
0.42* (0.06)
–0.08 (0.07)
0.19
III
0.15 (0.16)
0.35* (0.1)
–0.06 (0.08)
0.2
I
0.5* (0.04)
—
–0.14* (0.02)
0.21
0.005 (0.06)
0.28
II
—
0.3* (0.04)
–0.16* (0.04)
0.2
III
0.23* (0.13)
0.2* (0.08)
–0.13* (0.04)
0.2
I
0.17* (0.02)
—
–0.18* (0.02)
0.09
II
—
0.12* (0.04)
–0.2* (0.05)
0.09
III
0.13 (0.09)
0.06 (0.06)
–0.18* (0.05)
0.09
0.09* (0.02)
—
–0.11* (0.02)
0.08
I
II
—
III
0.07 (0.07)
I
0.11* (0.008)
0.054* (0.027)
–0.14* (0.03)
0.07
0.02 (0.04)
–0.13* (0.03)
0.07
—
–0.12* (0.006)
0.34
II
—
0.05* (0.01)
–0.17* (0.02)
0.21
III
0.08* (0.03)
0.01 (0.02)
–0.16* (0.02)
0.26
I
0.32* (0.02)
—
–0.41* (0.02)
0.32
II
—
0.16* (0.04)
–0.52* (0.06)
0.18
III
0.23* (0.07)
0.05 (0.05)
–0.5* (0.06)
0.23
I
0.16* (0.02)
—
–0.26* (0.01)
0.26
II
—
0.08* (0.02)
–0.32* (0.04)
0.15
III
0.12* (0.05)
0.03 (0.03)
–0.32* (0.04)
0.19
I
0.15* (0.01)
—
–0.15* (0.01)
0.21
II
—
0.07* (0.02)
–0.2* (0.03)
0.11
III
0.11* (0.04)
0.03 (0.03)
–0.19* (0.03)
0.14
NOTE: Coefficients from estimation of (4). Specification I uses annual data 1983-2002. Specifications II and III use only data from
1984, 1989, 1993, and 1997. Each regression includes year dummies. Heteroskedasticity-consistent standard errors are reported in
parentheses; * denotes significance at the 10 percent level.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
M AY / J U N E
2005
385
Wheeler
the mean value in dollar terms, this figure represents an increase of approximately $0.75 to $1.31
in the 90-10 differential. Such a magnitude is
roughly one-quarter of the standard deviation of
the 90-10 differentials in the sample.
Looking at the between-education-group gaps,
there are some sizable associations here too. A 1standard-deviation increase in the college fraction,
for example, correlates with a 3- to 7-percentagepoint ($0.27 to $0.62) increase in the college–some
high school gap and a 2- to 2.5-percentage-point
($0.14 to $0.18) increase in the college–high school
gap. For computer usage, a 1-standard-deviation
increase is associated with a 4.5- to 7-percentagepoint ($0.40 to $0.62) rise in the college–some high
school difference and a 1.5 to 2.5 percentage point
($0.11 to $0.18) increase in the college–high school
gap. Given sample standard deviations of, respectively, 36 and 30 percentage points for the college–
some high school and college–high school gaps,
these correlations are far from trivial.
There is, to be sure, some variation in the
coefficient magnitudes and statistical significance
of these two variables across the inequality measures. In particular, they tend to have the largest
associations with those measures involving the
position of the bottom of the distribution relative
to the middle and top, at least when considering
the overall and between-education-group gaps.
For example, for the overall percentile differences,
the coefficients are much larger for the 50-10 differentials than they are for the 90-50 differentials.
The positive associations between the college
and computer usage fractions and the overall 9010 differential, therefore, clearly seem to be driven
by the bottom half of the wage distribution.
A similar result can be inferred from the
between-education-group measures, which show
larger coefficients on the two SBTC variables when
considering the two “top-bottom” inequality
variables (college–no high school, college–some
high school) than when looking at the two “topmiddle” variables (college–high school, college–
some college). This pattern is consistent with the
idea that workers at the bottom ends of the wage
and educational attainment distributions were
the hardest hit by new technologies (or, at least,
benefited the least from them).
386
M AY / J U N E
2005
Endogeneity Considerations
Although the regressors have been treated as
exogenous thus far, it is possible that one in particular may be endogenous with respect to inequality: education. The fraction of an industry’s
workers with a college degree may, for example,
be an increasing function of the relative returns
paid to these workers. Hence, a rise in the college–
high school gap could increase the college fraction—either by attracting more college graduates
or driving away high school graduates, depending
on what causes the gap to increase—which would
bias the estimated coefficient on the college fraction upward.
In an effort to address this possibility, I consider the following simple exercise. I regress the
annual changes in an industry’s college employment fraction on the initial levels of inequality and
a set of year dummies.23 I then make inferences
about the extent to which inequality influences
the college fraction by examining the coefficients
on inequality. A significant coefficient, naturally,
would suggest that inequality levels have a nonnegligible influence on the educational mix of
workers.
The first column of figures in Table 5 shows
the results, which have a nearly uniform lack of
significance of initial inequality in explaining
subsequent changes in industry-specific college
fractions: Only 2 of the 12 coefficients are significant. These results seem to cast some doubt
on the notion that an industry’s college employment fraction is endogenous with respect to
inequality.
Of course, because this specification may not
adequately capture the response of education to
changes in inequality, I also consider an alternative
in which changes in the college employment
fraction are regressed on one lag of the change in
inequality (i.e., the change of an industry’s college
fraction between 2000 and 2001 is regressed on
the change in its level of inequality between 1999
and 2000). Hence, instead of correlating subsequent changes in education with initial levels of
inequality, this equation estimates how changes
in education are associated with recent changes
23
As before, I restrict these regressions to industry-year observations
based on at least 10 observations for the inequality calculations.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
Wheeler
Table 5
Education as a Function of Inequality
Specification
Measure
Overall variance
Initial levels
Lagged differences
–0.0007 (0.009)
–0.02* (0.01)
Overall 90-10 difference
Overall 90-50 difference
0.0002 (0.0003)
–0.007* (0.005)
0.0008 (0.005)
–0.005 (0.007)
Overall 50-10 difference
College–no high school
–0.008* (0.005)
–0.0003 (0.005)
–0.002 (0.002)
–0.006* (0.002)
College–some high school
0.007* (0.003)
College–high school
0.005 (0.004)
0.001 (0.002)
College–some college
0.005 (0.005)
–0.002 (0.004)
Residual variance
0.005 (0.01)
0.005 (0.02)
Residual 90-10 difference
0.003 (0.005)
0.003 (0.005)
Residual 90-50 difference
Residual 50-10 difference
0.01* (0.006)
–0.004 (0.01)
0.001 (0.002)
0.003 (0.006)
0.003 (0.008)
NOTE: Coefficients on inequality, in both initial levels and lagged first differences, from regressions of the annual change in an industry’s
college fraction on inequality. Regressions also include year dummies. Heteroskedasticity-consistent standard errors are reported in
parentheses; * denotes significance at the 10 percent level.
in inequality. Those results appear in the second
column of figures in Table 5.
Here, interestingly, a greater number of the
coefficients—4 of the 12—are significantly nonzero at conventional levels (i.e., at least 10 percent).
However, of these, all are negative, indicating
that increases in an industry’s inequality tend to
be followed by decreases in its college employment fraction. This particular result implies that,
if anything, the coefficients listed in Table 4 may
actually be biased downward (i.e., toward zero)
and, thus, understate the association between
education and inequality. Although certainly not
definitive, I take this evidence as suggesting that
endogenous education does not pose a significant
problem for the qualitative interpretation of the
results.
well be a nonlinear relationship between the
computer usage rate and the degree of spread in
the wage distribution. It may be, for instance, that
the relationship is positive at low levels of computer usage, but negative as the usage rate closes
in on unity.
The second augments the regression considered in (4) with industry-specific fixed effects:
(5)
Ineqi ,t = α + δt + µi + β X i ,t + ε i ,t ,
where µi is a constant element influencing the
degree of earnings inequality in industry i.
Doing so controls for all time-invariant industry
characteristics, unobserved or otherwise, that
may influence inequality and, thus, eliminates
any bias resulting from the omission of these
characteristics.24
Alternative Specifications
This section considers two alterations of the
analysis described here. In the first, I look at the
possibility that the dispersion of computer usage,
rather than the mean usage rate, influences the
degree of wage inequality. Indeed, there could very
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
24
One could also treat the industry-specific terms as stochastic and
estimate (5) by random effects. However, consistency of the random
effects estimator depends on the assumption that these terms are
uncorrelated with the regressors (see Wooldridge, 2002, p. 257).
Because the fixed-effects estimator is consistent whether this condition is satisfied or not, I treat the µi as a set of constants to be
estimated.
M AY / J U N E
2005
387
Wheeler
Table 6
Inequality and the Variance of Computer Usage
Dependent variable
College fraction
Computer rate
Computer variance
Overall variance
0.08* (0.03)
0.05* (0.02)
0.2* (0.06)
Overall 90-10 difference
0.26* (0.1)
0.13* (0.07)
Overall 90-50 difference
–0.01 (0.06)
–0.03 (0.04)
0.61* (0.18)
0.37* (0.11)
Overall 50-10 difference
0.27* (0.06)
0.16* (0.04)
0.24* (0.12)
College–no high school
0.16 (0.16)
0.32* (0.12)
0.1 (0.3)
College–some high school
0.24* (0.13)
0.16* (0.08)
0.14 (0.16)
College–high school
0.13 (0.09)
0.01 (0.05)
0.48* (0.12)
College–some college
0.07 (0.07)
Residual variance
0.075* (0.03)
0.01 (0.04)
0.29* (0.09)
–0.0004 (0.02)
0.11* (0.04)
Residual 90-10 difference
Residual 90-50 difference
0.2* (0.08)
0.03 (0.05)
0.32* (0.13)
0.11* (0.05)
0.01 (0.04)
0.2* (0.09)
Residual 50-10 difference
0.1* (0.04)
0.02 (0.03)
0.12* (0.07)
NOTE: Coefficients from estimation of Specification III of (4) in which the variance of computer usage has also been added.
Heteroskedasticity-consistent standard errors are reported in parentheses; * denotes significance at the 10 percent level.
Table 6 shows results from the inclusion of
the variance of computer usage. For the sake of
brevity, I have reported only the output from
specification III, in which Xi,t contains the college
graduate, computer usage, and union membership
fractions. While there is a slight dropoff in some
of the magnitudes of the coefficients relative to
the baseline estimates in Table 4, most are little
changed after including the variance of computer
usage. In fact, the same coefficients that are significant in Table 4 are significant here as well.
Computer use variance itself also enters positively and, for the most part, significantly, just
as one would expect. Each of the 12 coefficients
reported in the table is positive, 10 significantly
so. In these data, then, both the first and second
moments of the distribution of computer usage
correlate directly with wage inequality.25
Table 7 reports the results when both timeand industry-specific fixed effects are included
25
Since the majority of industry-year observations have computer
usage fractions less than 0.5, it is not surprising that the mean and
variance of the computer usage distribution are positively associated.
However, the correlation is relatively modest, 0.47, suggesting that
each variable may reasonably pick up some of the variation in
inequality independently of the other.
388
M AY / J U N E
2005
in the regressions. Two features of the results are
especially notable. First, the majority of the coefficients on both the college employment fraction
and frequency of computer use are positive, while
those on the unionization rate are negative, just
as in the baseline results. However, second, the
number of coefficients that differ statistically from
zero at conventional levels has dropped relative
to the results in Table 4. To be sure, among the
college fraction coefficients, more than half (15
of 24) remain significant, indicating that industryspecific changes in many of the inequality measures correlate strongly with changes in their
fractions of highly educated labor. At the same
time, only 13 of the 36 unionization coefficients
and 3 of the 24 computer usage coefficients differ
significantly from zero after conditioning on timeinvariant industry terms.
Very likely, this decrease in significance
stems from the decline in the extent of variation
in the data once industry-specific intercepts are
included. This particular aspect of the estimation
can be inferred from the sharp rise in the goodnessof-fit statistics reported in the final columns of
Tables 4 and 7. The average R2 rises from 0.21 to
0.67 with the addition of the industry effects.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
Wheeler
Table 7
Inequality Regressions—Industry Effects Included
Dependent variable
Specification
Overall variance
Overall 90-10 difference
Overall 90-50 difference
Overall 50-10 difference
College–no high school
College fraction
College–high school
Residual variance
Residual 90-10 difference
Residual 90-50 difference
Residual 50-10 difference
R2
–0.09* (0.02)
0.8
I
0.25* (0.02)
—
0.08* (0.05)
–0.16* (0.09)
0.8
III
0.24* (0.08)
0.07 (0.05)
–0.12 (0.09)
0.81
I
0.68* (0.12)
—
–0.5* (0.09)
0.77
II
—
0.08 (0.17)
–0.23 (0.4)
0.76
III
1.07* (0.4)
0.03 (0.17)
–0.13 (0.4)
0.77
I
0.17* (0.1)
—
–0.34* (0.07)
0.67
II
—
–0.04 (0.11)
–0.03 (0.25)
0.7
III
0.28 (0.4)
–0.06 (0.12)
0.02 (0.3)
0.7
I
0.5* (0.06)
—
–0.16* (0.06)
0.69
II
—
0.12 (0.12)
–0.2 (0.24)
0.72
III
0.79* (0.16)
0.09 (0.12)
–0.16 (0.22)
0.74
I
0.08 (0.14)
—
–0.24* (0.11)
0.59
II
—
0.06 (0.15)
–0.18 (0.27)
0.67
0.32 (0.4)
0.03 (0.16)
0.17 (0.11)
—
I
–0.13 (0.3)
0.67
–0.18* (0.08)
0.6
II
—
0.25* (0.12)
–0.32* (0.19)
0.67
III
0.27 (0.3)
0.25* (0.12)
–0.29 (0.2)
0.67
I
0.04 (0.07)
—
–0.16* (0.06)
0.6
II
—
0.1 (0.08)
–0.15 (0.13)
0.7
0.1 (0.08)
–0.12 (0.14)
0.7
—
–0.06 (0.06)
0.44
III
College–some college
—
Union rate
II
III
College–some high school
Computer rate
0.1 (0.2)
I
0.007 (0.07)
II
—
0.095 (0.08)
0.05 (0.14)
0.57
III
–0.17 (0.16)
0.11 (0.08)
0.007 (0.14)
0.57
I
0.13* (0.02)
—
–0.04* (0.02)
0.74
II
—
0.04 (0.03)
–0.13 (0.08)
0.7
III
0.13* (0.07)
0.03 (0.03)
–0.16* (0.08)
0.7
0.44* (0.1)
—
–0.16* (0.07)
0.7
0.03 (0.14)
0.28 (0.3)
0.69
0.17 (0.3)
0.7
I
II
—
III
0.78* (0.3)
–0.01 (0.1)
I
0.21* (0.07)
—
–0.03 (0.05)
0.59
II
—
–0.08 (0.11)
0.09 (0.22)
0.58
III
0.43* (0.2)
–0.02 (0.2)
0.59
0.23* (0.06)
—
–0.13* (0.05)
0.53
II
—
0.11 (0.07)
0.2 (0.17)
0.59
III
0.35* (0.18)
0.09 (0.07)
0.19 (0.16)
0.59
I
–0.1 (0.1)
NOTE: Coefficients from estimation of (5). Specification I uses annual data 1983-2002. Specifications II and III use only data from
1984, 1989, 1993, and 1997. Each regression includes year dummies and industry-specific fixed effects. Heteroskedasticity-consistent
standard errors are reported in parentheses; * denotes significance at the 10 percent level.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
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While this necessarily tempers the conclusions
that can be drawn from the results, one can still
interpret this evidence as consistent with the
SBTC hypothesis.
CONCLUSIONS
Despite the presence of a large literature
examining the rise of earnings inequality in the
United States, surprisingly few studies have
directly explored the role of information technology in driving this trend. Such an omission is
particularly surprising in light of the general consensus that has emerged in support of the skillbiased technological change hypothesis. This
paper has attempted to offer some evidence on
this issue.
The findings indicate that the vast majority
of the rise in U.S. wage inequality over the past
two decades is the product of increasing gaps
between workers within the same industry rather
than between workers across different industries.
This result holds whether considering workers
of differing levels of observable skill (overall
inequality) or those with the same levels (residual
inequality). What is more, within-industry
inequality—defined in overall, residual, and
between-education-group terms—tends to be positively associated with the two measures of skillbiased technological change considered here, the
college employment fraction and the frequency of
computer usage. Collectively, these two observations are compatible with the idea that skill-biased
technological change has been a significant element in the rise of wage dispersion in the United
States.
Of course, because the two measures of skillbiased technological change considered here are
less than ideal, there remains ample room for additional research on this topic. In particular, studies
examining the extent to which plants and industries have adopted specific production technologies, such as those considered by Dunne (1994),
and how the implementation of those technologies
correlate with earnings differentials would greatly
assist in clarifying the skill-biased technological
change hypothesis. Considering the popularity
of the theory, such an undertaking certainly seems
worthwhile.
390
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REFERENCES
Acemoglu, Daron. “Changes in Unemployment and
Wage Inequality: An Alternative Theory and Some
Evidence.” American Economic Review, December
1999, 89(5), pp. 1259-78.
Acemoglu, Daron. “Technical Change, Inequality,
and the Labor Market.” Journal of Economic
Literature, March 2002, 40(1), pp. 7-72.
Autor, David H.; Katz, Lawrence F. and Krueger,
Alan B. “Computing Inequality: Have Computers
Changed the Labor Market?” Quarterly Journal of
Economics, November 1998, 113(4), pp. 1169-213.
Autor, David H.; Levy, Frank and Murnane, Richard J.
“The Skill Content of Recent Technological Change:
An Empirical Exploration.” Quarterly Journal of
Economics, November 2003, 118(4), pp. 1279-333.
Berman, Eli; Bound, John and Griliches, Zvi. “Changes
in the Demand for Skilled Labor within U.S.
Manufacturing: Evidence from the Annual Survey
of Manufactures.” Quarterly Journal of Economics,
May 1994, 109(2), pp. 367-97.
Blau, Francine D. and Kahn, Lawrence M.
“International Differences in Male Wage Inequality:
Institutions versus Market Forces.” Journal of
Political Economy, August 1996, 104(4), pp. 791-837.
Borjas, George J.; Freeman, Richard B. and Katz,
Lawrence F. “How Much Do Immigration and
Trade Affect Labor Market Outcomes?” Brookings
Papers on Economic Activity, 1997, (1), pp. 1-90.
Card, David. “The Causal Effect of Education on
Earnings,” in Orley Ashenfelter and David Card,
eds., Handbook of Labor Economics. Volume 3A.
Amsterdam: Elsevier, 1999, pp. 1801-63.
Card, David and DiNardo, John E. “Skill-Biased
Technological Change and Rising Wage Inequality:
Some Problems and Puzzles.” Journal of Labor
Economics, October 2002, 20(4), pp. 733-83.
Caselli, Francesco. “Technological Revolutions.”
American Economic Review, March 1999, 89(1),
pp. 78-102.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
Wheeler
Doms, Mark; Dunne, Timothy and Troske, Kenneth
R. “Workers, Wages, and Technology.” Quarterly
Journal of Economics, February 1997, 112(1), pp.
253-90.
Krueger, Alan B. “How Computers Have Changed the
Wage Structure: Evidence from Microdata, 19841989.” Quarterly Journal of Economics, February
1993, 108(1), pp. 33-60.
Dunne, Timothy. “Plant Age and Technology Use in
U.S. Manufacturing Industries.” RAND Journal of
Economics, Autumn 1994, 25(3), pp. 488-99.
Levy, Frank and Murnane, Richard J. “U.S. Earnings
Levels and Earnings Inequality: A Review of Recent
Trends and Proposed Explanations.” Journal of
Economic Literature, September 1992, 30(3), pp.
1333-81.
Dunne, Timothy; Foster, Lucia; Haltiwanger, John
and Troske, Kenneth R. “Wage and Productivity
Dispersion in United States Manufacturing: The
Role of Computer Investment.” Journal of Labor
Economics, April 2004, 22(2), pp. 397-429.
Fortin, Nicole M. and Lemieux, Thomas. “Institutional
Changes and Rising Wage Inequality: Is There a
Linkage?” Journal of Economic Perspectives, Spring
1997, 11(2), pp. 75-96.
Johnson, George E. “Changes in Earnings Inequality:
The Role of Demand Shifts.” Journal of Economic
Perspectives, Spring 1997, 11(2), pp. 41-54.
Juhn, Chinhui; Murphy, Kevin M. and Pierce, Brooks.
“Wage Inequality and the Rise in Returns to Skill.”
Journal of Political Economy, June 1993, 101(3),
pp. 410-42.
Park, Jim Heum. “Estimation of Sheepskin Effects
and Returns to Schooling Using the Old and the
New CPS Measures of Educational Attainment.”
Working Paper No. 338, Industrial Relations
Section, Princeton University, December 1994.
Topel, Robert H. “Factor Proportions and Relative
Wages: The Supply-Side Determinants of Wage
Inequality.” Journal of Economic Perspectives,
Spring 1997, 11(2), pp. 55-74.
Wheeler, Christopher H. “Cities, Skills, and
Inequality.” Working Paper No. 2004-020A, Federal
Reserve Bank of St. Louis, September 2004.
Wooldridge, Jeffrey M. Econometric Analysis of
Cross Section and Panel Data. Cambridge, MA:
MIT Press, 2002.
Katz, Lawrence F. and Murphy, Kevin M. “Changes
in Relative Wages, 1963-1987: Supply and Demand
Factors.” Quarterly Journal of Economics, February
1992, 107(1), pp. 35-78.
APPENDIX
Data
Hourly wages are calculated as the ratio of a worker’s weekly earnings to usual hours worked per
week. The MORG files do topcode weekly earnings at various points ($999 for 1983 to 1988, $1,923 for
1989 to 1997, and $2,884 for 1998 to 2002). For topcoded values, I follow Card and DiNardo (2002) and
impute the weekly wages as 1.4 times the topcode value to approximate the mean of the upper tail of
the wage distribution. Similar techniques have been used by Katz and Murphy (1992), Juhn, Murphy,
and Pierce (1993), and Autor, Katz, and Krueger (1998). All hourly wages are converted to real terms
($2,000) using the personal consumption expenditure chain-type price index. Once these values are
computed, I then restrict the sample to workers with hourly wage earnings between $2.60 (which is
slightly in excess of one-half the current federal minimum wage) and $150 to eliminate outliers. Inequality
calculations are computed using the CPS “earnings” weight. For the educational attainment and union
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
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Wheeler
membership rates, a total of 2,693,370 observations are used. This corresponds to an average of 604.1
observations per industry-year (minimum = 2, maximum = 9,672). For the inequality calculations, a
total of 1,156,715 observations are used. This corresponds to 258.8 observations per industry-year
(minimum = 2, maximum = 7,090).
Since educational attainment is not coded in the CPS as years of schooling completed for all years
(i.e., there was a change in the education variable between 1991 and 1992), I follow previous work (e.g.,
Autor, Katz, and Krueger, 1998) and impute values from Table 5 of Park (1994), which establishes a
correspondence between the old and new CPS education variables. Potential work experience is then
calculated as the maximum of 0 and (age-years of education – 6).
Computer usage by industry is calculated using responses to the question: “Do you directly use a
computer at work?” reported in the October supplements for the years 1984, 1989, 1993, and 1997. Here,
I use the CPS “supplement” weights for 1984, 1989, and 1993 and the “final” weight for 1997. In all,
there are 59,642 observations for 1984, 60,304 for 1989, 54,273 for 1993, and 50,478 for 1997. The mean
number of observations per industry-year is 308.2 (minimum = 7, maximum = 4,298).
A consistent set of 230 industries (ranging in number from 219 to 230 in any given year) are identified
over the 20-year period. Because the CPS industry codes changed in 1992, a consistent classification
scheme was implemented using the crosswalk provided by the U.S. Bureau of the Census (and summarized by Barry Hirsch at his website: www.trinity.edu/bhirsch).
Derivation of Variance Expression
To show that equations (1) and (3) give equivalent expressions for the variance of wages, note first
that (1) expands to
I t N i ,t
1
Nt
Vt =
(1′)
∑ ∑ w 2j ,i,t −
i =1 j =1
I t N i ,tt
2
Nt
∑ ∑ w j ,i,t w t +
i =1 j =1
1
Nt
I t N i ,t
∑ ∑ w t2 ,
i =1 j =1
whereas (3) can be written as
(3′)
Vt =
1
Nt
I t N i ,t
∑ ∑ w 2j ,i,t −
i =1 j =1
2
Nt
I t N i ,tt
∑ ∑ w j ,i,t w i,t +
i = 1 j =1
2
Nt
I t N i ,t
∑ ∑ w i2,t −
i =1 j =1
2
Nt
I t N i ,t
∑ ∑ w t w i,t +
i =1 j =1
1
Nt
I t N i ,t
∑ ∑ w t2 .
i =1 j =1
Because
2
Nt
I t N i ,t
∑ ∑ w j ,i,t w i,t
=
i =1 j =1
2
Nt
It
∑ w i,t w i,t N i,t
=
i =1
2
Nt
It
∑ w i2,t N i,t
i =1
and
2
Nt
I t N i ,t
∑ ∑ w i2,t =
i =1 j =1
2
Nt
It
∑ w i2,t N i,t ,
i =1
the second and third terms on the right-hand side of (3′) sum to zero, leaving
Vt =
(3′′)
1
Nt
I t N i ,t
∑ ∑ w 2j ,i,t −
i =1 j =1
2
Nt
I t N i ,t
∑ ∑ w t w i,t +
i = 1 j =1
1
Nt
I t N i ,t
∑ ∑ w t2 .
i =1 j =1
Given that the middle term on the right-hand side of (3′′) can be expressed as
2wt
Nt
It
∑ w i,t N i,t =
i =1
2wt
Nt
It
∑ N i,t
i =1
1
N i ,t
N i ,t
∑ w j ,i,t =
j =1
2wt
Nt
I t N i ,t
∑ ∑ w j ,i,t =
i =1 j =1
N
2 I t i ,t
∑ ∑w w ,
N t i =1 j =1 j ,i ,t t
equations (1′) and (3′) are equivalent. Therefore, (1) and (3) are equivalent.
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F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
Wheeler
Table A1
Summary Statistics
Mean
Standard deviation
Minimum
Maximum
Observations
Overall variance
0.25
0.09
0
0.97
4,381
Overall 90-10 difference
1.26
0.27
0
2.82
4,381
Overall 90-50 difference
0.67
0.2
0
2.64
4,381
Overall 50-10 difference
0.59
0.17
0
1.76
4,381
College–no high school
0.68
0.35
–1.36
2.05
3,521
College–some high school
0.61
0.31
–1.17
2.02
3,943
College–high school
0.45
0.26
–0.96
2.14
4,251
College–some college
0.34
0.25
–0.81
2.51
4,263
Residual variance
0.18
0.07
0
0.67
4,379
Residual 90-10 difference
1.03
0.22
0
2.53
4,379
Residual 90-50 difference
0.52
0.15
0
1.82
4,379
Residual 50-10 difference
0.51
0.14
0
1.86
4,379
College fraction
0.21
0.14
0
0.75
4,384
Computer usage rate
0.38
0.23
0
1
Union membership rate
0.13
0.13
0
0.84
Variable
887
4,384
NOTE: Summary statistics for selected industry characteristics over the period 1983-2002.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
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393
394
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F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
Monetary Policy and Commodity Futures
Michelle T. Armesto and William T. Gavin
This paper constructs daily measures of the real interest rate and expected inflation using commodity
futures prices and the term structure of Treasury yields. We find that commodity futures markets
respond to surprise increases in the federal funds rate target by raising the inflation rate expected
over the next 3 to 9 months. There is no evidence that the real interest rate responds to surprises
in the federal funds target. The data from the commodity futures markets are highly volatile; we
show that one can substantially reduce the noise using limited information estimators such as the
median change. Nevertheless, the basket of commodities actually traded daily is quite narrow and
we do not know whether our observable rates are closely connected to the unobservable inflation
and real rates that affect economywide consumption and investment decisions.
Federal Reserve Bank of St. Louis Review, May/June 2005, 87(3), pp. 395-405.
T
he Federal Reserve targets the interest
rate on federal funds to implement
monetary policy. The interest rate is
composed of two unobservable factors,
the real interest rate and a premium for expected
inflation, which are important for understanding
the appropriate setting of the target. Knowing how
these two factors change in response to changes
in the target is also important for implementing
monetary policy. Empirical evidence about the
level and changes in these factors is complicated by the lack of direct observations on them.1
In this paper, we extract measures of the interest
rate and expected inflation from commodity
futures prices and use these measures to examine
how interest rates and expected inflation respond
to monetary policy shocks. Throughout this paper
we use the terms inflation and real interest rate
interchangeably with commodity price inflation
and commodity own rate. Whether our results
have important implications for monetary policy
1
Clark and Kozicki (2004) survey the literature and show that there
is a great deal of uncertainty in real-time estimates of the equilibrium real interest rate.
depends on how closely our measures derived
from commodity markets are connected to the
inflation rates and real interest rates that matter
for consumption and investment decisions.
Since 1997, the United States has issued
inflation-indexed bonds. By extracting observations about expected inflation and the real interest
rate in this market, several studies have found
evidence about how real and nominal interest
rates react to monetary policy surprises. For example, Gürkaynak, Sack, and Swanson (2003) show
that the implied forward 1-year rate at the 9-year
horizon responds significantly to a surprise in
the federal funds market. They find that the surprise is contained in the expected inflation premium and not in the implied forward real rate.
Kliesen and Schmid find a similar result for
the 10-year rate (2004a) and for the real rate
(2004b), but in their papers, it is not clear what
part of the 10-year term structure is responding
to the news. There is one drawback to these measures of the real rate and the expected inflation rate:
The maturity of these investments is measured in
years, and the analysis does not reveal information about the response of the real interest rate
Michelle T. Armesto is senior research associate and William T. Gavin is a vice president and economist at the Federal Reserve Bank of St. Louis.
© 2005, The Federal Reserve Bank of St. Louis.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
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Armesto and Gavin
or expected inflation in the short end of the term
structure.
Cornell and French (1986) provide indirect
observations on the short end of the term structure by using a measure of the real interest rate
extracted from commodity futures prices. They
use this measure to gauge the reaction of real
interest rates and expected inflation to surprises
in the weekly money supply announcements
between October 6, 1977, and March 23, 1984.
Their results were somewhat surprising: They
found that it was expected inflation in commodity
prices and not real returns that went up when
there was an unexpected increase in the money
supply. These results were obtained using data
after October 6, 1979, an era in which the Treasury
bill (T-bill) rate responded strongly and positively
to surprise increases in the money supply. Before
this result, previous authors concluded that these
increases in the T-bill rate were due to rising real
interest rates—a liquidity effect, perhaps associated with sticky prices (Roley and Walsh, 1985)
or with rationing in the market for borrowed
reserves (Gavin and Karamouzis, 1985).
We find results reminiscent of Cornell and
French (1986). We estimate the market’s reaction
to surprises in the Fed’s interest rate target. The
next few sections explain how the market variables
and the policy target surprises are constructed.
In the results section, we show that expected
inflation responds positively and significantly to
surprises in the federal funds rate target in the
horizon from 0 to 9 months. We also show that
there is no significant response of real interest
rates out to a year on the term structure. Although
the real interest rate and expected inflation rate
constructed using averages from commodity
futures data are highly volatile, limited information estimates such as the median change can
substantially reduce the noise in such measures.
MEASURING THE REAL INTEREST
RATE
The real own rate of return for each commodity is implied by the term structure of interest rates
in the market for T-bills and the term structure of
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M AY / J U N E
2005
futures prices in the commodity futures market.2
Suppose that there is a fixed bundle of consumption goods, Q, that is traded in futures markets in
every period. The real interest rate in terms of Q
from time t to time t + k is defined as the rate at
which the household can contract today to
exchange units of Q at time t for units of Q at t + k.
The cost of bundle Q at time t is St defined as
N
(1)
St = ∑ qi Sti ,
i =1
where there are N commodities indexed by i, qi
is the amount of good i in the bundle, and S it is
the price of good i at time t.
If there were complete futures markets for all
the goods in Q, then the household could contract
to buy the bundle at time t for consumption at
time t + k. The cost of the bundle is given by the
futures price, t Ft + k , which is a sum of individual
futures prices
N
(2)
t Ft + k
= ∑ qi t Fti+ k ,
i =1
where t F ti + k is the futures price of good i at time t
for delivery k periods ahead. At time t the household can purchase discount bonds that mature at
t + k and use the funds to buy the bundle of commodities, Q. The price of the bundle at time t then
is tFt + k tBt + k , where tBt + k is the price of a discount
bond that pays one dollar at t + k. The gross interest rate from t to t + k, 1+ t rt + k , is the ratio of the
cost of the bundle today to the cost of the future
bundle today:
(3)
1 + t rt + k =
St
t Ft + k t Bt + k
.
Cornell and French (1986) show that this real
rate is an expenditure-weighted average of the
commodity own rates.3
In the empirical application described here
2
This section draws heavily from Cornell and French (1986).
3
They assume that the commodity bundle includes all goods traded
in the market, so the commodity own rate is the relevant real
interest rate. To the extent that some goods are excluded, this real
rate may differ from the real rate that affects consumer and business
spending decisions. Gorton and Rouwenhorst (2004) show systematic differences between returns in commodity futures and bonds
at lower frequencies.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
Armesto and Gavin
later, date t is the day of the policy action. We use
the maturing contract as the spot price to ensure
that the spot and futures prices refer to exactly
the same item being traded. However, if the maturing contract does not mature within the next 46
days, we omit this spot price from our data set.
We construct a set of futures prices for commodity
contracts maturing at k days for k = {90, 180, 270,
360}. We then calculate the implied forward own
rates. When there are no spot prices available, we
are able to calculate the implied forward rates
because the spot price drops out of the formula.
For example, the own rate over the horizon t + k
+ 90 is given by
(4)
1 + t rt + k +90 =
St
t Ft + k + 90 t Bt + k + 90
,
and the implied forward rate from t + k to t + k + 90
is given by
(5)
1 + t + k rt + k +90 =
t Ft + k t Bt + k
t Ft + k + 90 t Bt + k + 90
MEASURING THE EXPECTED
INFLATION RATE
The expected inflation rate in commodities is
calculated from the relative bases in commodity
markets. The basis is defined as the difference
between the spot price and the futures price of a
commodity. Over the horizon t + k + 90, this
expected inflation rate in a given commodity,
then, is given as the relative basis, tbt + k+ 90 , which
is just the basis divided by the spot price:
t bt + k + 90
=
t Ft + k + 90
− St
St
,
or, in gross terms,
(7)
1 + t bt + k +90 =
t Ft + k + 90
St
(8)
1 + t + k bt + k +90 =
t Ft + k + 90
t Ft + k
,
where the implied forward expected inflation
rate is the 3-month inflation rate expected for
the period t + k through t + k + 90. Note that this
calculation includes the basis risk—that is, a
premium for bearing risk that the actual price
in the future will be different from today’s futures
price. Our web-based data appendix (which
appears with this article at
http://research.stlouisfed.org/publications/review/)
includes summary statistics for the changes in
commodity own rates and commodity bases
around Fed policy surprises.
,
where the implied forward rate is the rate at which
one can trade the bundle at t + k for the bundle
at t + k + 90.
(6)
for commodities. We calculate the term structure
of implied expected inflation rates in the same
manner as we calculated the implied own rates.
For example, the implied forward expected inflation rate from t + k to t + k + 90 is given by
.
We aggregate relative bases across the commodity bundle to get the expected inflation rate
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
THE COMMODITY DATA
The 34 commodities included in our futures
market data are listed in Table 1.4 The commodities were traded on several different North
American exchanges: the Coffee Sugar Cocoa
Exchange, the Chicago Board of Trade, the Chicago
Mercantile Exchange, the New York Mercantile
Exchange, the Kansas City Board of Trade, the
Minneapolis Grain Exchange, the New York
Cotton Exchange, and the Winnipeg Stock
Exchange. On average, commodity prices fell 2/3
of a percentage point per year during our sample
period. But there was substantial dispersion across
commodities. At the high end, palladium was an
outlier, rising on average 11.93 percent per year.
At the low end, orange juice fell on average 5.79
percent per year. There were contracts expiring
for all of the commodities except high-grade
copper throughout our full sample period. The
first futures contract in high-grade copper expired
in 1989.
4
We chose not to update the data set to include the post-2001 data.
Our data, which come directly from the market electronic feeds,
were purchased from the Institute for Financial Markets in August
2002. This company, sold to MJK Associates, no longer provides
data in the format used in 2002.
M AY / J U N E
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397
Armesto and Gavin
Table 1
Commodities Included in the Sample
No. of contracts
expiring in 1988
No. of contracts
expiring in 2001
Average
inflation rate
Commodity
Traded in market
Coffee (KC)
CSCE
5
5
–5.64%
CBT
5
7
–1.80%
Corn (CN)
Feeder cattle (FC)
CME
8
8
0.22%
Gold (GC)
NYMEX
6
12
–3.31%
High-grade copper (HG)
NYMEX
0
12
–5.01%
Live hogs (LH)
CME
7
7
3.53%
Live cattle (LC)
CME
6
6
–0.20%
Oats (OA)
CBT
5
5
–4.71%
NYMEX
4
4
0.26%
Platinum (PL)
Pork bellies (PB)
CME
5
5
5.46%
NYMEX
6
12
–2.61%
Soybeans (SY)
CBT
7
7
–4.36%
Soybean meal (SM)
CBT
8
8
–3.64%
Silver (SI)
Soybean oil (BO)
CBT
8
8
–2.62%
Wheat (WC)
CBT
5
5
–3.49%
Silver 1000 oz (AG)
CBT
6
12
–2.67%
Gold – kilo (KI)
CBT
6
6
–3.64%
Sugar (SB)
CSCE
5
4
–0.20%
Wheat (KW)
KCBT
5
5
–1.56%
Wheat – white (MW)
MGE
5
5
–1.20%
Cotton (CT)
NYCE
5
5
–1.60%
Crude oil – light (CL)
NYMEX
12
12
4.28%
Heating oil (HO)
NYMEX
12
12
2.93%
Liquid propane (PN)
NYMEX
12
12
6.85%
Palladium (PA)
NYMEX
4
4
11.93%
Unleaded gasoline (HU)
NYMEX
12
12
6.45%
Cocoa (CC)
CSCE
5
5
–3.15%
Orange juice (JO)
NYCE
6
6
–5.79%
CBT
5
6
–1.44%
Rice (NR)
Lumber (LB)
Flax seed (WF)
CME
6
6
2.85%
WINN
3
5
–2.76%
Oats (WO)
WINN
5
5
–3.50%
Rapeseed (WP)
WINN
5
7
–1.49%
Wheat (WW)
WINN
5
5
0.04%
NOTE: CSCE, Coffee Sugar Cocoa Exchange; CBT, Chicago Board of Trade; CME, Chicago Mercantile Exchange; NYMEX, New York
Mercantile Exchange; KCBT, Kansas City Board of Trade; MGE, Minneapolis Grain Exchange; NYCE, New York Cotton Exchange;
WINN, Winnipeg Stock Exchange.
398
M AY / J U N E
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F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
Armesto and Gavin
The initial format of the data consisted of
hundreds of individual files, each containing
detailed information about a particular commodity
futures contract: the underlying commodity; the
month and year the contract expired; and the
open, close, high, and low prices for each day that
the contract was traded. From these files we construct time series of prices for all 34 commodities
for days surrounding our measure of monetary
policy surprises. The difference between the close
price on the day before the Fed’s target change
and the opening price on the day after the Fed’s
target change is used to gauge how the market
responds to incoming information about monetary
policy.5 A term structure of prices for each commodity is constructed using contracts with different expiration dates.
The number and length of contracts varies
across commodities. The most frequently traded
commodities are crude oil, heating oil, liquid
propane, and unleaded gasoline, which have contracts expiring in every month. Others were not
as active. Contracts for platinum and palladium
expire just four times per year. Additionally, the
length of the individual contracts varied. For
example, the majority of coffee’s commodity contracts (92 percent) were traded for longer than one
year, while no contracts were traded for less than
one month. Conversely, the majority of flax seed
contracts traded within the horizon of 6 to 12
months (86 percent), whereas only two contracts
(3 percent) traded for longer than one year. Silver
(1000 oz) had the largest quantity of contracts that
traded for less than one month (7 percent).
There would be many gaps in the time series
of term structures if we insisted on using only
those contracts that expired exactly 3, 6, 9, and
12 months from the day of a monetary policy surprise. We use simple decision rules to construct
a term structure of prices that approximates prices
at spot, 3-month, 6-month, 9-month, and 12-month
horizons. First, we looked at all contracts that had
been traded in the individual commodity on the
5
Note that, since 1994, the announcements of policy changes are
scheduled for release at a preannounced time, so that today one
could use higher-frequency data and a much smaller window in
which to measure market reaction. But in the period before 1994,
we do not have good information about when, during the day, the
market learned about the policy change.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
day before and day after a monetary policy surprise. We used the maturing contract as a measure
of the spot price to ensure that the underlying
commodity for the spot price was the same as for
the futures contracts. A contract price was considered to be the spot price if the contract had less
than 47 days from the day before the policy surprise until expiration. For the 3-month price, a
contract was selected if it had between 48 and 137
days until expiration. Similar windows were constructed for the 6-, 9-, and 12-month horizons.
For the 6-month futures price, the window was
from 138 to 227 days. The 9-month window was
from 228 to 317 days, and the 12-month window
was from 318 to 417 days until expiration.
When there is no contract expiring in a window, then we have no observation for that commodity. When there was more than one contract
within the window, we chose the one closest to
our ideal term structure; that is, for the spot price,
we choose the contract with the closest date to
expiration. For all others, the preference was for
the center of the window. For example, for the 3month futures price for the day after the Fed’s
policy change, the contract used to represent the
3-month futures price was the one closest to expiring in 90 days. This selection method is similar
for the 6-, 9-, and 12-month futures price. These
prices were then used to compute our own rates
and bases.
WHAT IS A SURPRISE IN THE
FEDERAL FUNDS RATE TARGET?
We use measures of the monetary policy surprise as constructed by Poole, Rasche, and
Thornton (2002). Data from the federal funds
futures market is used to measure the expected
change in monetary policy. The federal funds
futures market is a bet on the average effective
federal funds rate for the month in which the
contract matures; as a result, it is an estimate of
market expectations about the average level of
the federal funds rate for that month.
The Chicago Board of Trade began trading
federal funds futures contracts in October 1988.
When this trading began, the Federal Reserve was
using a target or “expected trading level” for the
M AY / J U N E
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399
Armesto and Gavin
federal funds rate as a guide for daily open market
operations, but it did not announce its short-run
targets until 1994. Poole, Rasche, and Thornton
describe the history of Fed policy changes as
embodied in a target or expected trading level
for the federal funds rate for the pre-1994 period;
they also show that the market often could see
when the Fed’s target was changed. Fed policy
has been transparent since 1994, but what the
market expects as it compares with what actually
occurs is still a relevant issue.
The unexpected component of the Fed’s
actions is implied by the change in the futures
market price from the day before to the day after
the policy change. Suppose fff th denotes the rate
on the h-month federal funds futures contract on
day t. This rate is equivalent to the sum of the
expectation on day t of the federal funds rate on
each day of the month, averaged across the length
of the month. Hence,
(9)
m
fffth = 1 m ∑ i =1 Et ( ffih ),
where ff ih denotes the federal funds rate on day i
of the hth month, Et denotes the expectation on
day t, and m denotes the number of days in the
month.
Next, consider if the Fed successfully targets
the federal funds rate, so that the actual federal
funds rate is equal to the target plus an i.i.d. mean
zero error term:
fft = ffi* + ηt .
(10)
The expectation of the future federal funds rate
depends on expectations about the policy target.
The surprise in the federal funds market is calculated as the change in the federal funds futures
price following a monetary policy action. Substituting the federal funds target into the formula
for the federal funds futures rate and taking the
difference yields
(11)
m
∆fffth = 1 m ∑ i =1 Et ( ffi*h ) − Et −1( ffi*h ) .
If the policy change was perfectly anticipated, then
there will be no change in the futures price.
Before 1994, whether or not the market was
aware of the Fed’s actions is an issue. Poole,
Rasche, and Thornton (2002) use reports in the
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M AY / J U N E
2005
financial press to distinguish between days when
the market was aware and days when they were
unaware that policy had changed. We examine
only days in which they find that the market was
aware that policy had changed.
MEASURING THE MARKET
RESPONSE
The market response following a policy action
is measured as the change in the own rate or
expected inflation calculated using the closing
price from the day before the policy change to the
opening price on the day after. The expiration
date is fixed, so the actual horizon gets 2 days
shorter during the interval of the policy change.
The change in the 3-month-ahead own rate for a
given commodity is ∆ 0r i90,t = 0 r i90,t+1 – 0 r i90,t –1. The
change in the 9-month-ahead implied forward 3month rate is ∆ 270r i360,t = 270r i360,t+1 – 270r i360,t–1, and
so on for the other own rates and expected inflation rates. We calculate the average change in the
implied forward commodity own rate for the
bundle as ∆ krk + 90,t and the average change in
expected inflation as ∆ kbk + 90,t+1.6 We also calculate the aggregate commodity own rates and
expected inflation rates as the median commodity
change. The median changes are designated with
a med superscript. For example, the change in
the 9-month-ahead 3-month expected inflation
rate from the day before the monetary policy surprise to the day after is given as ∆ 270b med
360,t .
The volatility of the implied forward T-bill
rates, commodity own rates, and commodity
expected inflation rates following a monetary
policy surprise are shown in Table 2. In the first
row, we report summary statistics about the
change in the implied forward 3-month T-bill rates
following surprises in the federal funds rate. At
all four horizons, the standard deviation of the
change is 10 or 11 basis points. In the second and
third rows we report the volatility of changes in
the commodity own rates. As Mishkin (1990)
notes, this series is quite volatile relative to inter6 Cornell and French (1986) weighted the individual commodities
by the inverse of measures of volatility in each market. Mishkin
(1990) used an unweighted average.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
Armesto and Gavin
Table 2
Volatility of Changes in Rates Following Federal Funds Rate Surprises
0 to 3 months
3 to 6 months
6 to 9 months
9 to 12 months
10
11
11
11
Mean commodity
94
58
43
58
Median commodity
46
24
19
23
Mean commodity
94
57
42
55
Median commodity
46
24
18
19
Implied forward T-bill rates
Commodity own rates
Commodity inflation rates
NOTE: Standard deviations in basis points at annual rates.
est rates: The standard deviation of changes following surprises in the federal funds rate ranges
from a high of 94 basis points in the near term to
43 basis points for the implied own rate in the 6to 9-month horizon. In every case, the standard
deviations of the median changes are less than
half the standard deviations of the mean changes.
Here we find that the standard deviations of
changes in commodity own rates ranged from 46
basis points in the near horizon to 19 points for
the implied own rates in the 6- to 9-month horizon.
The fourth and fifth rows report the standard
deviations of the commodity expected inflation
rates. Here the volatility pattern is very similar to
the pattern for the own rates. The standard deviation of changes following surprises in the federal
funds rate ranges from a high of 94 basis points
in the near term to 42 basis points for the implied
own rate in the 6- to 9-month horizon. Also, the
standard deviations of the median changes are
less than half the standard deviations of the mean
changes. Here we find that the standard deviations
of changes in commodity expected inflation rates
ranged from 46 basis points in the near horizon
to 18 points for the implied own rate in the 6- to
9-month horizon.
RESULTS
We run simple regressions relating changes
in the mean and median commodity own rates
to surprises in the policy action. The rationale
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
for this model is simply that at the moment before
the policy change, market prices reflect all the
information that is relevant, including expectations about policy. The relationship between
changes in the mean and median own rates and
the policy surprise is measured using the following regressions:
(12)
∆ k rk +90,t = α1r + β1r ∆fffth + ε1r,t and
(13)
r
r
h
r
∆ k rkmed
+ 90,t = α 2 + β2 ∆ffft + ε 2,t ,
for k = 0, 90, 180, and 270. Similar regressions are
used to measure the response of the mean and
median commodity expected inflation rates to a
monetary policy surprise:
(14)
∆ k bk +90,t = α1b + β1b ∆ffftb + ε1b,t and
(15)
b
b
h
b
∆ k bkmed
+ 90,t = α 2 + β2 ∆ffft + ε 2,t .
The estimation results for these equations are
reported in Table 3. The important effect of idiosyncratic shocks results in very low R2s for the
regression of the commodity own rates and
expected inflation rates on the federal funds surprise.7 In the top half we see that in no case is the
7
Poole, Rasche, and Thornton (2002) note that the surprise in the
federal funds target is measured with error, leading to biased estimates of the coefficient on the federal funds surprise. The measurement error biases the coefficient toward zero. They show that the
variance of the measurement error is small and is unlikely to affect
the qualitative nature of our results.
M AY / J U N E
2005
401
Armesto and Gavin
Table 3
Regressions of Commodity Own Rates and Basis Changes on the Unexpected Component of
Federal Funds Announcements
β
t-Statistic
SEE
R2
∆ 0 r 90,t+ 1
–0.65
–0.62
0.96
0.00
∆ 0 r med
90,t+ 1
–0.40
–0.78
0.46
0.01
∆ 90r 180,t+ 1
–0.03
–0.04
0.54
0.00
Commodity own rates
∆ 90 r med
180,t+ 1
0.18
0.68
0.24
0.01
∆ 180 r 270,t+ 1
–0.41
–0.96
0.40
0.01
∆ 180 r med
270,t+ 1
0.02
0.08
0.18
0.00
∆ 270 r 360,t+1
0.73
1.25
0.54
0.02
∆ 270 r med
360,t+ 1
0.29
1.23
0.21
0.02
Commodity inflation rates
∆ 0 b90,t+ 1
1.36
1.31
0.95
0.02
∆ 0 bmed
90,t+1
1.10
2.23
0.45
0.06
∆ 90 b180,t+ 1
0.79
1.38
0.52
0.02
∆ 90 bmed
180,t+ 1
0.58
2.28
0.23
0.06
∆ 180 b270,t+ 1
1.11
2.61
0.39
0.07
∆ 180 bmed
270,t+1
0.68
3.84
0.16
0.15
∆ 270 b360,t+ 1
–0.12
–0.22
0.51
0.00
∆ 270 bmed
360,t+ 1
0.32
1.63
0.18
0.03
NOTE: Bold indicates that the t-statistic is significant at the 5 percent critical level. SEE is the standard error of the equation.
response of the own rate significantly different
from zero. At the 9- to 12-month horizon, the
response of the real rate is positive and relatively
large, but not statistically significant.
The bottom half reports the results for the
commodity price expected inflation. The results
for the mean response are not significant except
in the case of the implied 3-month expected
inflation rate from 6 to 9 months. We get significant results more often when we use the median
response. Mishkin (1990) argued that the Cornell
and French results are unreliable indicators of
real interest rate behavior because commodity
market returns are so highly variable relative to
expected inflation and nominal interest rates that
there is little signal about real interest rates in
the data. We reduce volatility by using the median
response measure, which increases reliability in
the significance of our results.
402
M AY / J U N E
2005
Using the median measure of commodity
price expected inflation, we find that expected
inflation responded positively and significantly
to surprises in the federal funds target for the first
three horizons. Only in the case of the 9- to 12month rate is the response not statistically significant at the 5 percent level. Relative to the mean
price or own rate, the median appears to effectively filter a substantial amount of idiosyncratic
noise from the commodity futures data.
DISCUSSION
The results in Table 2 appear to be at odds
with Gürkaynak, Sack, and Swanson (2003) and
Kliesen and Schmid (2004a), who report that inflation expectations decline when there is a surprise
increase in the federal funds target. The different
results, however, refer to different points on the
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
Armesto and Gavin
term structure. We find that the positive impact
is largest at the 3-month horizon and is not statistically significant at the 1-year horizon.
It is also quite possible that the high-frequency
response of commodity prices is not the same as
the response of prices across the broad spectrum
of goods in the economy. However, Gorton and
Rouwenhorst (2004) use monthly data to show
that nominal commodity returns are highly and
positively correlated with CPI inflation, both its
expected and unexpected components.
Our results appear to be at odds with conventional wisdom as well, which suggests that
inflation responds to policy actions only after a
long lag. The conventional view implies that the
immediate response of interest rates to a monetary
policy shock is by the real component. Recent
developments in macroeconomic theory focus on
policy in general equilibrium models. To capture
this conventional wisdom, economists have used
New Keynesian models that incorporate some
form of price stickiness.8 Gavin, Keen, and Pakko
(2004) analyze the effects of monetary policy
shocks in such a model where Calvo-style pricing
means that prices change on average once per year
and the central bank uses an interest rate rule to
implement policy. Within this framework, there
is an important difference in the effect of a shock
to the interest rate depending on whether the
shock is perceived to be temporary or persistent.9
Transitory policy shocks affect both expected inflation and the real interest rate. With a transitory
shock, the federal funds rate returns to its original
level within a few quarters and the implied future
short-term rate is essentially unaffected by the
shock at the 4-quarter horizon.
However, if the shock is persistent—that is,
the market expects that a change in the federal
funds target is likely to be fairly permanent—then
the effect of a positive shock on the implied future
short-term rate may be positive for many quarters.
But almost all the effect is due to higher expected
8
See Woodford (2003, Chap. 3) for a comprehensive analysis of the
New Keynesian model.
9
In that model the shocks follow an AR(1) process. The transitory
shock has an AR(1) parameter equal to 0.3 and the persistent
shock has a parameter value of 0.95.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
inflation. The predicted real interest rate effects of
a persistent shock to the federal funds rate target
are an order of magnitude smaller than are the
effects following a transitory shock. That is, stateof-the-art macroeconomic theory predicts that the
real interest rate will not respond to federal funds
rate target shocks that are highly persistent.
It is important to understand, then, whether
monetary policy shocks are perceived as relatively
transitory or relatively permanent. Many empirical studies find that the level of the federal funds
rate behaves as if it has a random walk component.
Using the futures market data to derive the shocks
as we do, Faust, Swanson, and Wright (2004)
report that shocks to the change in the federal
funds rate are highly persistent.
In the top panel of Table 4, we report the
response of the term structure of implied future
3-month T-bill rates to surprises in monetary
policy. These coefficients were calculated by
regressing the change in the implied forward Tbill rates on the monetary policy surprises in the
following regression:
(16)
∆ kTbill k +90,t = α1 + β1∆fffth + ε1,t ,
where ∆kTbillk +90,t is the change in the implied
forward T-bill rate for values of k equal to 0, 90,
180, and 270. We find that for the first four quarters, the response in the implied forward T-bill
rate is fairly equal across the term structure from
3 months to 12 months. A 10-basis-point surprise
in the federal funds rate leads to a 7-basis-point
rise in the 3-month rate and to a pattern of 8-, 7-,
and 6-basis-point increases in the implied future
3-month rates at horizons ending in 6, 9, and 12
months, respectively. In the bottom panel, we
report similar regressions in which the dependent
variables are changes in the Treasury bill rates,
∆0Tbillk +90,t , maturing in k + 90 days. The regression is given as
(17)
∆ 0Tbill k +90,t = α 2 + β2 ∆fffth + ε2,t .
The results show that the 12-month rate changes
by only very slightly less than the 3-month rate.
Markets appear to expect that a shock to the
federal funds target is relatively permanent—at
least that it persists intact for the first year. AccordM AY / J U N E
2005
403
Armesto and Gavin
Table 4
Response of T-Bill Rates to Federal Funds Target Surprises
β
t-Statistic
SEE
R2
∆ 0 Tbill90,t+ 1
0.71
9.89
0.07
0.54
∆ 90Tbill180,t+ 1
0.77
9.75
0.07
0.53
∆ 180Tbill270,t+ 1
0.69
7.61
0.08
0.41
∆ 270Tbill360,t+ 1
0.61
5.89
0.09
0.29
Maturity
Implied forward rates
T-bill rates
∆ 0 Tbill90,t+ 1
0.71
9.89
0.07
0.53
∆ 90Tbill180,t+1
0.73
11.04
0.06
0.58
∆ 180Tbill270,t+ 1
0.73
10.51
0.06
0.56
∆ 270Tbill360,t+1
0.69
9.12
0.07
0.49
NOTE: Bold indicates that the t-statistic is significant at the 5 percent critical level. SEE is the standard error of the equation.
ing to general equilibrium macro theory, the shock
to the federal funds rate should have significant
effects on expected inflation, but not on real interest rates, which is what we see in the commodity
futures market.
CONCLUSION
Although the commodity futures data contain
a substantial amount of idiosyncratic noise, they
remain an important source of information about
how markets respond to the implementation of
monetary policy. Evidence presented in this paper
shows that real rates of return in commodity
markets do not appear to react to surprises in the
federal funds target. This result complements
research showing that real rates in the long-term
market for inflation-protected Treasury securities
also do not respond to these surprises. This is also
the result predicted by New Keynesian macroeconomic models if the shocks to the federal funds
target appear to be persistent. Persistent shocks
lead to a significant (almost one-for-one) response
by expected inflation but no measurable response
by the real interest rate.
Our results show that despite the relative noise
in commodity futures markets, the commodity
expected inflation rate does respond significantly
404
M AY / J U N E
2005
to surprises in the federal funds rate. The result
is consistent with modern theory, but not with
conventional wisdom. Conventional wisdom
suggests that expected inflation does not respond
immediately, but only with a long lag—and the
response should be negative, as was found in the
long-term indexed bond market. Gürkaynak, Sack,
and Swanson (2003) and Kliesen and Schmid
(2004a) find that the long-term expected inflation
rate falls when there is a surprise increase in the
federal funds rate. Our results suggest that the
short-term response is different. That is, expected
inflation, at least as observed in commodity markets, over the next 3 to 9 months moves in the
same direction as a surprise in the federal funds
rate target.
REFERENCES
Clark, Todd E. and Kozicki, Sharon. “Estimating
Equilibrium Real Interest Rates in Real Time.”
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Cornell, Bradford and French, Kenneth R. “Commodity
Own Rates, Real Interest Rates, and Money Supply
Announcements.” Journal of Monetary Economics,
1986, 18, pp. 3-20.
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Armesto and Gavin
Faust, Jon; Swanson, Eric T. and Wright, Jonathan H.
“Identifying VARS Based on High Frequency Futures
Data.” Journal of Monetary Economics, 2004, 51,
pp. 1107-31.
Gavin, William T. and Karamouzis, Nicholas V. “The
Reserve Market and the Information Content of M1
Announcements.” Federal Reserve Bank of
Cleveland Review, 1985, Quarter I, pp. 11-28.
Gavin, William T.; Keen, Benjamin D. and Pakko,
Michael R. “The Monetary Instrument Matters.”
Working Paper 2004-026A, Federal Reserve Bank
of St. Louis, November 2004.
Gorton, Gary and Rouwenhorst, K. Geert. “Facts and
Fantasies About Commodity Futures.” NBER
Working Paper 10595, National Bureau of Economic
Research, June 2004.
Gürkaynak, Refet S.; Sack, Brian and Swanson, Eric.
“The Excess Sensitivity of Long-Term Interest Rates:
Evidence and Implications for Macroeconomic
Models.” Board of Governors of the Federal Reserve
System Finance and Economics Discussion Series
2003-50, August 13, 2003.
Kliesen, Kevin L. and Schmid, Frank A. “Monetary
Policy Actions, Macroeconomic Data Releases, and
Inflation Expectation.” Federal Reserve Bank of St.
Louis Review, May/June 2004a, 86(3), pp. 9-21.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
Kliesen, Kevin L. and Schmid, Frank A. “Do
Productivity Growth, Budget Deficits, and Monetary
Policy Actions Affect Real Interest Rates? Evidence
From Macroeconomic Announcement Data.”
Working Paper 2004-019A, Federal Reserve Bank
of St. Louis, September 2004b.
Kuttner, Kenneth N. “Monetary Policy Surprises and
Interest Rates: Evidence from the Federal Funds
Futures Market.” Journal of Monetary Economics,
June 2001, 47(3), pp. 523-44.
Mishkin, Frederic S. “Can Futures Market Data Be
Used to Understand the Behavior of Real Interest
Rates?” Journal of Finance, March 1990, 45, pp.
245-57.
Poole, William; Rasche, Robert H. and Thornton,
Daniel L. “Market Anticipations of Monetary Policy
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Roley, V. Vance and Walsh, Carl E. “Monetary Policy
Regimes, Expected Inflation, and the Response of
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F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
Using Implied Volatility to Measure Uncertainty
About Interest Rates
Christopher J. Neely
Option prices can be used to infer the level of uncertainty about future asset prices. The first two
parts of this article explain such measures (implied volatility) and how they can differ from the
market’s true expectation of uncertainty. The third then estimates the implied volatility of threemonth eurodollar interest rates from 1985 to 2001 and evaluates its ability to predict realized
volatility. Implied volatility shows that uncertainty about short-term interest rates has been falling
for almost 20 years, as the levels of interest rates and inflation have fallen. And changes in implied
volatility are usually coincident with major news about the stock market, the real economy, and
monetary policy.
Federal Reserve Bank of St. Louis Review, May/June 2005, 87(3), pp. 407-25.
E
conomists often use asset prices along
with models of their determination to
derive financial markets’ expectations
of events. For example, monetary economists use federal funds futures prices to measure expectations of interest rates (Krueger and
Kuttner, 1995; Pakko and Wheelock, 1996).
Similarly, a large literature on fixed and target
zone exchange rates has used forward exchange
rates to measure the credibility of exchange rate
regimes or to predict their collapse (Svensson,
1991; Rose and Svensson, 1991, 1993; Neely,
1994).
But it is often helpful to gauge the uncertainty
associated with future asset prices as well as their
expectation. Because option prices depend on
the perceived volatility of the underlying asset,
they can be used to quantify the expected volatility of an asset price (Latane and Rendleman, 1976).
Such estimates of volatility, called implied volatility (IV), require some heroic assumptions about
the stochastic (random) process governing the
underlying asset price. But the usual assumptions
seem to provide very reasonable forecasts of
volatility. That is, IV is a highly significant but
biased predictor of volatility, which often encompasses other forecasts.
Readers who are already familiar with the
basics of options might wish to skip the first section of this article; it explains how option prices
are determined by the cost of a portfolio of assets
that can be dynamically traded to provide the
option payoff. Readers who are unfamiliar with
options might wish to start with the glossary of
option terms at the end of this article and the insert
on the basics of options (boxed insert 1). The second section reviews the relation between IV and
future volatility, showing how option pricing
formulas can be “inverted” to estimate volatility.
The third section measures the IV of short-term
interest rates over time and discusses how such
measures can aid in interpreting economic events.
HOW DOES ONE PRICE
OPTIONS?
Options are a derivative asset. That is, option
payoffs depend on the price of the underlying
asset. Because of this, one can often exactly
replicate the payoff to an option with a suitably
Christopher J. Neely is a research officer at the Federal Reserve Bank of St. Louis. Joshua Ulrich provided research assistance.
© 2005, The Federal Reserve Bank of St. Louis.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
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Neely
BOXED INSERT 1: OPTION BASICS
A call is an option to buy an underlying asset; a put is an option to sell the underlying asset. A
European option can be exercised only at the end of its life; an American option can be exercised at
any time prior to expiry.
One can either buy or sell options. In other words, one can be long or short in call options or long
or short in put options. The payoff to a long position in a European call option with a strike price of
X is max(ST – X, 0). The payoff to a long position in a European put option with a strike price of X is
max(X – ST , 0). The payoffs to short positions are the negatives of these. The figure below shows the
payoffs to the four option positions as a function of the terminal asset price for strike prices of $40.
The relation of the current price of the underlying asset to the strike price of an option defines
the option’s “moneyness.” Options that would net a profit if they could be exercised immediately are
said to be “in the money.” Options that would lose money if they were exercised immediately are
“out of the money,” and those that would just break even are “at the money.” For example, if the
underlying asset price is $50, then a call option with a strike price of $40 is in the money, while a
put option with the same strike would be out of the money.
Because the holder of an option has limited risk from adverse price movements, greater asset
price volatility tends to raise the price of an option. Because the uncertainty about the future asset
price generally increases with time to expiry, options generally have “time value,” meaning that—
all else equal—American options with greater time to expiry will be worth more.1
Long Position in a Call Option
Short Position in a Call Option
Payoff and Profit
12
Payoff and Profit
10
4
8
2
6
6
0
4
–2
2
–4
0
35
–2
40
45
50
35
40
45
50
–6
–8
–10
–4
–6
–12
Terminal Asset Price
Terminal Asset Price
Long Position in a Put Option
Short Position in a Put Option
Payoff and Profit
12
Payoff and Profit
6
10
4
8
2
6
0
4
–2
2
–4
0
–2
30
35
40
45
–6
30
35
40
–8
–10
–4
–6
45
–12
Terminal Asset Price
Terminal Asset Price
NOTE: The four figures display the payoffs (blue dashed line) and the profits (black line) for the
four option positions as a function of the terminal asset price.
1
European options on equities can have negative time value in the presence of dividends.
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F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
Neely
managed portfolio of the underlying asset and a
riskless asset. The set of assets that replicates the
option payoff is called the replicating portfolio.
This section explains how arbitrage equalizes the
price of the option and the price of the replicating
portfolio.
must earn the riskless return. If it did not, there
would be an arbitrage opportunity. The initial
cost of the portfolio is the cost of the ∆ shares of
stock ($10∆) less the price of the call option ($C).
The initial cost of the portfolio must equal its
discounted riskless payoff ($4e –0.05):
Pricing an Option with a Binomial Tree
(1)
A simple numerical example will help explain
how the price of an option is equal to the price of
a portfolio of assets that can replicate the option
payoff. Suppose that a stock price is currently $10
and that it will either be $12 or $8 in one year.1
Suppose further that interest rates are currently
5 percent. A one-year European call option with
a strike price of $10 gives the buyer the right, but
not the obligation, to purchase the stock for $10
at the end of one year.2 If the stock price goes up
to $12, the option will be worth $2 because it confers the right to pay $10 for an asset with a $12
market price. But if the stock price falls to $8, the
option will be worthless because no one would
want to buy a stock at the strike price when the
market price is lower.
Suppose that the First Bank of Des Peres
(FBDP) sells one call option on one share of a nondividend-paying stock and simultaneously buys
some amount, call it ∆, shares of the stock. If the
stock price goes up to $12, the FBDP’s portfolio
will be worth the value of its stock, less the value
of the option: $12∆ – $2. If the stock price falls to
$8, the option will be worthless and the FBDP’s
portfolio will only be worth $8∆. The key to option
pricing is that the FBDP can choose ∆ to make the
value of its portfolio the same in either state of
the world: It chooses ∆ = 1/2, to make $12∆ – $2 =
$8∆ – $0. That is, if the FBDP buys ∆ = 1/2 units
of the stock after selling the call option, it will
have a riskless payoff to its portfolio of $4.
Because this payoff is riskless, the portfolio
of a short call option and 1/2 share of the stock
Using the fact that ∆ = 1/2, the price of the call
option must be
1
(2)
C = $10 − $4e −0.05 = $1.1951.
2
If the price of the call option were more than
$1.1951, one could make a riskless profit by selling the option and holding 1/2 shares of the stock.4
If the call option price were less than $1.1951, one
could make an arbitrage profit by buying the call
and shorting 1/2 shares of the stock.
An equivalent way to look at the problem is
to create the portfolio that replicates the initial
investment/payoff of the call option. That is, the
FBDP could borrow $5 and buy 1/2 of a share of
the stock. At the end of the year, the 1/2 share of
stock would be worth either $6 or $4 and the
FBDP would owe ($5e 0.05=) $5.2564 on the money
it borrowed. The initial investment would be zero
and the payoff would be $0.7436 in the first state
and –$1.2564 in the second state. This is the same
initial investment/payoff structure as borrowing
$1.1951 and buying the call option with a strike
price of $10. In other words, the portfolio that
replicates the call option in this example is a 1/2
share of the stock and an equal short position in
a riskless bond.
Introductory textbooks on derivatives, like
Hull (2002), Jarrow and Turnbull (2000), or
Dubofsky and Miller (2003), provide a much more
1
This example assumes that the stock pays no dividends. If it did
pay known dividends, it could be priced in a similar way.
2
A European option confers the right to buy or sell the underlying
asset for a given price at the expiry of the option. An American
option can be exercised on or before the expiry date. A call (put)
option confers the right, but not the obligation, to buy (sell) a particular asset at a given price, called the strike price.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
$10∆ − C = $4e −0.05 .3
3
If the continuously compounded interest rate is 5 percent, the
price of a riskless bond with a one-year payoff of $4 would have a
price of $4e –0.05.
4
Suppose that the call option cost $1.30. One would sell the call
option, borrow $3.70, and use the proceeds of the option sale and
the borrowed funds to buy 1/2 share of stock. If the first state of the
world occurs, the writer of the option will have $6 in stock but will
pay $2 to the option buyer and (3.70e 0.05 =) $3.89 to the bank that
loaned him the funds originally. He will make a riskless profit of
$0.11. Similarly, in the second state of the world, the option expires
worthless and the option writer sells the 1/2 share of stock for $4,
pays the loan off with $3.89 and again makes $0.11 riskless profit.
M AY / J U N E
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409
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Figure 1
Pricing a Call Option with a Binomial Tree
Stock Price = $12
Option Value = $2
Stock Price = $10
Option Price = ?
Stock Price = $8
Option Value = $0
NOTE: The figure illustrates values that a hypothetical stock
could take, along with the value of a call option on that stock
with a strike price of $10.
extensive treatment of binomial trees as well as
information about how options pricing formulas
change for different types of assets.
Black-Scholes Valuation
The preceding example, illustrated in Figure 1,
was a one-step binomial tree. The option price
was calculated under the assumption that the
stock could take one of two known values at
expiry. Suppose instead that the stock could move
up or down several times before expiration. In
this case, one can calculate an option price by
computing each possible value of the option at
expiry and working backward to get the price at
the beginning of the tree. As the asset prices rise
and the call option goes “into the money,” the
replicating portfolio holds more of the underlying
asset and less of the riskless bond.5 At each point
in time, the option writer chooses the position in
the underlying asset to maintain a riskless payoff
to the hedged portfolio—the combination of the
positions in the option, the underlying asset, and
the riskless bond. The position in the underlying
asset is equal to the rate of change in the option
value with respect to the underlying asset price.
5
A call (put) option is said to be “in the money” if the underlying
asset price is greater (less) than the strike price. If the underlying
asset price is less (greater) than the strike price, the call (put) option
is “out of the money.” When the underlying asset price is near (at)
the strike price, the option is “near (at) the money.”
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This rate of change is known as the option’s
“delta” and the continuous process of adjustment
of the underlying asset position is known as “delta
hedging.” The limit of the formula for an option
price from an n-step binomial tree, as n goes to
infinity, is the Black-Scholes (BS) formula (Black
and Scholes, 1972).6
The BS formula expresses the value of a
European call or put option as a function of the
underlying asset price (S), the strike price (X), the
interest rate (r), time to expiry (T), and the variance
of the underlying asset return (σ 2). Higher asset
price volatility means higher option prices because
the downside risk is always limited, whereas the
upside potential is not. Therefore, option prices
increase with expected volatility. The formula for
the price of a European call option on a spot asset
that pays no dividends or interest is the following:
C = S0 N (d1 ) − Xe − rT N (d2 ) ,
(3)
where d1 =
d2 =
ln(S0 / X ) + ( r + σ 2 / 2)T
σ T
ln(S0 / X ) + (r − σ 2 / 2)T
σ T
and
= d1 − σ T
and N (*) is the cumulative normal density function. Hull (2002), Jarrow and Turnbull (2000), and
Dubofsky and Miller (2003) provide formulas for
put options and options on other types of assets.
The BS formula strictly applies to European
options only—not to American options, which
can be exercised any time prior to expiry—and it
requires modifications for assets that pay dividends, such as stocks, or that don’t require an
initial outlay, such as futures.7 Further, the BS
model makes some strong assumptions: that the
underlying asset price follows a lognormal random
walk, that the riskless rate is a known function
of time, that one can continuously adjust one’s
6
There are several ways to derive the BS formula that differ in their
required assumptions (Merton, 1973b). Wilmott, Howison, and
Dewynne (1995) provide a nice introduction to the mathematics
of the BS formula and Wilmott (2000) extends that treatment to
cover the price of volatility risk. Boyle and Boyle (2001) discuss
the history of option pricing formulas.
7
Black (1976) provides the formula for options on futures, rather
than spot assets. Barone-Adesi and Whaley (1987) provide an
approximation to the BS formula that accounts for early exercise.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
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position in the underlying asset (delta hedging),
and that there are no transactions costs on the
underlying asset and no arbitrage opportunities.
Despite these strong assumptions, the BS model is
very widely used by practitioners and academics,
often fitting the data reasonably well even when
its assumptions are clearly violated.
Does IV Predict Realized Volatility?
The BS model expresses the price of a
European call or put option (C or P) as a function
of five arguments {S, X, r, T, and σ 2}. Of those six
quantities, five are observable as market prices or
features of the option contract {C, S, X, r, T}. The
BS formula is frequently inverted to solve for the
sixth quantity, the IV {σ } of log asset returns in
terms of the observed quantities. This IV is used to
predict the volatility of the asset return to expiry.
Ironically, the BS formula usually used to
derive IV assumes that volatility is constant. Hull
and White (1987) provide the foundation for the
practice of using a constant-volatility model to
predict stochastic volatility (SV): If volatility
evolves independently of the underlying asset
price and no priced risk is associated with the
option, the correct price of a European option
equals the expectation of the BS formula, evaluating the variance argument at average variance
until expiry:
T
C (St ,Vt , t ) = ∫t C BS (V )h(V σ t2 )dV
(4)
= E[C BS (Vt ,T ) Vt ],
where the average variance until expiry is
denoted as
Vt ,T =
1 T
∫ V dτ
T −t τ τ
ing the expectation through the BS formula. That
is, one cannot claim that the correct price of a call
option under stochastic volatility is the BS price
evaluated at the expected value of the standard
deviation until expiry. That is, it is not true that
(5)
)
(
)
(
C St , Vt , t = C BS E V t ,T Vt .
Instead, Bates (1996) approximates the relation
between the BS IV and expected variance until
expiry with a Taylor series expansion of the BS
price for an at-the-money option. That is, for atthe-money options, the BS formula for futures
reduces to
1
C BS = e − rT F 2N σ T − 1 .
2
This can be approximated with a second-order
Taylor expansion of N(*) around zero, which
yields
C BS ≈ e − rT Fσ T / (2π ) .
Another second-order Taylor expansion of that
approximation around the expected value of
variance until expiry shows that the BS IV is
approximately the expected variance until expiry:
2
(6)
2
σˆ BS
1 Var (Vt ,T )
≈ 1 −
EV .
8 ( EtVt ,T )2 t t ,T
2 ) understates
That is, the BS-implied variance (σBS
the expected variance of the asset until expiry
–
(EtVt,T ). Similarly, BS-implied standard deviation
(σBS) slightly understates the expected standard
deviation of asset returns.9
The Volatility Smile
and its square root is usually referred to as realized
volatility (RV).8
Bates (1996) points out that the expectation
in (4) is taken with respect to variance until expiry,
not standard deviation until expiry. Therefore,
one cannot use the linearity of the BS formula
with respect to standard deviation to justify pass-
Volatility is constant in the BS model; IV does
not vary with the “moneyness” of the option.
That is, if the BS model assumptions were literally
true, the IV from a deep-in-the-money call should
be the same as that from an at-the-money call or
an in-the-money put. In reality, for most assets, IV
does vary with moneyness. A graph of IV versus
moneyness is often referred to as the “volatility
8
9
Romano and Touzi (1997) extend the Hull and White (1987) result
to include models that permit arbitrary correlation between returns
and volatility, like the Heston (1993) model.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
Note that (6) depends on (4), which assumes that there is no priced
risk associated with holding the option. That is, (6) requires that
changes in volatility do not create priced risk for an option writer.
M AY / J U N E
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411
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smile” or “volatility smirk,” depending on the
shape of the relation. Research attributes the
volatility smile to deviations from the BS assumptions about the evolution of the underlying asset
prices, such as the presence of stochastic volatility,
jumps in the price of the underlying asset, and
jumps in volatility (Bates, 1996, 2003).
The existence of the volatility smile brings up
the question of which strike prices—or combinations of strike prices—to use to compute IV. In
practice, IV is usually computed from a few nearthe-money options for three reasons (Bates, 1996):
(i) The BS formula is most sensitive to IV for atthe-money options. (ii) Near-the-money options
are usually the most heavily traded, resulting in
smaller pricing errors. (iii) Beckers (1981) showed
that IV from at-the-money options provides the
best estimates of future realized volatility. While
researchers have varied the number and types of
options as well as the weighting procedure, it has
been common to rely heavily on a few at-themoney options.
price of the underlying futures contract. These
conditions apply because an American option—
which can be exercised at any time—must always
be worth at least its value if exercised immediately.
Options prices that did not obey these relations
were discarded. In addition, the observation was
discarded if there was not at least one call and
one put price.
THE PROPERTIES OF IMPLIED
VOLATILITY
How Well Does IV Predict RV?
Equation (6) says that BS IV is approximately
–
the conditional expectation of RV(Vt,T ). This
relation has two testable implications: IV should
be an unbiased predictor of RV; no other forecast
should improve the forecast from IV. If IV is an
unbiased predictor of RV, one should find that
{α , β1} = {0, 1} in the following regression:
(8)
Constructing IV from Options Data
At each date, IV is chosen to minimize the
unweighted sum of squared deviations of BaroneAdesi and Whaley’s (1987) formula for pricing
American options on futures with the actual settlement prices for the two nearest-to-the-money call
options and two nearest-to-the-money put options
for the appropriate futures contract.10 That is, IV
is computed as follows:
4
(7) σ IV ,t ,T = arg minσ t ,T ∑ ( BAWi (σ t ,T ) − Pri ,t )2 ,
i =1
where Pri,t is the observed settlement premium
(price) of the ith option on day t and BAWi (*) is
the appropriate call or put formula as a function
of the IV.
Before being used in the minimization of (7),
the data were checked to make sure that they
obeyed the inequality restrictions implied by the
no-arbitrage conditions on American options
prices: C $ F – X and P $ X – F, where F is the
10
The results in this paper are almost indistinguishable when done
with European option pricing formulas (Black, 1976) or the BaroneAdesi and Whaley correction for American options.
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σ RV ,t ,T = α + β1σ IV ,t ,T + εt ,
where σRV,t,T denotes the RV of the asset return
from time t to T and σIV,t,T is IV at t for an option
expiring at T.11 RV is the annualized standard
deviation of asset returns from t to T:
(9)
σ RV ,t ,T = Vt ,T =
250 T
∑ ln( Fi / Fi −1 ) ,
T − t i=t
where Ft is the asset price at t and there are 250
business days in the year.
The other commonly investigated hypothesis
about IV is that no other forecast improves its forecasts of RV. If IV does subsume other information
in this way, it is said to be an “informationally
efficient predictor” of volatility. Researchers
investigate this issue with variants of the following
encompassing regression:
(10)
11
σ RV ,t ,T = α + β1σ IV ,t ,T + β2σ FV ,t ,T + εt ,
Researchers also estimate (8) with realized and implicit variances,
rather than standard deviations. The results from such estimations
provide similar inference to those done with variances. Other
authors argue that because volatility is significantly skewed, one
should estimate (8) with log volatility. Equation (6) shows that
use of logs introduces another source of bias into the theoretical
relation between RV and IV.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
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where σFV,t,T is some alternative forecast of volatility from t to T.12 If one rejects that β2 = 0 for some
σFV,t,T, then one rejects that IV is informationally
efficient.
Across many asset classes and sample periods,
researchers estimating versions of (8) have found
that α̂ is positive and βˆ1 is less than 1 (Canina and
Figlewski, 1993; Lamoureux and Lastrapes, 1993;
Jorion, 1995; Fleming, 1998; Christensen and
Prabhala, 1998; Szakmary et al., 2003). That is, IV
is a significantly biased predictor of RV: A given
change in IV is associated with a larger change
in RV.
Tests of informational efficiency provide more
mixed results. Kroner, Kneafsey, and Claessens
(1993) concluded that combining time-series
information with IV could produce better forecasts than either technique singly. Blair, Poon, and
Taylor (2001) discover that historical volatility
provides no incremental information to forecasts
from VIX IVs.13 Li (2002) and Martens and Zein
(2004) find that intraday data and long-memory
models can improve on IV forecasts of RV in currency markets.
It is understandable that tests of informational
efficiency provide more varied results than do
tests of unbiasedness. Because theory does not
restrict what sort of information could be tested
against IV, the former tests suffer a data snooping
problem. Even if IV is informationally efficient,
some other forecasts will improve its predictions
in a given sample, purely as a result of sampling
variation. These forecasts will not add information to IV in other periods, however.
But some authors have found reasonably
strong evidence against the simple informational
efficiency hypothesis across assets and classes of
forecasts (Neely, 2004a,b). This casts doubt on the
data snooping explanation. It seems likely that
IV is not informationally efficient by statistical
12
13
One need not make the econometric forecast orthogonal to IV before
using it in (10). The β̂ 2 t-statistic provides the same asymptotic
inference as the appropriate F-test for the null that β2 = 0. And the
F-test is invariant to orthogonalizing the regressors because it is
based on the regression R2.
VIX is a weighted index of IVs calculated from near-the-money,
short-term, S&P 100 options. It is designed to correct measurement
problems associated with the volatility smile and early exercise.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
criteria and that the failure of unbiasedness and
inefficiency are related.
Several hypotheses have been put forward to
explain the conditional bias: errors in IV estimation, sample selection bias, estimation with overlapping observations, and poor measurement of
RV. Perhaps the most popular solution to the
conditional bias puzzle is the claim that volatility risk is priced. This theory requires some
explanation.
The Price of Volatility Risk
To understand the volatility risk problem,
consider that there are two sources of uncertainty
for an option writer—the agent who sells the
option—if the volatility of the underlying asset
can change over time: the change in the price of
the underlying asset and the change in its volatility.14 An option writer would have to take a position both in the underlying asset (delta hedging)
and in another option (vega hedging) to hedge
both sources of risk.15 If the investor only hedges
with the underlying asset—not using another
option too—then the return to the investor’s portfolio is not certain. It depends on changes in
volatility. If such volatility fluctuations represent
a systematic risk, then investors must be compensated for exposure to them. In this case, the HullWhite result (4) does not apply because there will
be risk associated with holding the option and
the IV from the BS formula will not approximate
the conditional expectation of objective variance
as in (6).
The idea that volatility risk might be priced
has been discussed for some time: Hull and White
(1987) and Heston (1993) consider it. Lamoureux
and Lastrapes (1993) argued that the price of
volatility risk was likely to be responsible for the
bias in IVs options on individual stocks. But most
empirical work has assumed that this volatility
risk premium is zero, that volatility risk could be
hedged or is not priced.
14
A more general model would imply additional sources of risk
such as discontinuities (jumps) in the underlying asset price or
underlying volatility.
15
Delta and vega denote the partial derivatives of the option price
with respect to the underlying asset price and its volatility,
respectively.
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413
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Is it reasonable to assume that the volatility
risk premium is zero? There is no question that
volatility is stochastic, options prices depend on
volatility, and risk is ubiquitous in financial
markets. And if customers desire a net long position in options to hedge against real exposure or
to speculate, some agents must hold a net short
position in options. Those agents will be exposed
to volatility fluctuations. If that risk is priced in
the asset pricing model, those agents must be compensated for exposure to that risk. These facts
argue that a non-zero price of volatility risk creates
IV’s bias.
On the other hand, there seems little reason
to think that volatility risk itself should be priced.
While the volatility of the market portfolio is a
priced factor in the intertemporal capital asset
pricing model (CAPM) (Merton, 1973a; Campbell,
1993), it is more difficult to see why volatility
risk in other markets—e.g., foreign exchange and
commodity markets—should be priced. One must
appeal to limits-of-arbitrage arguments (Shleifer
and Vishny, 1997) to justify a non-zero price of
currency volatility risk.
Recently, researchers have paid greater attention to the role of volatility risk in options and
equity markets (Poteshman, 2000; Bates, 2000;
Benzoni, 2002; Chernov, 2002; Pan, 2002;
Bollerslev and Zhou, 2003; and Ang et al., 2003).
Poteshman (2000), for example, directly estimated
the price of risk function and instantaneous variance from options data, then constructed a measure of IV until expiry from the estimated volatility
process to forecast SPX volatility over the same
horizon. Benzoni (2002) finds evidence that variance risk is priced in the S&P 500 option market.
Using different methods, Chernov (2002) also
marshals evidence to support this price of volatility risk thesis. Neely (2004a,b) finds that Chernov’s
price-of-risk procedures do not explain the bias
in foreign exchange and gold markets.
THE IMPLIED VOLATILITY OF
SHORT-TERM INTEREST RATES
The IV of options on short-term interest rates
illustrates how IV might be applied to understand
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M AY / J U N E
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economic forces. Central banks are particularly
concerned with short-term interest rates because
most central banks implement monetary policy
by targeting those rates.16 Financial market participants and businesses likewise often carefully
follow the actions and announcements of central
banks to better understand the future path of
short-term interest rates.
Eurodollar Futures Contracts
Interest rate futures are derivative assets
whose payoffs depend on interest rates on some
date or dates in the future. They enable financial
market participants to either hedge their exposure to interest rate fluctuations, or speculate on
interest rate changes. One such instrument is the
Chicago Mercantile Exchange futures contract
for a three-month eurodollar time deposit with a
principal amount of $1,000,000. The final settlement price of this contract is 100 less the British
Bankers’ Association (BBA) three-month eurodollar rate prevailing on the second London
business day immediately preceding the third
Wednesday of the contract month:
(11)
FT = 100 = RT ,
where FT is the final settlement price of the futures
contract and RT is the BBA three-month rate on
the contract expiry date. The relation between
the three-month eurodollar rate at expiry and the
final settlement price ties the futures price at all
dates to expectations of this interest rate.
For concreteness, consider what would happen if the First Bank of Des Peres (FBDP) sold a
three-month eurodollar futures contract for a
quoted price of $97 on June 7, 2004, for a contract
expiring on September 13, 2004. Banks might
take such short positions to hedge interest rate
fluctuations; they borrow short-term and lend
long-term and will generally lose (gain) when
short-term interest rates rise (fall). The FBDP’s
16
The fact that central banks implement policy by targeting shortterm interest rates does not mean that nominal interest rates can
be interpreted as measuring the stance of monetary policy. For
example, if inflation rises and interest rates remain constant, policy
passively becomes more accommodative, all else equal.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
Neely
short position means that it has effectively agreed
to borrow $1,000,000 for three months, starting
on September 13, 2004, at an interest rate of
(100 – 97 =) 3 percent.
If the market had expected no change in
interest rates through September and risk premia
in this market are constant, then realized changes
in spot interest rates will translate directly into
changes in futures prices.17 If interest rates unexpectedly rise 45 basis points between June 7, 2004,
and September 13, 2004, the FBDP futures prices
will fall and the FBDP will have gained by precommitting to borrow at 3 percent. If interest rates
unexpectedly decline, however, the FBDP will
lose on the futures contract.
How much will the FBDP gain (lose) for each
basis-point decrease (increase) in interest rates?
With quarterly compounding it will gain 1 basis
point of interest for one quarter of a year on
$1,000,000. This translates to $25 per basis point.
(12)
$1, 000, 000
0.0001
= $25 .
4
If the BBA three-month eurodollar rate is 3.45
percent on the day of final settlement, the final
settlement price of the futures contract will be
100 – 3.45 = 96.55 percent. The FBDP will gain
$25 × 45 = $1,125 because it shorted the contract
at $97 and the contract price fell to $96.55 at
final settlement.18 Such a gain would be used to
offset losses from the reduced value of its asset
portfolio (loans).
Because the final futures price will be determined by the BBA three-month eurodollar rate
at final settlement, the futures price can be used
to infer the expected future interest rate if there
is no risk premium associated with holding the
futures contract. Or, if there are stable risk premia
associated with holding the contract, one can still
measure changes in expected interest rates from
changes in futures prices if the risk premia are
fairly stable.
17
More generally, only unanticipated changes in interest rates will
result in changes in futures prices and risk premia will play some
role in futures returns.
18
This example assumes the FBDP holds the position until final
settlement.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
Splicing the Futures and Options Data
To examine the behavior of IV on short-term
interest rates, we consider settlement data on
each three-month eurodollar futures and option
contract for the period March 20, 1985, through
June 29, 2001. Because exchange-traded futures
and options contracts expire on only a few dates
a year, one cannot obtain a series of options priced
with a fixed expiry horizon for each business day
of the year.19 To obtain as much information as
possible, the usual practice in dealing with futures
and options data is to “splice” data from different
contracts at the beginning of some set of contract
expiry months, usually monthly or quarterly. This
article uses data from futures and options contracts expiring in March, June, September, and
December. For example, settlement prices for the
futures contract and the two nearest-the-money
call and put options expiring in March 1986 are
collected for all trading days in December 1985
and January and February 1986. Then data pertaining to June 1986 contracts are collected from
March, April, and May 1986 trading dates. A
similar procedure is followed for the September
and December contracts. Such a procedure avoids
pricing problems near final settlement that
result from illiquidity (Johnston, Kracaw, and
McConnell, 1991). This method collects data on
a total of 4,040 business days, with 8 to 76 business
days to option expiry.
Summary Statistics
Table 1 shows the summary statistics on log
futures price changes in percentage terms, absolute
log futures price changes in annual terms, and
IV and RV in annual terms. Futures price changes
are very close to mean-zero and have some modest
positive autocorrelation. The absolute changes
are definitely positively autocorrelated, as one
would expect from high-frequency asset price
data. IV and RV until expiry have similar mean
and autocorrelation properties. But IV is somewhat less volatile than RV, as one would expect
if IV predicts RV. The mean of RV is slightly lower
19
Additional expiry months were introduced in 1995; previously,
there were four expiry months per year.
M AY / J U N E
2005
415
Neely
Table 1
Summary Statistics
100 · ln(F(t)/F(t–1))
249 · 100 · |ln(F(t)/F(t–1))|
σIV,t,T
σRV,t,T
Total observations
4,040
4,040
4,040
4,040
Nobs
3,975
3,975
3,953
4,039
µ
0.003
10.088
0.953
0.769
σ
0.070
14.141
0.458
0.494
Max
1.272
316.645
3.601
3.861
Min
–0.449
0.000
0.251
0.076
ρ1
0.070
0.213
0.986
0.989
ρ2
0.023
0.241
0.973
0.977
ρ3
–0.014
0.226
0.960
0.965
ρ4
–0.025
0.246
0.948
0.954
ρ5
–0.007
0.247
0.936
0.942
NOTE: The table contains summary statistics on log futures price changes (percent), annualized absolute log futures price changes, and
annualized IV and RV until expiry. The rows show the total number of observations in the sample, the non-missing observations, the mean,
the standard deviation, the maximum, the minimum, and the first five autocorrelations. The standard error of the autocorrelations is
about 1/√T ≈ 0.016.
than that of IV, indicating that there might be a
volatility premium.
Figure 2 clearly illustrates the right skewness in the distribution of IV and changes in IV.
Although it is difficult to see in the lower panel
of Figure 2, very large positive changes in IV are
much more common than very large negative
changes in IV. The fact that IV must be positive
probably partly explains the right skewness in
these distributions.
Eurodollar Rates and the Federal Funds
Target Rate
The futures and options data considered here
pertain to three-month eurodollar rates. The Fed,
however, is more concerned about the federal
funds rate, the overnight interbank interest rate
used to implement monetary policy, than about
other short-term interest rates, such as the eurodollar rate.20 This is because the federal funds
futures prices are often interpreted to provide
market expectations of the Fed’s near-term policy
actions. Short-term interest rates are closely tied
20
Carlson, Melick, and Sahinoz (2003) describe the recently developed options market on federal funds futures contracts.
416
M AY / J U N E
2005
together, however, so there might be information
about the federal funds rate in three-month eurodollar futures.
Figure 3 shows that, although the three-month
eurodollar is much more variable than the federal
funds target over a period of a few days, the two
series closely tracked each other over periods
longer than a few days from March 1985 through
June 2001. One can assume that the expected path
of the funds rate is closely related to the expected
path of the three-month eurodollar rate.21 And
therefore the IV on three-month eurodollars probably tracks the uncertainty about the federal funds
target over horizons greater than a few days.
Options on Eurodollar Rates
Because option prices depend on the volatility of the underlying asset (among other factors),
one can measure the uncertainty associated with
expectations of future interest rates from IV from
option prices on eurodollar futures contracts. And
21
The payoff to the federal funds futures contract depends on the
average federal funds rate over the course of a month, whereas
the three-month eurodollar futures contract payoff depends on the
BBA quote for the three-month eurodollar rate at one point in time,
the expiry of the contract.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
Neely
Figure 2
The Distributions of Implied Volatility and Changes in Implied Volatility
Percent
3.6
2.4
1.2
0.0
0.4
0.8
1.2
1.6
2.0
2.4
2.8
3.2
3.6
IV
Percent
18
12
8
4
0
–0.2
0.2
0.6
1.0
Change in IV
NOTE: The figure shows the empirical distributions of IV and changes in IV on three-month eurodollar futures prices.
the volatility of interest rates will be very close
to the volatility of futures prices because of the
linear relation between the two series at final
settlement: 100 – FT = RT.
The usual BS measure of IV is a risk-neutral
measure, meaning that it assumes that all risk
associated with holding the option can be arbitraged away.22 This is probably not exactly true.
And the eurodollars futures prices don’t necessarily follow the assumptions of the BS model. In
particular, the underlying asset price is probably
subject to jumps. Yet Figure 4, which shows the
One can test the unbiasedness hypothesis—
that IV is an unbiased predictor of RV—with the
predictive regression (8):
22
(8)
Boxed insert 2 explains the concept of risk-neutral measures.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
IV and RV until expiry of the three-month eurodollars futures price, appears to show that the
BS IV tracks RV fairly well. So, one might think
that IV from options on three-month eurodollar
rates measures the uncertainty about future
interest rates reasonably well.
How Well Does IV Predict RV for
Eurodollar Futures?
σ RV ,t ,T = α + β1σ IV ,t ,T + εt .
M AY / J U N E
2005
417
Neely
BOXED INSERT 2: RISK-NEUTRAL VALUATION
The calculation of the price of the option in Figure 1 did not include any assumptions about the
probabilities that the stock price would rise or fall. But the assumptions used to value the stock do
imply “risk-neutral probabilities” of the two states of the world. These are the probabilities that
equate the expected payoff on the stock with the payoff to a riskless asset that requires the same
initial investment. Recall that the stock in the example in Figure 1 was worth $12 in the first state
of the world and $8 in the second state of the world. If the initial price of the stock is $10, the riskneutral probabilities solve the following:
p ?Ê $12 + (1 − p) ?Ê $8 = $10e 0.05.
(b1)
This implies that—if prices were unchanged and stocks were valued by risk-neutral investors—the
probability that the stock price rises—the probability of state 1—is the following:
p=
(b2)
(10e 0.05 − 8)
= 0.6282 .
12 − 8
It is important to understand that this risk-neutral probability is not the objective probability that
the stock price will rise. It is a synthetic probability that the stock price will rise if actual prices had
been determined by risk-neutral agents.
No assumption in this example provides the objective probability that the stock price will rise;
neither can one calculate the expected return to the stock. But even without the objective probabilities,
one could calculate the option price through the assumption of the absence of arbitrage. It is counterintuitive but true that the expected return on the stock is not needed to value a call option. One might
think that a call option would depend positively on the expected return to the stock. But, because
one can value the option through the absence of arbitrage, the expected return to the stock doesn’t
explicitly appear in the option pricing formula.
And the risk-neutral probabilities can be used to calculate the value of the option ($C) by discounting the value of the (risk-neutral) expected option payoff. Recalling that the option is worth $2 in the
first state of the world, which has a probability of 0.6282 and $0 in the second state of the world, the
option price can be calculated as the discounted risk-neutral expectation of its payoff as follows:
C = e –0.05[ p ?Ê2 + (1 − p) ?Ê 0] = e −0.05[0.6282 ?Ê2 + (1 − 0.6282) ?Ê 0] = $1.1951.
This calculation provides the same answer as the no-arbitrage argument used in Figure 1. In some
cases, it is easier to derive option pricing formulas from a risk-neutral valuation.
The concept of risk-neutral valuation implies that IV from option prices measures the volatility
of the risk-neutral probability measure. To the extent that an asset price’s actual stochastic process
differs from a risk-neutral process, perhaps because there is a risk-premium in its drift or a volatility risk premium in the option price, the information obtained by inverting option pricing formulas
will be misleading. The true distribution of the underlying asset price is often called the objective
probability measure.
418
M AY / J U N E
2005
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
Neely
Figure 3
Figure 4
Federal Funds Targets and Three-Month
Eurodollar Rates
Realized and Implied Volatility on
Three-Month Eurodollar Rates
Percent
Percent
14
4.0
Eurodollar
12
IV
RV
Federal Funds
3.2
10
2.4
8
6
1.6
4
0.8
2
0
1984
1989
1994
1999
2004
NOTE: The figure displays federal funds targets and the threemonth eurodollar rate from January 1, 1984, to July 25, 2003.
For overlapping horizons, the residuals in (8)
will be autocorrelated and, while ordinary least
squares (OLS) estimates are still consistent, the
autocorrelation must be dealt with in constructing standard errors (Jorion, 1995). Such data sets
are described as “telescoping” because correlation
between adjacent errors declines linearly and then
jumps up at the point at which contracts are
spliced.
Table 2 shows the results of estimating (8)
with σIV,t,T and σRV,t,T on three-month eurodollar
futures. βˆ1 is statistically significantly less than
1—0.83—indicating that IV is an overly volatile
predictor of subsequent RV. This is the usual
finding from such regressions: See Canina and
Figlewski (1993), Lamoureux and Lastrapes
(1993), Jorion (1995), Fleming (1998), Christensen
and Prabhala (1998), and Szakmary et al. (2003),
for example. As discussed previously, there are
many potential explanations for this conditional
bias—sample selection, overlapping data, errors
in IV—but the most popular story is that stochastic volatility introduces risk to delta hedging,
making writing options risky.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
0.0
1984
1988
1992
1996
2000
2004
NOTE: The figure displays three-month eurodollar IV and RV
from March 20, 1985, through June 29, 2001.
Figure 5 shows a scatterplot of {IV, RV} pairs
along with the OLS fitted values from Table 2, a
45-degree line and the mean of IV and RV. If IV
were an unbiased predictor of RV, the 45-degree
line would be the true relation between them.
The fact that the OLS line is flatter than the 45degree line illustrates that IV is an overly volatile
predictor of RV. The cross in Figure 5—which is
centered on {mean IV, mean RV}—lies beneath
the 45-degree line, illustrating that the mean IV
is higher than mean RV.
What Does IV Illustrate About
Uncertainty About Future Interest Rates?
Comparing Figure 3 with Figure 4 shows that
IV has been declining with the overall level of
short-term interest rates, which have been falling
with inflation since the early 1980s. One interpretation of the data is that the sharp rise in inflation
in the 1970s and the subsequent disinflation of
the 1980s created much uncertainty about the
level of future interest rates, which has gradually
fallen over the past 20 years. The reduction in
uncertainty with respect to interest rates probably
M AY / J U N E
2005
419
Neely
Figure 5
Table 2
Implied Volatility as a Predictor of Realized
Volatility
Predicting Realized Volatility with Implied
Volatility
α̂
RV until Expiry
4.0
3.2
2.4
0.052
β̂1
0.834
(s.e.)
0.064
Wald
40.814
Wald PV
0.000
Observations
3,952
1.6
R2
0.599
0.8
NOTE: The table shows the results of predicting three-month
eurodollar RV with IV, as in (8). The rows show α̂ , its robust
standard error, βˆ1 , its robust standard error, the Wald test
statistic for the null that {α, β } = {0, 1}, the Wald test p-value,
the number of observations, and the R2 of the regression.
0.0
0.4
0.8
1.2
1.6
2.0
2.4
2.8
3.2
3.6
4.0
IV
NOTE: The figure shows a scatterplot of {IV, RV} pairs along
with the ordinary least-squares fitted values from Table 2 (solid
black line), a 45-degree line (short dashes) and the IV and RV
(cross). The data are in percentage terms.
stems from both a reduction in the level of interest
rates and greater certainty about both monetary
policy and the level of real economic activity.
A close look at Figure 4 also hints that there
might be some seasonal pattern in IV, associated
with the expiry of contracts. Indeed, long-horizon
IVs tend to be larger than short-horizon IVs (which,
for brevity, are not shown). As IV is scaled to be
interpretable as an annual measure, comparable
at any horizon, this is a bit of a mystery. It might
simply be an artifact of the simplifying assumptions of the BS model.
What Sort of News Is Coincident with
Changes in IV?
Events of obvious economic importance and
large changes in the futures price, itself, often
accompany the largest changes in IV. To examine
news events around large changes, the Wall Street
Journal business section was searched for news
on the dates of large changes and on the days
immediately following those changes—from
420
–0.017
(s.e.)
M AY / J U N E
2005
March 20, 1985, through June 29, 2001. Table 3
shows some of the largest changes in IV during
the sample and the event that might have precipitated it.
The largest change in IV, by far, is a rise of
1.2 percentage points on October 20, 1987, coinciding with the stock market crash of 1987, when
the S&P 500 lost 22 percent of its value in one
day. Four more of the top 20 changes (including
the second largest) happened in the six weeks
following the crash and one happened eight weeks
before the crash, on August 27, 1987. The large
changes in the IV of three-month eurodollar interest rates reflected uncertainty about future interest
rates prior to the crash. A change in Federal
Reserve Chairmen might have fueled the apparent
uncertainty about the economy and the stance of
monetary policy. Alan Greenspan took office as
Chairman of the Board of Governors of the Federal
Reserve on August 11, 1987.
The third largest change, a 0.44-percentagepoint increase, occurred on November 28, 1990.
It coincided with reports that President George
H.W. Bush would go to Congress to ask for endorsement of plans to use military force to evict Iraqi
forces from Kuwait. The possibility of war in such
an economically important area of the world
clearly spooked financial markets.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
Neely
Table 3
News Events Coincident with Large Changes in Three-Month Eurodollar IV
Rank
∆ in IV
Date
∆ in federal
funds target?
Relevant financial news
1
1.182
10/20/87
No
Stock market crash of 1987: S&P 500 declined 22 percent in one day.
2
–0.526
11/12/87
No
Decline in U.S. trade deficit.
3
0.438
11/28/90
No
Gulf War fears: Bush going to Congress to ask for authority to evict
Iraq from Kuwait.
4
0.411
8/27/98
No
Russian debt crisis: Yeltsin may resign, along with an indefinite
suspension of ruble trading and fear Russia may return to Sovietstyle economics.
5
–0.375
1/15/88
No
The sharp narrowing of the trade deficit triggered market rallies.
6
0.353
12/2/96
No
Retailers reported stronger-than-expected sales over Thanksgiving.
7
0.339
10/15/87
No
Stocks and bonds slid further as Treasury Secretary Baker tried to
calm the markets, saying the rise in interest rates isn’t justified.
8
0.332
9/3/85
No
The farm credit system is seeking a federal bailout of its $74 billion
loan portfolio…As much as 15 percent of its loans are
uncollectible.
9
0.330
11/27/87
No
Inflation worries remain despite the stock crash, due to higher
commodity prices and the weak dollar.
10
–0.321
10/29/87
Yes
Post-stock market crash reduction in the federal funds target.
11
0.315
6/7/85
No
Bond prices declined for the first time in a week, as investors awaited
a report today on May employment…The Fed reported a surge
in the money supply, leaving it well above the target range.
12
–0.302
10/30/87
No
Stocks and bonds reversed course after an early slide, helped by
G-7 interest-rate drops.
13
–0.301
8/16/94
Yes
FOMC meeting: The Fed boosted the funds rate 50 basis points,
sending a clear inflation-fighting message.
14
–0.298
7/11/86
Yes
The Fed’s discount-rate cut prompted major banks to lower their
prime rates.
15
–0.285
12/2/91
No
Under strong pressure to resuscitate the economy, President
George H.W. Bush promised not to do “anything dumb” to
stimulate the economy.
16
0.279
4/20/89
No
Financial markets were roiled by a surprise half-point boost in
West German interest rates. The tightening was quickly matched
by other central banks.
17
0.278
8/27/91
No
Federal funds target rate was increased on August 6 and
September 13, 1991.
18
0.275
8/31/89
No
Federal funds target rate was increased on August 20 and October 18,
1989.
19
0.275
8/27/87
Yes
Federal funds target rate raised by 12.5 basis points.
20
0.266
6/2/86
No
Bond prices tumbled amid concern the economy will speed up,
renewing inflation.
NOTE: The table contains the largest changes in IV (in percentage points, in descending order) and the news (as reported in the Wall
Street Journal ) that was associated with those changes. The sample includes changes from March 20, 1985, through June 29, 2001.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
M AY / J U N E
2005
421
Neely
Another large increase, of 0.41 percentage
points, occurred on August 28, 1998. This rise was
coincident with the Russian debt crisis, rumors
that President Yeltsin had resigned, and the possibility of a reversal of Russian political and
economic reforms. The Russian debt crisis had
potentially serious implications for international
investors. Neely (2004c) discusses the episode
and its potential effect on U.S. financial markets.
Several of the 20 largest changes in threemonth eurodollar IV were also associated with
large changes in the futures price. It is likely that
these changes in the futures price were unanticipated because large, anticipated changes in futures
prices provide profit-making opportunities.
Additionally, anticipated changes are unlikely to
cause a substantial revision to IV. Four of the 20
largest changes in IV were also associated with
presumably unanticipated changes in the federal
funds target rate. It seems that unanticipated
monetary policy can be an important determinant
of uncertainty about future interest rates.
Finally, one might note that the large IV
changes shown in Table 3 refute the BS assumptions of a constant or even continuous volatility
process. As such, they might be partly responsible
for delta hedging errors, which require a risk
premium that causes IV to be a conditionally
biased estimate of RV.
CONCLUSION
This article has explained the concept of IV
and applied it to measure uncertainty about
three-month eurodollar rates. The IVs associated
with three-month eurodollars can be interpreted
to reflect uncertainty about the Federal Reserve’s
primary monetary policy instrument, the federal
funds target rate.
As with IV in most financial markets, the IV
of the three-month eurodollar rate has been an
overly volatile predictor of RV. IV on the threemonth eurodollar rates has been declining since
1985, as inflation and interest rates have fallen
and the Fed has gained credibility with financial
markets. The largest changes in IV were coincident
with important economic events such as the stockmarket crash of 1987, fears of war in the Persian
422
M AY / J U N E
2005
Gulf, and the Russian debt crisis. Most of the rest
of the largest changes in IV have similarly been
associated with important news about the real
economy or the stock market or revisions to
expected monetary policy.
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GLOSSARY
A European option is an asset that confers the right, but not the obligation, to buy or sell an underlying
asset for a given price, called a strike price, at the expiry of the option.
An American option can be exercised on or before the expiry date.1
Call options confer the right to buy the underlying asset; put options confer the right to sell the
underlying asset.
If the underlying asset price is greater (less) than the strike price, a call (put) option is said to be in the
money. If the underlying asset price is less (greater) than the strike price, the call (put) option is
out of the money. When the underlying asset price is near (at) the strike price, the option is near
(at) the money.
The firm or individual who sells an option is said to write the option.
The price of an option is often known as the option premium.
1
The terms European and American no longer have any geographic meaning when referring to options. That is, both types of options are
traded worldwide.
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