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Declining labor force participation and its implications
for unemployment and employment growth
Daniel Aaronson, Luojia Hu, Arian Seifoddini, and Daniel G. Sullivan
Introduction and summary
The labor force participation (LFP) rate—the share of
the working-age population that is either employed or
jobless and actively looking for employment—has fallen
from 66 percent at the beginning of the Great Recession
in December 2007 to 62.7 percent in September 2014.1
To some, this decline suggests the possibility that there
may be labor market slack over and above that captured
by the unemployment rate. The existence of such extra
slack might imply that it would be appropriate for monetary policy to remain highly accommodative for longer
than would otherwise be the case. However, to properly
judge the extent to which the drop in the LFP rate reflects
additional slack, one must account for the effects of
several long-running trends not associated with the
latest recession. Such pre-recession trends include the
movement of baby boomers into retirement ages, longrunning declines in the labor force participation of
males of prime working age (25–54), the flattening
out of once-rising female participation, sharp declines
in teen participation, and the increasing participation
of adults aged 55 and older. All but the last trend imply
that a decline in aggregate LFP was to be expected
even before the Great Recession began. Indeed, after
rising from the 1960s through the 1990s, LFP has been
falling since 2000, reflecting most of these factors.
In this article, we extend the methodologies of
Aaronson and Sullivan (2001), Sullivan (2007),
Aaronson, Davis, and Hu (2012), and Aaronson and
Brave (2013) to provide estimates of the long-run trend
rate of LFP2 based on pre-recession data (data before
2008). Our models (with different specifications) suggest that the actual LFP rate as of the third quarter of
2014 is 0.2 to 1.2 percentage points lower than what
would have been expected before the recession started,
with our preferred model estimating the gap at the high
end of this range.3 We also provide a prediction of the
LFP rate that would have been expected given the high
100
unemployment rates of recent years and find that the
actual LFP rate as of late is 0 to 0.8 percentage points
lower than that benchmark, with our preferred estimate
again being at the high end of the range. The results
from our models suggest that there may indeed be
greater slack in the labor market than is signaled by
the unemployment rate.
Daniel Aaronson is a vice president and director of microeconomic
research, Luojia Hu is a senior economist and research advisor,
Arian Seifoddini is a senior associate economist, and Daniel G.
Sullivan is the director of research and an executive vice president
in the Economic Research Department at the Federal Reserve
Bank of Chicago. The authors thank Lisa Barrow, Han Choi,
Jason Faberman, Bo Honore, and Spencer Krane for helpful
comments and suggestions. They also thank the Congressional
Budget Office, National Association for Business Economics,
Banque de France, and Federal Reserve Bank of Dallas for
opportunities to present earlier versions of this article and
receive useful feedback.
© 2014 Federal Reserve Bank of Chicago
Economic Perspectives is published by the Economic Research
Department of the Federal Reserve Bank of Chicago. The views
expressed are the authors’ and do not necessarily reflect the views
of the Federal Reserve Bank of Chicago or the Federal Reserve
System.
Charles L. Evans, President; Daniel G. Sullivan, Executive Vice
President and Director of Research; Spencer Krane, Senior Vice
President and Economic Advisor; David Marshall, Senior Vice
President, financial markets group; Daniel Aaronson, Vice President,
microeconomic policy research; Jonas D. M. Fisher, Vice President,
macroeconomic policy research; Richard Heckinger, Vice President,
markets team; Anna L. Paulson, Vice President, finance team;
William A. Testa, Vice President, regional programs; Lisa Barrow,
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Han Y. Choi, Editors; Rita Molloy and Julia Baker, Production
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ISSN 0164-0682
4Q/2014, Economic Perspectives
Our analysis is based on the full set of micro-level
data on labor force participation collected in the U.S.
Bureau of Labor Statistics’ (BLS) Current Population
Survey (CPS)—often referred to as the household
survey—since 1982. These BLS data allow us to estimate statistical models that independently account for
the long-running patterns we have mentioned. In particular, microdata allow our statistical models to identify
life-cycle work patterns by very fine age groups and,
further, to account for how specific cohorts follow these
life-cycle patterns to varying degrees depending on when
they were born. This is useful because cohorts that have
high LFP early in their working careers tend to continue
to have high LFP later in their careers as well.4
There have been important changes over time in
these birth-cohort-specific LFP tendencies. On the one
hand, successive cohorts of men, especially those with
low levels of education, have had lower and lower LFP
tendencies. On the other hand, for several decades
successive cohorts of women tended to work more than
earlier cohorts. However, those born after roughly 1960
did not show much further increase in LFP and the latest
cohorts of women may even be showing some declines
relative to earlier cohorts—similar to the pattern that
has prevailed among men for several decades. Thus, as
the women born before 1960 have exited their prime
working years, their upward influence on women’s
LFP has largely disappeared.
Our models also allow LFP to vary by education
level, reflecting the well-known positive association
between educational attainment and LFP. During the
latter half of the twentieth century, substantial increases
in educational attainment were a factor in the longrunning increase in LFP. More recently, however,
educational improvement has slowed considerably,
implying there is less impetus for LFP to rise. Additionally, we control for other factors that might drive
participation decisions, including longer life spans,
changes over time in the prevalence of young children
(those under five years old), and factors such as the real
minimum wage and the adult-to-teen wage ratio that
might influence teen participation.
Finally, we allow LFP to vary with business cycle
conditions. LFP tends to be below trend when unemployment is high—as has been the case for several years—
and above trend when unemployment is low. Like Erceg
and Levin (2013), we see evidence that this association
is present with long lags. We also find that the strength
of the relationship between unemployment and LFP
varies with age, sex, and education levels. We exploit
state variation in unemployment rates to estimate models
that allow for long lags and demographic variation in
the association between LFP and the unemployment
Federal Reserve Bank of Chicago
rate. Properly controlling for unemployment has the
important effect of stabilizing our estimates of the
trend LFP rate. That is, we get almost the same trend
LFP rate whether we end the estimation in 2007 or
2014 and very similar estimates even if we stop the
estimation as early as 2002. Our findings contrast with
some other estimates of the long-run trend rate of LFP,
such as those provided by the BLS, which have changed
considerably over time.
That said, our estimates of the gap between the
actual and trend LFP rates depend on several particular
modeling assumptions. So it is worth emphasizing
that tweaks to the model naturally cause the results
to vary somewhat. Most notably, our preferred model,
whose results we highlight throughout this article,
allows for separate birth-cohort coefficients for four
age categories (16–24, 25–54, 55–79, and 80 and older5).
This model, which we call our “baseline,” implies
that the actual LFP rate as of the third quarter of 2014
is about 1.2 percentage points lower than the trend LFP
rate. If, instead, we force the cohort coefficients in the
model to be the same for ages 16–79 (as in the “pooled
model”), the LFP gap falls to around 0.2 percentage
points. We discuss these different models and other
robustness checks in detail later in the article.
Figure 1 shows the history of the actual LFP rate
data from the CPS (solid green line), along with our
baseline estimate of the long-run trend LFP rate (solid
red line) and the corresponding prediction of the LFP
rate given the recent history of state-level unemployment gaps6 (dashed red line). According to our estimates,
after rising for many years, the trend LFP rate began
to decline after 2000. Recently, according to our baseline
model, that decline has accelerated to about 0.3 percentage points per year—an annual rate of decline that our
model suggests will persist for the foreseeable future.
By 2020, our baseline model predicts the trend LFP
rate to be 62.3 percent, its lowest level since the mid1970s. The 2020 rate is even lower when we force the
cohort coefficients in the model to be the same for
ages 16–79 (as in our pooled model, whose results
are not shown in figure 1).
As of the third quarter of 2014, our baseline
estimate of the trend LFP rate is 64.2 percent, about
2 percentage points below our estimate of this trend
rate at the end of 2007. However, while the trend rate
fell by about 2 percentage points, the actual LFP rate
dropped even more, leaving it 1.2 percentage points
below the long-term trend. Additionally, until the third
quarter of 2013, the LFP rate had followed relatively
closely its predicted path based on prevailing labor
markets conditions. However, since then, the actual
LFP rate has dipped below even the rate predicted
101
FIGURE 1
Labor force participation (LFP) rates, 1982–2020
percent
68
67
66
65
64
63
62
61
1982
’84
’86
’88
’90
’92
’94
’96
’98
2000
’02
’04
’06
’08
’10
’12
’14
’16
’18
’20
LFP rate from CPS data
Estimate of long-run trend LFP rate
LFP rate prediction based on unemployment
Notes: The figure plots quarterly data for those aged 16 and older over the period 1982:Q1–2020:Q4. The long-run trend LFP rate is based
on data through 2007:Q4. The LFP rate prediction based on unemployment is the rate based on contemporaneous state unemployment
gaps (and their lags). See the text for further details. The shaded bars indicate recessions as defined by the National Bureau of Economic
Research.
Source: Authors’ calculations based on data from the U.S. Bureau of Labor Statistics, Current Population Survey.
with the high unemployment rates of the past several
years (see figure 1). This gap suggests there is an extra
margin of slack over and above what one would infer
from the unemployment rate alone.
Our results also have implications for the natural
rate of unemployment7 that may suggest greater labor
market slack. In particular, the decline in the trend LFP
rate that we find has not been uniform across different
populations. Certain groups, such as those under age 25,
have seen particularly large drops in LFP, while the LFP
of other groups, such as those over age 54, has actually
increased. In addition to these uneven LFP trends,
educational attainment, while not improving as rapidly
as in earlier decades, has steadily advanced. These trends
have led the labor force to be somewhat more heavily
weighted toward groups that tend to have low unemployment, such as older people and those with higher
levels of educational attainment. We estimate that on
their own, these developments would have lowered the
natural rate of unemployment by about 0.3 percentage
points since 2007 and 0.6 percentage points since 2000.
Recent estimates of the natural rate have focused on
developments such as the increase in long-term unemployment that some argue have raised the natural
rate. The demographic and educational effects on the
natural rate we document here are large enough to offset
102
most of those adverse influences, suggesting that the
natural rate may be lower than is often assumed.
Another implication of our results is that once
employment and output have returned to their longrun trends, they will grow more slowly than in the
past. All else being equal, an LFP rate that is declining by 0.3 percentage points per year translates into
0.5 percentage points less growth in hours worked
per year and thus, if productivity growth is unchanged,
0.5 percentage points less potential output growth per
year, compared with an economy with a flat LFP rate.
The slow fall in the natural rate of unemployment implied by our results offsets a small portion of those
effects. In combination with the U.S. Census Bureau’s
assumption about population growth, our results imply
that trend payroll employment growth8 will fall to
under 50,000 jobs per month later in the current decade.
However, that “normal” employment growth rate will
only become apparent in the data after a still sizable
employment gap (that is, the difference between the
actual and trend level of total payroll employment)
that opened up during 2008–09 is finally closed.
To understand why LFP has been running below
expectations, it is helpful to identify the groups for
which the LFP gap has been especially large. Much
of the surprise has occurred among adults without a
4Q/2014, Economic Perspectives
college degree (high school dropouts, in particular)—
whose actual LFP rates have dropped by even more
than our estimates of the trend rates. At the end of the
article, we speculate on possible reasons for these discrepancies and whether they might be resolved eventually or instead turn out to be signs that the model
might be missing important developments.
Finally, we should add a note of caution about
these LFP forecasts. The statistical models underlying
our estimates of the trend in LFP and other variables
mainly just extrapolate long-running trends. We do
not attempt to explain the decline in LFP at the level
of the underlying supply and demand for labor. Thus,
the trends we identify could be altered by policy changes
in such areas as disability insurance or education policy.
It is also possible that a continued drop in LFP might
elicit endogenous macroeconomic responses—for instance, more rapid wage growth—that might limit the
phenomenon in the future. Developing a deeper understanding of the drop in LFP might thus be a fruitful
area for future research.
In the next section, we briefly explain the key reasons behind long-running trends in LFP over roughly
the past 60 years. We then describe the data we use and
outline the methodology behind our estimate of the trend
LFP rate. Afterward, we present our results, beginning
with our aggregate estimates and then moving on to
decompositions that quantify the demographic (age and
sex), “behavioral” (for example, educational attainment,
fertility rate, and life expectancy), and business cycle
factors driving our findings; we follow this up with
a discussion on the robustness of our results. In the
final sections, we examine the impact of our LFP
results on the estimate of the natural rate of unemployment and describe our estimates of trend payroll
employment growth.
Background
The LFP rate began to steadily increase in the
mid-1960s, persistently expanding through the 1990s
and peaking at 67.3 percent in 2000. According to the
BLS, as of September 2014, however, the LFP rate is
62.7 percent—back toward the levels that were prevalent in the late 1970s.9
Many factors can be associated with the upsurge
in LFP from the mid-1960s through the late 1990s and
its subsequent drift back down since 2000. Perhaps
the upswing and certainly the more recent downward
pattern mirror the life-cycle work decisions of the large
baby boom cohort, born during the two decades following World War II. Like every birth cohort, the LFP
of baby boomers follows a distinct lifetime pattern.
Labor force participation is low for teenagers, rises
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as individuals finish school in their late teens and early
twenties, flattens out for those in their prime working
years when work decisions are particularly insensitive to wages and economic conditions, and then falls
for those in their late fifties and sixties as they enter
retirement (see the blue and red lines in figure 2).10
The baby boomers entered their prime working years
during the 1970s and 1980s; and because of their sheer
numbers, they caused an upsurge in aggregate LFP that
lasted for decades. However, starting around 2000, a
growing number of baby boomers reached their fifties
and started to transition out of the labor force. Today,
those same workers are now in their sixties and seventies,
when LFP is much lower. To help make this point, we
feature orange bars in figure 2 representing changes in
the share of the working-age population for different
age groupings over the years 2010–15.
To quantify the importance of population aging,
we compare in figure 3 the actual aggregate LFP rate
with the LFP rate implied by demographic change—
specifically, one that holds age-sex groups’ actual LFP
rates fixed at 2007 levels while allowing their population shares to vary according to the actual data and U.S.
Census population projections. Since 2007, the actual
aggregate LFP rate fell by 3.2 percentage points, while
the rate implied by demographic change fell by 1.8 percentage points. The difference means that changing
demographics alone explain only about half of the
decline in LFP since 2007.
As figure 3 makes clear, even within demographic
groups, there have been important changes in labor
force attachment over time. The dramatic increase in
the number of working women (red line in figure 4)
was clearly a driving force behind rising LFP rates
during the second half of the twentieth century. Only
one in three women were in the labor force in 1948,
but by the late 1990s, the female LFP rate was roughly
60 percent. However, by the end of the twentieth century, the female LFP rate had, more or less, leveled off.
The female LFP rate has even declined some since
the onset of the latest recession.11
By contrast, the male LFP rate has been on an
uninterrupted decline since the 1950s, falling from
86.7 percent in 1948 to 69.2 percent in 2014 (blue line
in figure 4). There is significant uncertainty about the
precise cause of this secular decline, but researchers
have linked it to stagnating overall real wage increases
or declining real wages for low-skill workers; changes
in safety net programs, in particular Social Security
Disability Insurance (DI) and Supplemental Security
Income (SSI); and increases in the labor force participation of women.12 Over the past decade, the disappearance of manufacturing and other “middle-skill,”
103
FIGURE 2
Labor force participation (LFP) rates, by age and sex, and working-age population change, by age
percent
100
percent change
1.5
80
1.0
60
0.5
40
0.0
20
−0.5
0
−1.5
16–19 20–24
25–29
30–34
35–39
40–44
45–49 50–54
age
55–59
60–64
65–69
70–74
75+
Male LFP rate (left-hand scale)
Female LFP rate (left-hand scale)
Change in working-age population share over period 2010–15 (right-hand scale)
Note: The LFP rates for males and females aged 16 and older (of working age) are for 2014:Q3.
Source: Authors’ calculations based on data from the U.S. Bureau of Labor Statistics, Current Population Survey.
FIGURE 3
Labor force participation (LFP) rate and LFP rate implied by demographic change, 1982–2020
percent
68
67
66
65
64
63
62
61
1982 ’84
’86
’88
’90
’92
’94
’96
’98
2000
’02
’04
’06
’08
’10
’12
’14
’16
’18
’20
LFP rate from CPS data
LFP rate implied by demographic change
Notes: The figure plots quarterly data for those aged 16 and older over the period 1982:Q1–2020:Q4. The LFP rate implied by demographic
change is the LFP rate that holds the actual LFP rates fixed at their 2007 levels for single age groups by sex while allowing group-specific
population shares to vary according to the actual data and U.S. Census population projections. The shaded bars indicate recessions as
defined by the National Bureau of Economic Research.
Source: Authors’ calculations based on data from the U.S. Bureau of Labor Statistics, Current Population Survey (CPS).
104
4Q/2014, Economic Perspectives
FIGURE 4
Labor force participation rate, by sex, 1948–2014
percent
90
80
70
60
50
40
30
1948 ’51
’54 ’57 ’60
’63 ’66
’69
’72
’75
’78
Male
’81
’84
’87 ’90
’93
’96
’99 2002 ’05
’08
’11
’14
Female
Note: The figure plots official quarterly data for those aged 16 and older over the period 1948:Q1–2014:Q3.
Source: U.S. Bureau of Labor Statistics, Current Population Survey, from Haver Analytics.
middle-income jobs may have contributed.13 Indeed,
the most recent recession and slow recovery have been
particularly difficult for men; the LFP rate for men
has fallen by 4.0 percentage points since December
2007—1.3 percentage points more than for women.14
Moreover, participation for many narrow age-sex
groups has been changing over time (see panels A
through F of figure 5). Because prime-working-age
participation rates (shown in panels C and D of figure 5)
echo the aggregate gender-specific trends (down for men,
but up and then flat or down somewhat for women),
we will focus on trends for teens and older individuals.
Teen participation has declined dramatically since
the late 1970s (panel A of figure 5), particularly during
the past decade (Aaronson, Park, and Sullivan, 2006).
One explanation is that teens are spending more time
in school, especially during downturns when the opportunity cost of schooling is low (Barrow and Davis, 2012).
In addition, Smith (2011) argues that the decline of
low-skill jobs and middle-skill, middle-income jobs
has pushed workers who used to fill those positions
into other jobs that have traditionally been performed
by teens. Increased immigration of low-skill workers
could have the same impact on teen jobs (Smith, 2012).
At the other end of the working life (panels E and F
of figure 5, p. 108), retirement is starting at later ages.
For example, relative to the first quarter of 2000, an
additional 6.0 percentage points of men aged 60–64 and
10.6 percentage points of women aged 60–64 are
working.15 Research suggests several factors have
Federal Reserve Bank of Chicago
contributed to people working longer. Improvements
in health technology may have boosted labor force
participation directly, by improving the health and
longevity of the work force, and indirectly, by requiring
individuals to work longer to accumulate the wealth
to support lengthier retirements. Changes to private
pensions and Social Security (Blau and Goodstein, 2010;
and French and Jones, 2012), as well as volatile retirement account balances and housing prices (French and
Benson, 2011), may have increased the need to postpone retirement, particularly early in the expansion
following the Great Recession, when household wealth
dipped, a pattern that may be reversing as net worth
recovers (Fujita, 2014). Note also that the increase in
LFP has been particularly strong among older women.
That might be a consequence of the rising participation
of women in the late twentieth century; cohorts that
worked more throughout their prime working years
carry that work behavior forward into older ages.
Accommodating the observed demand for elongating
careers, part-time “bridge” jobs have become a more
common way to transition slowly into retirement
(Ruhm, 1990; Schirle, 2008; and Casanova, 2013).
A final factor in our analysis that is not considered
in other LFP studies (for example, BLS studies such
as Toossi, 2004, 2005, 2007; Aaronson et al., 2006;
and Aaronson et al., 2014) is education. Rising rates
of return to skills during the 1980s and 1990s encouraged human capital investment (Katz and Murphy,
1992; and Katz and Autor, 1999), resulting in a shift
105
FIGURE 5
Labor force participation (LFP) rates, by age and sex, 1977–2014
A. LFP rates, ages 16–19
percent
65
60
55
50
45
40
35
30
1977
’81
’85
’89
’93
’97
2001
’05
’09
’13
’85
’89
’93
’97
2001
’05
’09
’13
B. LFP rates, ages 20–24
percent
90
85
80
75
70
65
60
1977
’81
Male
away from occupations that tend to have shorter average career lengths. During the prime working years,
the relationship between educational attainment and
work is unambiguously positive (see figure 6). For
instance, at age 40, the LFP rates for male high school
dropouts, high school graduates, and college graduates
are 84.7 percent, 87.8 percent, and 95.1 percent,
respectively (see figure 6, panel A). Moreover, individuals with less education tend to retire earlier. At age
62, the LFP rate for male high school dropouts, high
school graduates, and college graduates is 53.4 percent,
58.4 percent, and 73.8 percent, respectively. Any feature of the labor market that encourages human capital
investment will likely result in higher aggregate labor
force participation down the road.
106
Female
Methodology
To measure the trend LFP rate, we estimate a statistical model of LFP that is capable of simultaneously
considering various explanations based on demographic
(age and sex), “behavioral” (for example, educational
attainment, fertility rate, and life expectancy), and business cycle factors. First, we describe the data and then
the statistical methodology.
Data
Our LFP estimates are derived from the basic
files of the U.S. Bureau of Labor Statistics’ Current
Population Survey. The CPS—the source of such wellknown statistics as the unemployment rate and the labor
force participation rate from the BLS—is a monthly,
nationally representative survey of approximately
4Q/2014, Economic Perspectives
FIGURE 5 (continued)
Labor force participation (LFP) rates, by age and sex, 1977–2014
C. Male LFP rates, ages 25–54
percent
100
95
90
85
80
75
1977
’81
’85
’89
’93
’97
2001
’05
’09
’13
’89
’93
’97
2001
’05
’09
’13
D. Female LFP rates, ages 25–54
percent
80
75
70
65
60
55
50
1977
’81
’85
25–29
35–39
45–49
30–34
40–44
50–54
60,000 households conducted by the U.S. Census
Bureau. Participating households are surveyed for
four consecutive months, ignored for the next eight
months, and then surveyed again for four more straight
months. Important for our purposes is the fact that
basic demographic data, such as age, sex, and race,
as well as educational level and labor market status,
are collected in the CPS. In the subsequent analysis,
we use the microdata from January 1982 through
September 2014.16
While the CPS contains information on many
of the key determinants of labor force participation,
we supplement our analysis with additional data to
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create controls used in the estimation of our statistical
models.17 Our additional controls are as follows:
■ The natural rate of unemployment, or the nonaccelerating inflation rate of unemployment (NAIRU).
We use the Congressional Budget Office’s (CBO)
calculation of the short-run NAIRU.18
■ State unemployment rate. Since the state unem-
ployment rates tabulated from the CPS data can
be quite noisy, especially for small states, we use
the state-level unemployment statistics published
by the BLS. The BLS series is estimated using the
CPS but augmented with data on unemployment
insurance claims and payroll employment counts.19
107
FIGURE 5 (continued)
Labor force participation (LFP) rates, by sex and age, 1977–2014
E. LFP rates, ages 55–64
percent
90
80
70
60
50
40
30
1977
’81
’85
’89
’93
’97
Male, ages 55–59
Female, ages 55–59
2001
’05
’09
’13
’09
’13
Male, ages 60–64
Female, ages 60–64
F. LFP rates, ages 65 and older
percent
40
30
20
10
0
1977
’81
’85
’89
’93
Male, ages 65–69
Female, ages 65–69
’97
2001
’05
Male, ages 70 and older
Female, ages 70 and older
Note: Each panel plots official quarterly data over the period 1977:Q1–2014:Q3.
Source: U.S. Bureau of Labor Statistics, Current Population Survey, from Haver Analytics.
■ Minimum wage. State minimum wage data are
taken from the January issues of the BLS’s Monthly
Labor Review supplemented with minimum wage
histories reported at the U.S. Department of Labor
website.20 The minimum wage data are deflated
using the BLS’s Consumer Price Index for All
Urban Consumers (CPI-U).
■ Life expectancy. Life expectancy, by sex and age,
is taken from the Social Security Administration
108
life tables (as in Bell and Miller, 2005) for the
years 1980–2020. Missing years are linearly
interpolated.
LFP model for ages 16–79
Our baseline logistic regression model associates
the probability that an individual aged 16–79 is in the
labor force with that individual’s sex, age, year of birth,
race, and education level, as well as the economic
4Q/2014, Economic Perspectives
FIGURE 6
Labor force participation (LFP) rates, by sex and education level, in 2014:Q3
A. Male LFP rates
percent
100
80
60
40
20
0
25
30
35
40
45
50
35
40
45
50
age
55
60
65
70
75
80
55
60
65
70
75
80
B. Female LFP rates
percent
100
80
60
40
20
0
25
30
age
High school dropout
College graduate
High school graduate
Postcollege degree
Some college
Source: Authors’ calculations based on data from the U.S. Bureau of Labor Statistics, Current Population Survey.
conditions facing that individual and a few covariates
specific to his or her age group:
The determinants of LFP (the right-hand side of
the equation) include the key characteristics that drive
the decision to work. For each sex-education-level group,
psebai
a series of indicators for every single year of age, αsea,
log
= α sea + βseb + w( a +b )i λ se + xsebai γ se + zseba δ se ,
1−
p
accounts for the typical lifetime pattern of labor force
sebai
participation (see figure 6). A second series of indicawhere psebai is the probability individual i of sex s and
tors βseb are a full set of year-of-birth indicators for each
education level e born in year b is in the labor force at
sex-education-level group. According to the model,
every birth cohort follows the same basic life-cycle
psebai
age a. The left-hand side, log
, is the log
pattern implied by αsea but at a uniformly higher or
1− psebai
lower
level in terms of the log odds. This adjustment
odds of being in the labor force.
Federal Reserve Bank of Chicago
109
FIGURE 7
Log odds of labor force participation (LFP) of unmarried white female high school dropouts
aged 25–54 without a young child
log odds
0.6
0.5
0.4
0.3
0.2
0.1
0
25
27
29
31
33
35
37
39
age
41
43
45
1955 cohort
1960 cohort prediction
1960 cohort
1965 cohort prediction
47
49
51
53
1965 cohort
Notes: The figure plots the log odds of LFP of unmarried white female high school dropouts aged 25–54 without a young child (under five
years old) based on model estimates using quarterly data through 2007:Q4. The dashed lines represent projections.
Source: Authors’ calculations based on data from the U.S. Bureau of Labor Statistics, Current Population Survey.
might reflect opportunities, preferences, and norms
that are specific to particular birth cohorts.
To see the intuition underlying the cohort method
for forecasting LFP, consider, for example, the problem
of forecasting in 2007 the future participation of women
who were then 42. We can compare the LFP rates at
ages 25–42 of these women, who were born in 1965,
against those of earlier birth cohorts at the same ages.
The cohort method assumes that the average difference
in LFP rates of these women and those of earlier cohorts
will persist beyond age 42, allowing us to forecast their
labor force participation for the remainder of their lives.
The idea is illustrated in figure 7 for one particular
demographic group. This figure plots the predicted
p
log odds log sebai
1− psebai
of being in the labor force
at ages 25–54 for unmarried white women without
young children (under five years old) and without a
high school diploma, born in 1955, 1960, and 1965,
based on estimates using data through 2007. Note first
that the age-to-age patterns for each line have a nearly
identical shape. The only difference is that the lines are
shifted up or down, with the size of that shift determined
by our estimate of the cohort effect, βseb. Through 2007,
110
the cohort born in 1965 has been more likely to work
at the same ages than the cohort born in 1960, which
has been more likely to work than the cohort born in
1955, again at the same ages. By 2007, those in the
1965 cohort are only 42 years old. To forecast their
LFP for the remainder of their careers, we assume the
cohort difference up to age 42 will persist into older
ages but the pattern over the remaining life cycle will
look like that of past cohorts. This allows us to trace
out their future participation (in a dashed line) for
ages that we have yet to observe.
The cohort-based approach has an advantage over
an alternative strategy (used most prominently by the
BLS, as in Toossi [2004, 2005, 2007]) that bases the
forecast on an extrapolation of the time series of the
trend LFP rate for each age-sex group (using the last
13 years of data). A drawback of the BLS methodology
is that it mixes different cohorts of women together,
which could be problematic during periods when the
level of trend LFP might be changing. That has been
the case for much of the past few decades.
An individual’s labor force participation decision
will also be affected by the state of the economy and
labor market conditions, w(a+b)i. Statistical models of
this sort (for example, Aaronson and Sullivan, 2001;
and Aaronson et al., 2006) have typically relied on the
4Q/2014, Economic Perspectives
contemporaneous gap between the actual unemployment rate and trend unemployment rate (that is, the
natural rate of unemployment) to measure the state of
the economy. However, this might misstate the role of
the labor market for at least three reasons. First, Erceg
and Levin (2013) provide evidence that LFP responds
to unemployment with long lags. Consequently, we also
account for the unemployment gap over the past three
years—specifically, the average of this gap over the
past zero to three quarters, four to seven quarters,
and eight to 11 quarters. Like Erceg and Levin (2013),
we find that there are substantial lags in the effects
of unemployment rates on labor force participation.
Second, labor market conditions vary substantially
on a geographic basis, with some parts of the country
experiencing more distress than others at a given date.
Thus, our baseline model utilizes a state-level unemployment gap to account for more geographically
detailed labor market conditions. Third, indicators other
than the unemployment rate may be necessary to characterize the tightness of the labor market. Once we
account for lagged state-level unemployment gaps,
we find that the unemployment rate does an adequate
job in characterizing labor market conditions. However,
later on, we explore the robustness of our LFP results
to the use of other measures, such as the national
median length of unemployment.21
Finally, we introduce additional conditioning
variables that are common to all demographic groups,
xsebai , and specific to certain age groups, zseba. The main
covariate common to all demographic groups is indicators for race. For 16–24 year olds, we also control
for the real minimum wage and the hourly wage ratio
of 16–24 year olds (youths) to 25–54 year olds (adults).22
A higher minimum wage acts to encourage labor force
participation, but perhaps to reduce the employment
of teens (Neumark and Wascher, 2008, and references
therein). Similarly, the overall ratio of teen to adult
wages influences the market for teen employment
(Aaronson, Park, and Sullivan, 2006; and Smith, 2011).
For 25–54 year olds, we augment the model to include
indicators for being married with a young child (under
five years old), being married with no young child, and
being unmarried with a young child (the omitted category is being unmarried with no young child). The
impact of childbearing, particularly among women, can
be seen in the dip in the LFP rate in the late twenties
and early thirties for women (Leibowitz and Klerman,
1995; and Blau, 1998). Finally, we include measures
of gender-specific life expectancy for 55–79 year olds
to account for the delay in retirement caused by longer
life expectancy.23
Federal Reserve Bank of Chicago
For flexibility, the baseline model is estimated
separately by combinations of age, sex, and education
level groups. Specifically, we break up the sample into
28 combinations of age (16–24, 25–54, and 55–79),
sex, and educational attainment (high school dropout,
high school graduate, some college, college graduate,
and postcollege degree).24 This allows the cohort effects
and coefficients on other controls to flexibly vary across
these groups. In particular, note that in the baseline,
for each sex-education-level group, the parameters λse
and γse also vary by the three age groups.25 Later, we
describe how the results change when we estimate the
model forcing the cohort coefficients, βseb , to be the
same for the different age ranges.
LFP model for ages 80 and older
A key feature of the baseline model for 16–79 year
olds is the capacity to differentiate age and cohort
effects. Unfortunately, this is not possible for individuals aged 80 and older because the CPS does not distinguish age beyond 80 in some years. Therefore, for
those aged 80 and older, we replace age and cohort
effects with a linear time trend:26
p
log seti = t θse + wti λ se + xseti γ se + zset δ se ,
1−
p
seti
where t indexes calendar time.27
The age group that is 80 and older is a very small
share of the work force (about 4.5 percent of the working-age population and 0.43 percent of the employed
in 2014).28 Therefore, when we combine our LFP
estimates of the 16–79 and 80-and-older populations,
the resulting LFP rate for those aged 16 and older is
not sensitive to the precise specification of the worker
model for those aged 80 and older.
Estimation of the trend LFP rate
The models are estimated using the CPS for the
years 1982–2007. The additional exogenous variables
are included at the quarterly frequency.29 The trend rate
is computed as the predicted LFP rate free of any variation due to the business cycle. In particular, we apply
the coefficient estimates from the logit models we have
just described to the data in order to predict age-, sex-,
and education-level-specific group trend LFP rates
∧
Psea assuming that the economy is at its current estimate of the natural rate of unemployment (that is, the
current and lagged unemployment gaps w( a +b )i = 0).
The aggregate trend LFP rate is then the sum of the
weighted group-specific trend LFP rates, where weights
are allowed to vary over time based on a group’s share
of the overall population in that year. From the model,
111
we can also compute a predicted LFP rate based on
contemporaneous and lagged state unemployment
gaps. This measure, which we label the “LFP rate
prediction based on unemployment” (see figure 1,
p. 102), reveals whether the actual LFP rate is unusually
high or low given the present labor market situation
as summarized by the history of unemployment gaps.
In this way, it serves as another key benchmark.
Forecast of the trend LFP rate
There are two additional issues in forecasting the
trend LFP rate beyond 2007.
First, some birth cohorts had not reached one or
more of our age groups by 2007. For example, no one
born in 1995 was of legal age to work by 2007, implying
that we cannot estimate a cohort effect for that birth
year. Similarly, because our models are estimated
separately for 25–54 year olds and 55–79 year olds,
using data only through 2007, we have no estimated
cohort effect for those born in, say, 1960 to determine
their participation when they reach age 55 in 2015.
To overcome the lack of estimates for some birth
cohorts, we forecast their cohort coefficients using a
linear time trend over the last ten birth year coefficients.
In other words, we project that cohort effects will slowly
evolve in the future in the same way that they have
over the previous decade. We do this separately for
each sex, education level, and age group combination.
The idea is illustrated in figure 8, panels A, B, and
C. The three panels plot the coefficients on the cohort
dummies βseb for unmarried white women aged 25–54
without a child under five years old, by education level
(high school dropout, high school graduate, and college
graduate). The dashed lines at the end are the projections.
In addition to age and birth cohort dummies, our
model also includes other time-varying (or age-varying)
covariates (for example, family structures during prime
working age or life expectancy at older ages). Therefore, the coefficients on the birth year dummies alone
do not present a full cohort profile, but rather a profile
conditional on specific values of the covariates. For
example, the coefficients plotted in panels A, B, and C
of figure 8 show the average differences across birth
cohorts in (the log odds of) labor force participation for
prime-working-age white women who are unmarried
and have no young child, by educational attainment.
Thus, the figure illustrates the evolution of cohort
effects over time for this particular demographic
group of women.30
Starting with those born in the late 1920s and
continuing unabated for about four decades, newer
birth cohorts were more likely to participate in the
labor force during their prime working years, regardless
112
of education level. This pattern reflects the dramatic increase in female labor force participation over the
twentieth century (see figure 4, p. 105). However, for
this group of women with at least a high school diploma (figure 8, panels B and C), that upward pattern reversed by the late 1960s. Cohorts with the same
educational background born during the 1970s and early
to mid-1980s were less likely to work than those born
a decade or two earlier. Ultimately, this contributed to
the flattening out of the female LFP rate by the mid-1990s
and 2000s, offsetting the positive impact of higher
female educational attainment on LFP throughout this
period. By contrast, for women without a high school
diploma, prime-working-age labor force participation
has continued to slowly rise into the 1980s birth cohorts.31
Also of note, we do not attempt to estimate timevarying age effects (or other regression coefficients)
in the forecasted trend. Instead, we simply apply the
estimates obtained from the 1982–2007 sample to the
simulated populations defined by age, education level,
race, and sex (as well as by marital status and the
presence of young children for certain age groups).32
A second issue in making forecasts of LFP arises
from the U.S. Census Bureau’s forecast of the population. To forecast the trend LFP rate, we construct simulated populations for the rest of our forecast horizon
using the civilian noninstitutional population projections by age, sex, and race prepared by the U.S. Census
Bureau. But these projections are not broken down by
education level. As a solution, we use a statistical
model (see box 1) to predict educational attainment for
age-sex-race groups, and then apply the LFP model to
project the fraction of the people in these population
groups that will be in the labor force.
The LFP model includes other age-group-specific
demographic controls, such as marital status and the
presence of young children for 25–54 year olds, which
are, like education level, unavailable in the U.S. Census
Bureau’s population projections. Rather than build a
model for these additional controls, we simply estimate
the distribution of marital status and presence of young
children within each age-sex-race group from the 2014
CPS and assume this distribution persists for the remainder of our forecast horizon. We similarly assume
the unemployment gap, minimum wage, and youthto-adult wage ratio return to their averages. We also
assume life expectancy follows projections made by
the Social Security Administration.33
These procedures are updates and extensions of
Aaronson and Sullivan (2001). Aaronson et al. (2006)
and Aaronson et al. (2014) follow a similar methodology.
Compared with the methodology of these two papers,
the main differences are as follows: 1) We estimate the
4Q/2014, Economic Perspectives
FIGURE 8
Birth year coefficients for unmarried white females aged 25–54 without a young child, by education level
A. High school dropout
log odds
0.8
0.6
0.4
0.2
0.0
−0.2
−0.4
−0.6
−0.8
1927
’31
’35
’39
’43
’47
’51
’55
’59
’63
birth cohort
’67
’71
’75
’79
’83
’87
’91
’95
’39
’43
’47
’51
’55
’59
’63
birth cohort
’67
’71
’75
’79
’83
’87
’91
’95
’39
’43
’47
’51
’55
’59
’63
birth cohort
’67
’71
’75
’79
’83
’87
’91
’95
B. High school graduate
log odds
0.8
0.6
0.4
0.2
0.0
−0.2
−0.4
−0.6
−0.8
1927
’31
’35
C. College graduate
log odds
0.8
0.6
0.4
0.2
0.0
−0.2
−0.4
−0.6
−0.8
−1.0
1927
’31
’35
Notes: The coefficients plotted in panels A, B, and C show the average differences across birth cohorts in (the log odds of) labor force
participation for unmarried white females aged 25–54 without a young child (under five years old), by education level. See the text for
further details. The solid lines represent cohorts that are fully seen in the age range 25–54, while the dashed lines represent projections.
Source: Authors’ calculations based on data from the U.S. Bureau of Labor Statistics, Current Population Survey.
Federal Reserve Bank of Chicago
113
model at the individual level rather than at the age-sex
group level; 2) we estimate the model conditioning
on completed schooling, thus allowing demographics
to affect LFP differently by education level; 3) we use
the state unemployment gap to control for business
cycle conditions at more geographically detailed labor
markets; and 4) we allow the dynamic cyclical relationship between LFP and unemployment to vary by education level and demographics. These differences are
detailed in the preceding discussion.
Results
In this section, we discuss the results from our
LFP models. We go over the baseline aggregate results
first. Then we analyze the sources of changes in the
trend LFP rate by examining the LFP of specific demographic groups; while doing so, we distinguish between
shifts in the share of particular age groups and changes
in certain groups’ LFP behavior. Next, we study the
gap between the actual LFP rate and our estimated trend
LFP rate, first by educational attainment and then by
age. Finally, we discuss the robustness of our results.
Baseline aggregate results
As previously noted, figure 1 (p. 102) plots our
measure of the LFP rate from CPS data (solid green line)
against our baseline estimate of the long-run trend LFP
rate (solid red line) between 1982 and 2020. Starting
in the early 1980s, the trend rate of labor force participation rose uninterrupted through 2000. Since 2000,
it has been falling—and at a steeper pace than that of
the ascent. Consequently, as of the third quarter of 2014,
our baseline model estimates the trend LFP rate to be
64.2 percent, almost 1 percentage point below its estimated level in the first quarter of 1982.
By construction, the trend LFP rate removes the
effects of the business cycle by setting the unemployment gap to zero. As such, the gap between the actual
and trend LFP rates is typically positive in periods
such as the late 1990s, when the economy is growing
rapidly, wage growth is strong, and more individuals
are, therefore, willing to work than we might expect
given the composition of the working-age population.
By contrast, a negative LFP gap appears during recessions and weak recoveries. Indeed, we estimate that the
negative LFP gap in 1982 was large (about –1.1 percentage points) and took much of the 1980s expansion
to eliminate.
Similarly, during the most recent business cycle,
the LFP gap was positive at the end of the last expansion in 2007. But the actual LFP rate fell more rapidly
than the (declining) trend LFP rate, causing the LFP
gap to turn negative during 2009, where it has remained
since. As of the third quarter of 2014—over five years
114
BOX 1
Educational attainment models
The U.S. Census Bureau’s population data that
we use to compute population weights in order
to forecast the trend LFP rate are only available
by sex, race, and age. Therefore, we follow the
statistical model described in Aaronson and
Sullivan (2001) to predict educational attainment.
Let pitj = Prob { yit = j | j = 1, …, 5} be the
probability that individual i in year t has education
level j, where j = 1 is high school dropout, j = 2
is high school graduate, j = 3 is some college,
j = 4 is college graduate, and j = 5 is postcollege
degree, and let qitj = Prob { yit ≥ j | yit ≥ j − 1} ,
j = 2, …, 5 be the probability that an individual
reaches at least level j given that he reached level
j – 1. We fit a statistical model to predict the qitj
and recover pitj from pitj = Π kj= 2 qitk (1 − qitj +1 ) .
The q itj is predicted based on a logistic
regression model similar to the LFP models:
qe
log sbaie = α esa + βesb + w( a +b )i λ es + xsbai γ es ,
1− qsbai
where the right-hand-side variables include indicators for age α esa , birth year βesb , and race xsbai ,
as well as business cycle controls w(a+b)i .1 The
model is estimated separately by sex and race.2
In all models, we also include an indicator variable for
post-1992. This is because there was a redesign of the education question in the CPS in 1992, which causes a discrete
change in some of the education categories. The parameters λ es and γ es are the regression coefficients on the w and
x variables, respectively.
1
The model for postcollege degree includes race as a control and generates estimates separately by sex only. Note
that we impose different minimum age restrictions for each
education-level-specific model to acknowledge that higher
education levels begin at later ages. In particular, the high
school graduate model includes only those aged 17 and
older. Likewise, the some college, college graduate, and
postcollege degree models include only those aged 19 and
older, 21 and older, and 25 and older, respectively.
2
after the official end of the 2008–09 recession according to the National Bureau of Economic Research—
the participation rate remains 1.2 percentage points
below the long-run trend. This is much larger than
our estimate of the LFP gap in 1988, just over five
years after the end of the 1981–82 recession.
We project that the trend LFP rate will continue
to fall by about 0.3 percentage points annually through
at least 2020, at which point it will be 62.3 percent.
The last time the actual LFP rate was that low was in
the mid-1970s.
4Q/2014, Economic Perspectives
The dashed red line in figure 1 plots a prediction
of the LFP rate that uses the contemporaneous state
unemployment gaps (and their lags). This measure,
which we label the “LFP rate prediction based on unemployment,” reveals whether the actual LFP rate is
unusually high or low given the present labor market
situation. For example, during the late 1990s, the actual
LFP rate was running above not only our estimate of
the trend rate but also what we would have expected
given the tight labor markets at the time. During the
most recent recession and the ensuing expansion up
through late 2013, the predicted LFP rate that accounts
for contemporaneous economic conditions fell about
the same as the actual LFP rate data (see figure 1).
But since the fourth quarter of 2013, the actual LFP rate
has fallen sharply, while our LFP rate prediction based
on unemployment has not.34 As of the third quarter of
2014, the actual LFP rate is 0.8 percentage points below
where we would have expected given the unemployment
rates that have prevailed over the past few years, suggesting there is significant slack in the labor market
beyond that signaled by the unemployment rate.
A decomposition of the trend LFP rate
Next, we unpack the sources of changes in the
trend LFP rate over the past 30 years into two parts:
that due to changing demographics, in particular age
and sex (which we call “demographic”), and that due
to changing participation decisions within a given demographic group (which we call “behavioral”). The
latter includes changes in some observed characteristics,
such as education level, fertility rate, and life expectancy,
as well as changes in unobservables captured by the
cohort dummies.
In particular, let pt be the overall trend LFP rate at
time t, pdt be the trend LFP rate for demographic group
d at time t, and fdt be the share of the population in group
d at time t. We can write the aggregate trend LFP rate as
the weighted average of group-specific trend LFP rates,
pt = Σ d f dt pdt ,
and the change in the aggregate trend LFP rate as the
sum35
∆pt = Σ d ( pdt −1 − pt −1 ) ∆f dt + Σ d f dt ∆pdt .
The first term on the right-hand side reflects the
contribution from changing demographics (Δfdt ). An
important recent example of Δfdt is the changing share
of workers in their sixties. Since the standard life-cycle
pattern suggests that those in their sixties work less
than the aggregate working-age population (that is,
Federal Reserve Bank of Chicago
pdt−1 − pt−1 < 0), the aggregate trend LFP rate declines
(that is, Δpt < 0) when the population share in their
sixties increases and the trend rate rises when the
population share in their sixties declines. The second
term reflects the contribution from changing behavior
for a given demographic group (Δpdt ). If those in their
sixties are working longer today than in the past (that
is, Δpdt > 0 ), the aggregate trend LFP rate will rise (that
is, Δpt > 0). Table 1 reports the results of this decomposition of the aggregate trend LFP rate (based on the
baseline estimates), split further by age for the demographic contribution and by gender and age for the
behavioral contribution.
The top row in panel A of table 1 shows the annualized change in the aggregate trend LFP rate, reported
over different subperiods (1982–97, 1997–2007,
2007–14, and 2014–20). The 1980s and 1990s were an
era of rising LFP, and this is reflected in the increases
of 0.11 percentage points per year in our trend LFP
rate during 1982–97. Changing demographics (table 1,
panel A, second row) explain a small part of this gain.
Behavioral changes (table 1, panel A, third row), especially among prime-working-age women, play a more
important role. In particular, rising LFP among women
on account of behavioral factors contributed 0.17 percentage points per year to the change in the aggregate trend
LFP rate over the 1982–97 period (table 1, panel C, sixth
row). However, men’s falling LFP throughout the 1980s
and 1990s (table 1, panel C, second row) offset about
half of these positive developments.
The tide began to turn around the turn of the century. After decades of increasing LFP, the trend LFP rate
declined by 0.08 percentage points per year between
1997 and 2007 (table 1, panel A, first row). We attribute most of this decline to demographics (table 1,
panel A, second row), as the oldest baby boomers hit
their late fifties and began to exit the labor force (see
also table 1, panel B, fourth row). While behavioral
changes were virtually a neutral contributor (table 1,
panel A, third row), that masks several continuing stories:
increases in prime-working-age and older female participation (table 1, panel C, eighth and ninth rows) offsetting declines in prime-working-age male participation
(table 1, panel C, fourth row) and in youth participation
among both men and women (table 1, panel C, third
and seventh rows). Falling youth LFP for both genders
on account of behavioral factors contributed a total of
–0.09 percentage points per year to the change in the
aggregate trend LFP rate during 1997–2007.
Since around 2007, both the behavioral and demographic patterns have intensified, with the trend LFP
rate falling by roughly 0.3 percentage points per year
(table 1, panel A, first row). Demographic factors,
115
TABLE 1
Decomposition of the trend labor force participation percentage change per year
over subperiods of 1982–2020
1982 – 97
1997– 2007
2007–14
2014 –20
– 0.08
– 0.07
– 0.01
– 0.33
– 0.29
– 0.05
– 0.27
– 0.22
– 0.04
A. Decomposition of the trend percentage change per year
Total change
Demographic
Behavioral
0.11
0.03
0.09
B. Decomposition of demographic contribution to trend percentage change per year, by age
Total demographic
Age 16–24
Age 25–54
Age 55 and older
0.03
– 0.02
0.07
– 0.02
– 0.07
0.00
– 0.06
– 0.02
– 0.29
0.03
– 0.12
– 0.20
– 0.22
0.01
– 0.04
– 0.19
C. Decomposition of behavioral contribution to trend percentage change per year, by sex and age
Total behavioral
Male
Age 16–24
Age 25–54
Age 55 and older
Female
Age 16–24
Age 25–54
Age 55 and older
0.09
– 0.08
– 0.03
– 0.04
– 0.01
0.17
0.01
0.12
0.04
– 0.01
– 0.06
– 0.05
– 0.05
0.04
0.05
– 0.04
0.02
0.08
– 0.05
– 0.07
– 0.07
– 0.05
0.05
0.03
– 0.06
0.00
0.08
– 0.04
– 0.03
– 0.04
– 0.03
0.04
– 0.02
– 0.04
– 0.04
0.06
Notes: The estimated values shown are the annualized percentage changes in the trend rate of labor force participation based on
data through 2007. The columns in each panel may not total because of rounding. See the text for details on demographic and
behavioral contributions.
Source: Authors’ calculations based on data from the U.S. Bureau of Labor Statistics, Current Population Survey.
especially the baby boomers reaching their fifties and
sixties, explain about 90 percent of this decline; but
behavioral factors are important as well (table 1,
panel A, second and third rows). Continuing declines
in prime-working-age male LFP and youth LFP (table 1,
panel C, fourth and third and seventh rows) put downward pressure on the aggregate LFP rate, without the
offsetting positive influences from prime-working-age
female LFP (table 1, panel C, eighth row) that drove
much of the gains in the late twentieth century. Older
men and women are working more than in the past;
but to date, the magnitude has been too small to offset
other behavioral patterns (table 1, panel C, fifth and
ninth rows).
Over the remainder of the decade, we expect many
of these trends to continue. The trend LFP rate will
continue to fall by nearly 0.3 percentage points per year.
Demographics will still account for most (80 percent)
of the decline, as baby boomers reach their seventies.
In fact, the increase in the population share of those
aged 70 and older alone will account for roughly half
of the decline in the aggregate trend LFP rate (not shown
in table 1). This occurs notwithstanding our expectation that the baby boomers will be working far longer
than any past generation.
116
While evolving demographics (particularly those
related to the large baby boom generation approaching
or entering retirement) have been the focus in much of
the recent discussion on the decline in LFP, we want to
emphasize that long-running secular changes in work
participation decisions within demographic groups have
been an important part of the story as well. To show
this more clearly, we plot in figure 9 a trend LFP rate
that holds the age-sex groups’ population shares fixed
at their 2007 levels but allows the group-specific trend
LFP rates to vary over time as predicted by our model.
This demographically adjusted hypothetical trend LFP
rate is still moving down between 2007 and 2013, highlighting that there are factors besides an aging population at play. Next, we turn to some of these specific
patterns in more detail.
LFP gap by education level
Figure 10 plots the actual and trend LFP rates for
those aged 25 and older by education level.36 Between
the late 1990s and 2007, the actual and trend LFP rates
moved steadily down for those with at least a high school
diploma. The LFP of high school dropouts was the
exception (figure 10, panel A).37 However, since 2007,
the actual LFP rate of high school dropouts has stopped
4Q/2014, Economic Perspectives
FIGURE 9
Demographically adjusted trend labor force participation (LFP) rate, 1982–2020
percent
67
66
65
64
63
1982 ’84
’86
’88
’90
’92
’94
’96
’98
2000
’02
’04
’06
’08
’10
’12
’14
’16
’18
’20
Note: The figure plots a trend LFP rate that holds the population shares fixed at their 2007 levels by single age and sex while allowing
the group-specific trend LFP rates to vary over the period 1982:Q1–2020:Q4.
Source: Authors’ calculations based on data from the U.S. Bureau of Labor Statistics, Current Population Survey.
increasing and has even fallen a little, opening up a
large gap between itself and our estimated trend LFP
rate. As of the third quarter of 2014, the actual high
school dropout LFP rate is about 2.5 percentage points
below where we would expect given other demographic
characteristics and a neutral labor market. Since 2007,
the actual LFP rates have fallen for groups with higher
educational attainment as well. However, these declines
were better anticipated by long-running demographic
patterns within these groups. For example, as of the third
quarter of 2014, the LFP gap is about –1.1 percentage
points for high school graduates (figure 10, panel B)
and essentially zero (+0.2 percentage points) for college
graduates (figure 10, panel D). Indeed, for the latter
group, a significant LFP gap never materialized throughout the recent recession and slow recovery.
A similar pattern emerges when we measure the
gap between the actual LFP rate and our LFP rate
prediction based on unemployment (whose aggregate
measure is featured in figure 1 on p. 102 but which is
not shown in figure 10). This predicted measure takes
into account the high unemployment in recent years.
As of the third quarter of 2014, the LFP gap between
the actual rate and this predicted rate based on unemployment is –1.4 percentage points for high school
dropouts and –0.7 percentage points for high school
graduates but +0.3 percentage points for college graduates. That is, given the recent labor market conditions
and demographic characteristics, a surprising share of
workers without a college degree have dropped out of
the labor force since 2007.
Federal Reserve Bank of Chicago
Why an LFP gap has opened up for workers without a college degree is of significant policy interest.
One interpretation is that it reflects an extra measure
of labor market slack not reflected in unemployment
rates. However, it is also possible that some of the gap
may reflect new but potentially long-running phenomena
not captured by our model. For example, middle-incomepaying jobs, often in manufacturing, that in the past
could have been filled by less educated workers are
disappearing (Acemoglu and Autor, 2011, and the
references therein). Workers who traditionally have
filled those occupations are being forced to adapt by
taking on jobs that have traditionally been filled by
low-skill workers, such as teens. That, in turn, has put
significant wage pressures on the low-skill labor market,
potentially pushing many to leave the labor force
altogether. The 2000s housing boom may have temporarily stopped the slide of real wage rates of loweducation workers (Charles, Hurst, and Notowidigdo,
2014a, 2014b), and thus temporarily held up the actual
LFP rate, as well as our estimated trend rate, for loweducation workers; but eventually, the housing collapse
led to both wage and LFP rate declines.
Once a worker experiences a long spell of unemployment, it can be difficult to overcome. Employers
may use length of unemployment as a signal of quality,
and shun those who are unemployed beyond short-term
spells (Blanchard and Diamond, 1994). A recent experiment reported in Kroft, Lange, and Notowidigdo (2013)
indicates that callback rates are lower for those with
117
FIGURE 10
Labor force participation rates for those aged 25 and older, by education level, 1982–2020
A. High school dropout
percent
51
49
47
45
43
41
39
37
35
1982 ’84
’86
’88
’90
’92
’94
’96
’98
2000
’02
’04
’06
’08
’10
’12
’14
’16
’18
’20
’88
’90
’92
’94
’96
’98
2000
’02
’04
’06
’08
’10
’12
’14
’16
’18
’20
’88
’90
’92
’94
’96
’98
2000
’02
’04
’06
’08
’10
’12
’14
’16
’18
’20
B. High school graduate
percent
71
69
67
65
63
61
59
57
55
1982 ’84
’86
C. Some college
percent
78
76
74
72
70
68
66
64
62
1982 ’84
’86
Actual rate
118
Trend rate
4Q/2014, Economic Perspectives
FIGURE 10 (continued)
Labor force participation rates for those aged 25 and older, by education level, 1982–2020
D. College graduate
percent
87
85
83
81
79
77
75
73
71
1982 ’84
’86
’88
’90
’92
’94
’96
’98
2000
’02
’04
’06
’08
’10
’12
’14
’16
’18
’20
’90
’92
’94
’96
’98
2000
’02
’04
’06
’08
’10
’12
’14
’16
’18
’20
E. Postcollege degree
percent
87
85
83
81
79
77
75
73
71
1982 ’84
’86
’88
Actual rate
Trend rate
Notes: Each panel plots quarterly data for those aged 25 and older over the period 1982:Q1–2020:Q4. The shaded bars indicate recessions
as defined by the National Bureau of Economic Research.
Source: Authors’ calculations based on data from the U.S. Bureau of Labor Statistics, Current Population Survey.
longer ongoing unemployment spells, conditional on
other aspects of a resume that employers value.
It is also possible that the decline in LFP among
low-education workers is related to social safety net
programs—in particular, the Social Security Disability
Insurance program. DI rolls have been increasing
throughout the most recent business cycle, continuing
a pattern that has been more or less uninterrupted since
the 1990s (Autor, 2011; and Burkhauser and Daly, 2011).
DI tends to be countercyclical partly because eligibility
standards ease amid deteriorating labor market conditions (Mueller, Rothstein, and von Wachter, 2013). That
is, people with moderate disabilities are more likely
Federal Reserve Bank of Chicago
to qualify for the program when there are fewer suitable jobs available.
Finally, the expected upward trend in LFP of
those without high school diplomas may have been
driven by the welfare reforms of the 1990s, when
policy induced more low-education women to work.
That policy intervention may have been interpreted
by the model as a trend that would continue rather
than as a one-time change to the level of LFP.
LFP gap by age
Figure 11 plots the actual and trend LFP rates by
age. A sizable gap between the actual LFP rate and
our estimated trend LFP rate opened up among 16–24
119
FIGURE 11
Labor force participation rates, by age, 1982–2020
A. 16–24
percent
70
66
62
58
54
50
1982
’84
’86
’88
’90
’92
’94
’96
’98
2000
’02
’04
’06
’08
’10
’12
’14
’16
’18
’20
’86
’88
’90
’92
’94
’96
’98
2000
’02
’04
’06
’08
’10
’12
’14
’16
’18
’20
B. 25–54
percent
90
86
82
78
74
70
1982
’84
Actual rate
year olds during the Great Recession and the early part
of the subsequent recovery, but that gap has largely
closed. Today, the negative LFP gap is concentrated
among prime-working-age workers (figure 11, panel B).
Robustness of results
We experimented in a number of ways to gauge
the robustness of our estimated trend LFP rate to reasonable alternative specification and measurement
choices. Table 2 summarizes some of these exercises.
Estimating our model with data through the third
quarter of 2014 rather than 2007 has little impact (a
difference of about 0.2 percentage points) on our current estimates of the trend LFP rate and the LFP gap between the actual and trend rates (compare the first and
second rows of table 2). We also estimate our model
120
Trend rate
through the final quarter of 2002, 2004, and 2006 and
the results remain similar—the estimates for the LFP
gap in the third quarter of 2014 are –1.1, –0.4, and
–0.9 percentage points, respectively. It is worth emphasizing that our estimate of the trend LFP rate has
remained quite stable since 2002 (see dashed lines in
figure 12, panel A). This stands in stark contrast to the
BLS’s estimate of the trend LFP rate (Toossi, 2004,
2005, 2007), which panel B of figure 12 shows has
changed considerably over time (dotted lines). The
robustness of our results (as demonstrated by the dashed
trend LFP rate lines all heading similarly lower in
figure 12, panel A) reflects our methodology, which
extrapolates labor force participation decisions from
specific birth cohorts.
4Q/2014, Economic Perspectives
FIGURE 11 (continued)
Labor force participation rates, by age, 1982–2020
C. 55–79
percent
50
46
42
38
34
30
1982
’84
’86
’88
’90
’92
’94
’96
’98
2000
’02
’04
’06
’08
’10
’12
’14
’16
’18
’20
’88
’90
’92
’94
’96
’98
2000
’02
’04
’06
’08
’10
’12
’14
’16
’18
’20
D. 80 and older
percent
7
6
5
4
3
2
1
1982
’84
’86
Actual rate
Trend rate
Notes: Each panel plots quarterly data over the period 1982:Q1–2020:Q4. The shaded bars indicate recessions as defined by the
National Bureau of Economic Research.
Source: Authors’ calculations based on data from the U.S. Bureau of Labor Statistics, Current Population Survey.
Using alternative measures of labor market tightness such as the national unemployment gap (table 2,
third row), using a different lag structure (unreported),
or adding the median duration of national unemployment (table 2, fourth row) had a small impact, altering
our current estimate of the trend LFP rate by at most
0.3 percentage points.
That said, our estimate of the trend LFP rate is
relatively sensitive to one critical modeling choice. The
baseline model stratifies the estimation sample into four
age groups (16–24, 25–54, 55–79, and 80 and older).
However, when we estimate a model that forces cohort
coefficients to be the same for ages 16–79 (the pooled
Federal Reserve Bank of Chicago
model), we find that the trend LFP rate is almost identical
to the one estimated from the baseline model through
2007, but diverges appreciably from then on. As of
third quarter of 2014, the aggregate trend LFP rate
estimated from the pooled model is 1.0 percentage point
lower than that estimated from the baseline model. Thus,
the LFP gap between the actual rate and the trend rate
estimated from the pooled model is relatively smaller,
at about –0.2 percentage points (table 2, fifth row).38
The differences between the trend and gap estimates in the first row and the fifth row of table 2 can
be partly explained by how each model estimates and
extrapolates the coefficients for the cohorts who were
121
born too late to appear in the age-group estimation
samples. The baseline model estimates the cohort
effects separately by three age groups and extrapolates
the future cohorts based on the evolution of the recent
cohorts when they were at the same age. In contrast,
the pooled model estimates a single set of cohort effects
for all ages 16–79. This reduces the number of cohort
effects that needs to be forecasted, but it imposes strong
restrictions on the data. One problem with the pooled
model approach is that data for the 16–24 year olds
might not be very informative about LFP later in people’s
careers. This is a particular concern for high school
dropouts. Many of those without a high school diploma
at young ages will go on to get a diploma and thus won’t
be a good benchmark for older high school dropouts.
However, as it turns out, when we pool the 16–24 and
25–54 year old samples together, the estimated aggregate trend LFP rate (table 2, sixth row) is not very
different from that estimated from the baseline model.
Instead, the divergence between the estimates of
the trend LFP rates from the baseline and pooled models
arises from how we handle the older population. To
derive the results shown in the final row of table 2,
we combine the age 25–54 sample with the age 55–79
sample and find that the estimate of the trend LFP
rate is similar to that from the pooled model (table 2,
fifth row). We interpret this to mean that if the cohort
effects impact labor force participation differently over
the life cycle, then restricting them to be constant across
all ages, as in the pooled model, could lead to misleading inferences.
To illustrate this point, we generated panel A of
figure 13, which compares the coefficients on the birth
year dummies from the baseline and the pooled models
for unmarried white male high school dropouts without
a young child (under five years old). The pooled model
(solid green line) suggests that birth cohort effects have
been fairly stable for much of the twentieth century. In
the baseline model, however, the cohort effects exhibit
different patterns at the three stages of the life cycle.
Similar to cohort effects of the pooled model, cohort
effects in the baseline model are relatively stable during
youth and prime working age (purple and orange lines,
respectively). By contrast, the birth cohort coefficients
are rising quickly over time for the 55–79 age group
(solid red line), indicating a notable difference in the
likelihood of working past age 54 for those born at
the beginning versus the middle of the twentieth century—a trend that we expect to continue for cohorts
born later in the century (dashed red line).
Since the models also include other time-varying
(or age-varying) covariates, the cohort effects alone
do not give a full picture of the differences in the
122
TABLE 2
Trend rate of labor force participation (LFP)
and LFP gap in 2014:Q3
Trend
LFP rate
Model change
LFP
gap
(percent)
(percentage
points)
Baseline
64.2
– 1.2
Estimate model through
2014:Q3
64.0
– 1.0
National unemployment gap
64.0
–1.0
Median duration of national
unemployment
64.5
– 1.5
Pooled model
63.2
– 0.2
Age groups 16–54, 55–79,
and 80 and older
64.0
– 1.0
Age groups 16–24, 25–79,
and 80 and older
63.0
0.1
Notes: The LFP gap is the difference between the actual and trend
rates of LFP. The pooled model forces cohort coefficients to be
the same for ages 16–79 (instead of differentiated for ages 16–24,
25–54, and 55–79). See the text for further details on the baseline
model and variations of this model.
Source: Authors’ calculations based on data from the U.S. Bureau
of Labor Statistics, Current Population Survey.
likelihood of labor force participation. So, in panel B
of figure 13, we compare the predicted LFP rates of
individuals of different ages in the third quarter of
2014 from the two models. As expected, while the
two models yield similar predictions for prime-working-age workers (for example, those born in 1970),
the pooled model predicts much lower labor force participation for individuals aged 55 and older (for example,
the 1950 birth cohort) than the baseline model.
In principle, since the pooled model can mask important changes in cohort effects, we prefer the more
flexible baseline model. Moreover, formal statistical
tests also favor our baseline model over the pooled
model, which is more restricted. In particular, we can
reject the null that the cohort coefficients are the same
across ages (that is, the restriction imposed by the
pooled model) at the 1 percent level for all ten sexeducation-level variations of the baseline model that
we estimate.39
To summarize, while there is some uncertainty
about the exact size of the current LFP gap, we view
the robustness exercises as confirming that a significant part (but not all) of the decline in LFP rate since
2000—and since 2007—can be explained by changing demographic and behavioral factors. Relative to
the results from two recent and related Chicago Fed
Letter articles (Aaronson, Davis, and Hu, 2012; and
Aaronson and Brave, 2013), the magnitude of the
4Q/2014, Economic Perspectives
FIGURE 12
Chicago Fed versus U.S. Bureau of Labor Statistics (BLS) labor force participation (LFP)
rates and projections, 1990–2016
A. Chicago Fed model projections
percent
68
67
66
65
64
63
62
1990
’92
’94
’96
’98
2000
’02
’04
’06
’08
’10
’12
’14
’16
’14
’16
Chicago Fed’s actual LFP rate from CPS data
Trend LFP rate from Chicago Fed baseline model estimated through 2002:Q4
Trend LFP rate from Chicago Fed baseline model estimated through 2004:Q4
Trend LFP rate from Chicago Fed baseline model estimated through 2006:Q4
B. BLS projections
percent
68
67
66
65
64
63
62
1990
’92
’94
’96
’98
2000
’02
’04
’06
’08
’10
’12
BLS’s actual LFP rate
Projection of trend LFP rate made by BLS in 2002
Projection of trend LFP rate made by BLS in 2004
Projection of trend LFP rate made by BLS in 2006
Notes: The figure plots quarterly data for those aged 16 and older over the period 1990:Q1–2016:Q4. The blue lines in both panels
show actual LFP data; the light blue line in panel A is from the Chicago Fed’s CPS calculations, while the dark blue line in panel B is
from the BLS’s CPS calculations. The difference between the actual LFP rates from the Chicago Fed and from the BLS is discussed
in note 16. The dashed lines in panel A show the forecasted trend LFP rates from the Chicago Fed baseline model (described in the
text) using data through different end dates. The dotted lines in panel B represent BLS forecasts starting at various dates.
Sources: Authors’ calculations based on data from the U.S. Bureau of Labor Statistics, Current Population Survey (CPS); and Toossi
(2004, 2005, 2007).
Federal Reserve Bank of Chicago
123
FIGURE 13
Labor force participation (LFP) of unmarried white male high school dropouts without a young child:
Baseline model versus pooled model
A. Birth year coefficients
log odds
2.5
1.5
0.5
−0.5
−1.5
−2.5
−3.5
−4.5
1902 ’06 ’10
’14
’18
’22
’26
’30
’34
’38
’42 ’46 ’50
birth cohort
’54
’58
’62 ’66
’70
16−24 (baseline)
55−79 (baseline)
25−54 (baseline)
16−79 (pooled)
’74
’78
’82
’86
’90
B. LFP rates in 2014:Q3
percent
100
80
60
40
20
0
16
20
24
28
32
36
40
44
48
age
Baseline (16–24, 25–54, 55–79 age groups)
52
56
60
64
68
72
76
80
Pooled (16–79 age group)
Notes: The pooled model forces cohort coefficients to be the same for ages 16–79 (instead of differentiated for ages 16–24, 25–54,
and 55–79, as in the baseline model); see the text for further details. In panel A, the solid lines represent cohorts that are fully seen
in those age ranges, while the dashed lines represent forecasts. A young child is a child aged under five years old.
Source: Authors’ calculations based on data from the U.S. Bureau of Labor Statistics, Current Population Survey.
baseline LFP gap in 2011 (the latest comparable period)
is somewhat smaller in this article. This change can
be explained by data and modeling improvements. First,
we now use real-time BLS population estimates that
were released with the CPS data. In the previous two
studies, we used the resident population estimates that
were released by the U.S. Census Bureau in 2008.
Second, we now reference the civilian noninstitutional
population rather than the total population, to be
124
consistent with published BLS figures. Finally, we have
made a number of modeling improvements, including
using higher-frequency data (quarterly versus annual),
using fewer age groups, and allowing for long lags of
the state unemployment rate. In total, these data and
modeling changes cut our estimate of the LFP gap in
2011 by a quarter of a percentage point—from just
over 1 percentage point to about 0.8 percentage points.
The gap has widened slightly since 2011.
4Q/2014, Economic Perspectives
FIGURE 14
Natural rates of unemployment, 1982–2020
percent
6.5
6.0
5.5
5.0
4.5
4.0
1982
’84
’86
’88
’90
’92
’94
’96
’98
2000
’02
’04
’06
’08
’10
’12
’14
’16
’18
’20
CBO short-run natural rate
CBO long-run natural rate
Natural rate implied by demographics and education
Adjusted natural rate implied by demographics and education
Notes: The figure plots quarterly data for those aged 16 and older over the period 1982:Q1–2020:Q4. The natural rate implied by demographics
and education is the natural rate of unemployment that holds the specific natural rates of unemployment for age-sex-education-level groups
fixed at their values in the second half of 2005 while allowing group-specific shares of trend labor force participation to vary over time. For
further details on the groups, see the text. The dashed green line is this natural rate implied by demographics and education adjusted with
the same post-2007 adjustment as the CBO estimate for its long-run natural rate; see the text, particularly note 42, for further details.
Sources: Authors’ calculations based on data from the U.S. Bureau of Labor Statistics, Current Population Survey; and Congressional Budget
Office (CBO) from Haver Analytics.
Impact on the natural rate of unemployment
As we have documented, declining trend labor
force participation is a widespread phenomenon, but
the magnitude of the decline differs across demographic
groups. A consequence of this heterogeneity in the
decline of trend LFP is that the composition of the
aggregate labor force has changed over time, which
in turn can impact the natural rate of unemployment,
or trend unemployment rate. For example, we estimate
that the trend LFP rate has fallen especially rapidly
for teens—a group that happens to have particularly
high rates of unemployment today. As teens become
a smaller share of the labor force, the natural rate of
unemployment will decline. In addition, educational
attainment has been increasing over time—a development that increases the share of workers with lowerthan-average unemployment.
To broadly assess the likely magnitude of this
compositional effect, we calculate (from CPS data)
a trend unemployment rate implied by demographics
and education—specifically, one that holds the specific
trend unemployment rates for the age-sex-educationlevel groups fixed at their respective levels in the
second half of 2005 (a time when the actual aggregate
Federal Reserve Bank of Chicago
unemployment rate was equal to the Congressional
Budget Office’s estimate of the natural rate of unemployment) but allows these groups’ shares of the trend
LFP to vary over the entire period 1982–2020. As
figure 14 shows, this hypothetical natural rate of unemployment rate (solid green line) declines by 0.3
percentage points over the period 2007–14 and by 0.6
percentage points over the period 2000–14, or about
0.05 percentage point per year over the past 15 years.
In other words, the aggregate natural rate of unemployment is 0.3 percentage points lower in the third
quarter of 2014 than it would have been if the composition of the trend LFP had remained the same as in
2007 and 0.6 percentage points lower than it would
have been if this composition had remained the same
as in 2000.40 The decline since 1982 in the natural
rate of unemployment implied by demographics and
education is also quite similar to that of the CBO’s
natural rate of unemployment series (in figure 14, the
CBO’s short-run natural rate is the blue line, and its
long-run natural rate is the red line41), though the timing
is somewhat different. Both of the CBO’s natural
rate of unemployment series declined from 6.1 percent
at the beginning of the series in 1982 and flattened to
125
FIGURE 15
Employment-to-population ratios, 1982–2020
percent
66
64
62
60
58
56
54
52
1982
’84
’86
’88
’90
’92
’94
’96
’98
2000
’02
’04
’06
’08
’10
’12
’14
’16
’18
’20
Trend ratio using CBO short-run natural rate of unemployment
Trend ratio using adjusted natural rate of unemployment implied by demographics and education
Actual ratio from BLS
Notes: The figure plots quarterly data for those aged 16 and older over the period 1982:Q1–2020:Q4. See the notes of figure 14 and the
text for further details on the natural rates of unemployment. The shaded bars indicate recessions as defined by the National Bureau of
Economic Research.
Sources: Authors’ calculations based on data from the U.S. Bureau of Labor Statistics, Current Population Survey (CPS); and Congressional
Budget Office (CBO) from Haver Analytics.
5.0 percent from 2000 through 2007, whereas the trend
unemployment rate implied by demographics and education declined steadily from about 6.2 percent in the early
1980s to 4.8 percent in 2007. According to the CBO’s
estimates, the short-run natural rate rose sharply during
the most recent recession that began in late 2007, peaking
at 6.0 percent in 2012, while the CBO’s long-run natural
rate increased more steadily, hitting 5.5 percent in 2013
before declining slightly to meet the short-run rate by
the 2020 estimate of 5.4 percent (both CBO series have
yet to return to pre-recession levels). When we apply the
same post-2007 increase in the CBO long-run estimate
of the natural rate to our hypothetical trend unemployment rate, this adjusted natural rate (dashed green line)
currently stands at 5.0 percent.42 In the next section, we
use this adjusted natural rate implied by demographics
and education, as well as the CBO’s short-run natural
rate, to calculate trend payroll employment growth.
Figure 15 shows the implication of our trend LFP
and natural rate of unemployment results for the trend
employment-to-population ratio.43 As the figure shows,
the trend employment-to-population ratio has been
falling for over a decade because of the drop in the LFP
rate. The value of the trend employment-to-population
ratio using the CBO’s short-run natural rate of unem-
126
ployment (blue line) is 60.5 percent in the third quarter of 2014—about 1.5 percentage points greater than
the actual BLS data (orange line). Relative to the
trend employment-to-population ratio using the adjusted
hypothetical trend unemployment rate described in
the previous paragraph (green line), the actual ratio is
2 percentage points lower in the third quarter of 2014.
Impact on trend payroll employment growth
In order to calculate trend payroll employment
growth from 1982 through 2020, we use four estimated
components: our baseline estimate of the trend labor
force participation rate; the trend civilian noninstitutional population aged 16 and older; one minus the
CBO’s short-run natural rate of unemployment (or the
adjusted natural rate of unemployment implied by
demographics and education); and the trend ratio of
payroll to household survey employment.44 Trend
payroll employment growth is the monthly average
change implied by the product of these four constructed
measures. Aaronson and Brave (2013) provide more
supporting details.
Figure 16 plots the additional series needed for this
calculation. Trend population growth45 climbed steadily
through the 1990s, peaking in the late 1990s at about
1.3 percent (figure 16, panel A). Trend population
4Q/2014, Economic Perspectives
FIGURE 16
Underlying data series in trend payroll employment growth calculation
A. Population growth
percent
1.7
1.5
1.3
1.1
0.9
0.7
0.5
1982 ’84
’86
’88
’90
’92
’94
’96
’98
2000
’02
’04
’06
’08
’10
’12
’14
’16
’18
’20
’08
’10
’12
’14
’16
’18
’20
Actual
Trend
B. Unemployment rate
percent
12
10
8
6
4
2
1982 ’84
’86
’88
’90
’92
’94
’96
’98
2000
’02
’04
CBO short-run natural rate of unemployment
’06
Adjusted natural rate of unemployment implied
by demographics and education
Actual unemployment rate
C. Ratio of payroll to household employment
percent
98
96
94
92
90
88
1982 ’84
’86
’88
’90
’92
’94
’96
’98
2000
Trend
’02
’04
’06
’08
’10
’12
’14
’16
’18
’20
Actual
Notes: The figure plots quarterly data for those aged 16 and older over the period 1982:Q1–2020:Q4. The dashed lines in all three panels
represent projections of the trends. Both natural rates of unemployment in panel B also appear in figure 14; see the notes of figure 14 and the
text for further details.
Sources: Authors’ calculations based on data from the U.S. Census Bureau; U.S. Bureau of Labor Statistics, Current Population Survey and
Current Employment Statistics, from Haver Analytics; and Congressional Budget Office (CBO) from Haver Analytics.
Federal Reserve Bank of Chicago
127
FIGURE 17
Trend payroll employment growth, 1983–2020
thousands of jobs per month
250
200
150
100
50
0
1983
’85
’87
’89
’91
’93
’95
’97
’99
2001 ’03
’05
’07
’09
’11
’13
’15
’17
’19
Trend calculated using CBO short-run natural rate of unemployment
Trend calculated using adjusted natural rate of unemployment implied by demographics and education
Notes: The figure depicts the average monthly change in the trend in payroll employment on a quarterly basis. The data are smoothed
using a four-quarter moving average. Solid lines denote estimates based on historical data, while dashed lines signify estimates based
on projected data. See the notes of figure 14 and the text for further details on the natural rates of unemployment.
Sources: Authors’ calculations based on data from the U.S. Census Bureau; U.S. Bureau of Labor Statistics, Current Population Survey
and Current Employment Statistics, from Haver Analytics; and Congressional Budget Office (CBO) from Haver Analytics.
growth then decelerated to 0.9 percent in 2012, and
the U.S. Census Bureau expects it to fall through 2016
and then stabilize at about 0.8 percent per year for the
remainder of the decade. Panel B of figure 16 shows
the CBO short-run natural rate of unemployment and
the adjusted natural rate of unemployment implied by
demographics and education discussed in the previous
section, as well as the actual unemployment rate from
the BLS. Finally, to derive an estimate of the trend in
the more commonly referenced BLS payroll survey of
employment requires an additional multiplication by the
trend ratio of payroll to household survey employment.46
The trend ratio of payroll to household employment
recently stabilized at about 94.8 percent after a long
ascent during the 1980s and 1990s and subsequent
decline since 2000 (figure 16, panel C).47 We expect
it to stay at its current level of about 94.9 percent
through 2020.
Figure 17 plots our estimate of trend payroll
employment growth from 1983 through 202048 using
both the CBO short-run natural rate of unemployment
and the adjusted trend unemployment rate implied by
demographics and education discussed before. Trend
payroll employment grew by roughly 130,000 jobs per
month during the mid-1980s through the early 1990s
and by roughly 200,000 jobs per month during the middle
to late 1990s. In the early 2000s, trend employment
128
growth fell to under 100,000 jobs per month, where it
has roughly remained.
The historically high rates of trend job growth in
the 1980s and 1990s were driven by a confluence of
all four factors described in this section—an increase
in the trend labor force participation rate, higher trend
population growth, a decline in the natural rate of
unemployment, and an increase in the trend ratio of
payroll to household survey employment. As discussed
before, the trend LFP rate, along with the trend ratio
of payroll to household survey employment, reversed
course around the turn of the century, causing trend
payroll employment growth to fall.
During the Great Recession, trend payroll employment growth fell substantially, driven by a sharp rise in
the natural rate of unemployment (especially in the CBO’s
short-run natural rate). With trends in the unemployment
rate turning down during the recovery, trend payroll
employment growth has subsequently picked up, averaging roughly 60,000–70,000 jobs per month since the
expansion started in June 2009. We project trend employment growth to continue at the 60,000–70,000 jobs
per month pace through the end of 2015 and then drop
to under 50,000 per month, on average, in 2016–20.
The projected slowdown is based on the continuing
decline in trend labor force participation, along with a
lower level of projected population growth from now on.
4Q/2014, Economic Perspectives
FIGURE 18
Payroll employment gap, 2000–20
thousands of jobs
150,000
145,000
140,000
135,000
130,000
125,000
2000
’02
’04
’06
’08
’10
’12
’14
’16
’18
’20
Trend
Actual
Projection based on average monthly job gains of approximately 170,000 (closing gap by end of 2016)
Projection based on average monthly job gains of approximately 130,000 (closing gap by end of 2017)
Projection based on average monthly job gains of approximately 115,000 (closing gap by end of 2018)
Notes: The figure plots quarterly data for those aged 16 and older over the period 2000:Q1–2020:Q4. The colored dotted lines are
potential future paths for when the gap between the actual and trend levels of total payroll employment would be closed.
Sources: Authors’ calculations based on data from the U.S. Census Bureau; U.S. Bureau of Labor Statistics, Current Population
Survey and Current Employment Statistics, from Haver Analytics; and Congressional Budget Office (CBO) from Haver Analytics.
It is worth noting that the calculations here are
for trend payroll employment growth. While the trend
is expected to slow down substantially over the rest
of the decade, a large employment gap (that is, the
difference between the actual and trend level of total
payroll employment) that opened up during 2008–09
needs to be closed by above-trend employment growth.
To illustrate some potential future paths, we show in
figure 18 that if payroll employment grows by roughly
130,000 jobs per month, it will take three years for the
gap to completely disappear (in 2017). Stronger employment growth of roughly 170,000 jobs per month
closes the gap one year earlier (in 2016), while weaker
employment growth of roughly 115,000 jobs per month
closes the gap one year later (in 2018).
Conclusion
This article extends previous methodology for
estimating the long-run trend in LFP as well as its
dependence on business cycle conditions. We find
that our methodology—which 1) takes into account
Federal Reserve Bank of Chicago
the changing distribution of educational attainment
and other characteristics of the population, 2) uses
state variation in unemployment gaps to identify the
sensitivity to labor market conditions, 3) accounts for
the life-cycle pattern of LFP, and 4) allows for flexible
variation by birth cohort in how the life-cycle pattern
develops—is quite robust in its implication that the
trend LFP rate is moving down by about 0.3 percentage
points per year. Our baseline results use data through
2007 to estimate the trend in LFP. However, we get
very similar predictions of the decline in the trend if we
estimate the model using data through the third quarter of 2014 or limit the data to a date as early as 2002.
Of course, there are many questions that our statistical models are not designed to answer. We do not
account for the detailed functioning of the many public
policy programs that impact work decisions. We also
do not model the underlying supply and demand for
labor in a manner that would provide insight into how
LFP and wages are jointly determined. As a result, it
is possible that policy changes such as those pertaining
129
to disability insurance or education programs or endogenous changes to wage growth could alter the path of
the LFP rate in the years ahead. Future research that
builds such structural representations of the supply and
demand for labor could thus be very valuable. That
said, the trends our model identifies have been stable
for nearly 15 years, so their predictions may provide
a reasonable benchmark for future research. They imply that once employment has returned to its long-run
trend, it will grow much more slowly than in the past,
with typical employment gains of under 50,000 per
month. Estimates of potential output growth and the
natural rate of unemployment should also reflect lower
projections for LFP and changes in the composition
of the work force.
There is a good deal of interest among policymakers
in the gap between the current level of the LFP rate
and its long-term trend because it has implications for
the stance of monetary policy. With regard to how large
the LFP gap is, our results suggest a somewhat wider
range of possible answers. Clearly, a large portion of
the decline in the trend LFP rate since 2007 reflects
demographics and other long-running factors. However,
plausible models imply gaps of between 0.2 and 1.2
percentage points, depending on various details, especially on how we treat cohort effects for different age
groups. Our preferred model, which allows the cohort
patterns to be different for older and younger people,
estimates the current gap relative to expectations in
2007 at about 1.2 percentage points.
We estimate that much of today’s gap between
the actual LFP rate and its trend is accounted for by
low-education workers, possibly reflecting the especially
difficult labor market circumstances such workers face.
Alternatively, it is possible that the large gap relative
130
to pre-recession expectations could reflect developments left out of our models. One possibility is that
welfare reform in the late 1990s was a one-time boost
to LFP that should not have been extrapolated into
further LFP increases for low-education workers in the
2000s. Indeed, the largest gap today arises from female
high school dropouts, the primary group affected by
changes in the welfare laws. Another possibility is that
the construction boom of the 2000s masked a longerterm deterioration of opportunities for low-education
workers (Charles, Hurst, and Notowidigdo, 2014a,
2014b)—which could have also led our models to
overestimate the trend in LFP.
Finally, in order to judge whether the level of actual
LFP represents additional labor market slack over and
above what is captured by the still somewhat elevated
unemployment rate, one must ask whether LFP is low
relative to expectations given the path of unemployment
over the past few years. Accounting for those unemployment rates, plausible models for the trend LFP rate
place the actual LFP rate between 0 and 0.8 percentage
points below expectations. As noted earlier, there is
ample reason for uncertainty about such estimates.
However, our preferred estimate of 0.8 percentage
points for the LFP gap would represent a nontrivial
amount of additional labor market slack over and
above that represented by the unemployment rate. In
addition, our results suggest that compositional changes in the labor force may have reduced the natural
rate of unemployment by up to 0.6 percentage points
since 2000—a development not accounted for in
prominent estimates of the natural rate. Such additional slack would suggest that monetary policy should
remain more accommodative than would otherwise
be the case.
4Q/2014, Economic Perspectives
NOTES
Data from the U.S. Bureau of Labor Statistics, Current Population
Survey, from Haver Analytics.
1
U.S. Bureau of Labor Statistics’ (BLS) official LFP rate (available
at http://data.bls.gov/timeseries/LNS11300000).
14
2
The trend LFP rate is the LFP rate consistent with the contemporaneous composition of the work force and an economy growing at
its potential.
15
Our estimates of the actual and trend LFP rates reported throughout this article are computed from the U.S. Bureau of Labor Statistics’
Current Population Survey (CPS). However, it should be noted that
our actual LFP rate differs slightly from the official BLS LFP rate
mentioned in the first paragraph of the article, probably because we
do not use the composite estimation that the BLS does (we explain
the difference in greater detail in note 16). We explicitly note where
official BLS LFP data are used or referenced—as in figures 4, 5,
12, and A1 and related discussion.
3
4
However, as we discuss in other parts of this article, there is evidence
of changes in cohorts’ LFP tendencies between youth and prime
working age and also between prime working age and older ages.
For the last age category, please note that the CPS does not distinguish age beyond 80 in some years.
5
The unemployment gap is the gap between the actual unemployment
rate and the Congressional Budget Office’s (CBO) short-run NAIRU
series. NAIRU stands for nonaccelerating inflation rate of unemployment and is one notion of the natural rate of unemployment, or the
trend rate of unemployment. The natural rate of unemployment
represents the unemployment rate that would prevail in an economy
making full use of its productive resources. We further discuss this
measure later in the text.
6
See note 6.
7
Trend (payroll) employment growth is the level of employment growth
that is consistent with a flat unemployment rate. Employment growth
above (below) trend will put downward (upward) pressure on the
unemployment rate.
8
A longer view of the LFP rate is available in the appendix’s figure
A1. These values are official numbers from the U.S. Bureau of
Labor Statistics, Current Population Survey, from Haver Analytics.
9
We plot in figure 2 the age-specific LFP rates for men and women
in 2014. Because the data are from a cross section of a single year,
they combine many birth cohorts rather than following a single cohort
over the life cycle. We discuss this issue in more depth later. However,
the overall shape of the life cycle would look similar if we followed
birth cohorts over time or chose a base year other than 2014.
10
While the female LFP rate remains about 10 percentage points
below the male LFP rate, a number of studies suggest that women’s
labor force decisions—that is, how they respond to changes in wages,
aggregate employment conditions, and public policies—now closely
resemble those of men (Blau and Kahn, 2007; Heim, 2007; and
Bishop, Heim, and Mihaly, 2009).
11
Ibid.
As mentioned earlier, although the BLS uses the same basic CPS
files to compute the official LFP rate series, our estimate of the aggregate LFP rate differs slightly. This difference may stem from the
fact that in calculating the LFP rate, we do not use the composite
estimation that the BLS does; this estimation exploits the CPS’s
rotation sample design (with households in the survey for four months,
then out for eight months, and finally in again for four months). The
sample rotation scheme results in a positive correlation between
CPS estimates from different months, improving measures of change
over time. The CPS composite estimate for a given labor force statistic (for example, the number of people unemployed or employed)
is based on a weighted average of two estimates for the same statistic:
1) the CPS estimate and 2) the previous month’s composite estimate
plus an estimate of change since the previous month. In addition,
the composite estimate also incorporates an adjustment to partially
correct for bias associated with time in the sample (by assigning
higher weights to data from households completing their first and
fifth interviews in the month).
16
The data series for these controls are plotted in the appendix’s
figure A2. The series for marital status and the presence of a young
child (under five years old) are computed from the CPS data. The
ratio of youth to adult wages is computed at the state level from
the CPS microdata using average hourly wages of those paid at
an hourly rate. (Youth is defined as 16–24 year olds and adult as
25–54 year olds.)
17
The CBO short-run NAIRU series—which accounts for temporary
factors, such as unemployment insurance extensions—is from
Haver Analytics. See also note 6 for further details.
18
19
The state unemployment rates are from Haver Analytics.
20
See www.dol.gov/whd/state/stateminwagehis.htm.
One issue with these alternative labor market measures is, as far
as we know, there are no standard estimates of their long-run trends.
For the state-level unemployment rate, we adjust the national natural
rate of unemployment for the deviation of the state unemployment
rate relative to the national unemployment rate averaged over the
estimation sample period. Specifically, the adjusted state-level
unemployment gap is us , t − ut* − ( us − u ) and its lags. Note that state
is the most detailed geographic unit that includes all CPS respondents. For the unemployment spell duration measure, we include the
median spell (in additional to the rate) of national unemployment.
We use median instead of mean spell because the CPS recorded
unemployment spell duration up to two years through 2011 and up
to five years thereafter, which causes a discrete change in mean
duration but leaves median duration intact. To isolate a cyclical
component in duration, we used deviations of median spells from
the sample time period’s mean.
21
Both wage variables are measured as deviations from the sample
time period’s means.
22
See, for example, Juhn and Murphy (1997), Peracchi and Welch
(1994), Autor and Duggan (2003), Blau (1998), and Blau and Kahn
(2007). See also Juhn and Potter (2006) for a review. For details on
DI and SSI programs, see www.ssa.gov/disability/.
12
See, for example, Charles, Hurst, and Notowidigdo (2014a, 2014b),
Autor (2010), and Acemoglu and Autor (2011), as well as the references therein.
13
Federal Reserve Bank of Chicago
Ideally, we would also condition life expectancy on education,
since mortality has varied over time by education levels (Meara,
Richards, and Cutler, 2008). However, we have been unable to
find a time series on education-specific life expectancy with a
high enough frequency.
23
131
Because of the negligible sample sizes, we do not estimate the
model for those with a postcollege degree aged 16–24. This leaves
us with (3 × 2 × 5) – 2 = 28 groups. Additionally, we exclude from
the data small numbers that are high school graduates younger than
17, high school graduates with some college younger than 19, and
college graduates younger than 21.
24
The parameters λse , γse , and δse are the regression coefficients on
the w, x, and z variables, respectively.
25
We also allow for a trend break in 1992 to account for the redesign
of the education question in the CPS (see note 1 of box 1, p. 114)
and to extrapolate the trend based on the more recent and relevant
time period.
26
The parameter θse is the regression coefficient on the t variable.
27
Authors’ calculations based on data from the U.S. Bureau of Labor
Statistics, Current Population Survey.
28
29
The model includes quarterly dummies to adjust for seasonal patterns
in work. Later on, we also discuss the results when the model is run
through other time periods, including from the beginning of 1982
through the third quarter of 2014.
Keep in mind that each estimate is based on a single birth year and
further stratified by sex and education level. Therefore, the series
plotted in panels A, B, and C of figure 8 are noisy. For our purposes,
the noise washes out once we aggregate many series together to
form our national trend LFP rate.
30
However, the cohort effects on the later career work activity of
women aged 55–79 (not shown in figure 8) have generally been
rising over time.
31
Recall that we stop our estimation sample in 2007 and forecast
trend LFP for 2008 and onward. For forecasts for 2008–13, we use
the actual population data.
32
See Bell and Miller (2005).
33
The actual LFP rate fell by 0.5 percentage points in the fourth
quarter of 2013. As of third quarter of 2013, the actual LFP rate was
only 0.3 percentage points below where we would have expected
given economic conditions.
34
The derivation of the equation uses the fact that
∑ d pt −1∆f dt = pt −1 ∑ d ∆f dt = 0. The second equality follows because
fdt is a share and always sums to 1 at a given t.
35
We examine the population aged 25 and older in order to exclude
younger individuals who might not have completed their education.
Of course, many individuals continue their education beyond age
25. See, for example, figure 5 in Aaronson and Sullivan (2001).
36
The rising LFP rate of high school dropouts over this period is
mainly due to the increasing LFP of prime-working-age women.
Many researchers have studied the implications of policy changes,
such as welfare reform and the expansion of the earned income tax
credit (EITC), on the LFP decisions of female low-skill workers
(Eissa and Liebman, 1996; Meyer and Rosenbaum, 2001; Moffitt,
2003; and Eissa and Hoynes, 2006).
37
Specifically, this model includes single-year age dummies, singleyear birth cohort dummies, dummies for the three baseline age-groups
(16–24, 25–54, 55–79) interacted with the state unemployment gaps
as well as the race and quarter dummies, and subsets of age group
dummies interacted with group-specific controls (for instance, a
dummy for ages 16–24 interacted with minimum wage and with
38
132
youth-to-adult wage ratio and a dummy for ages 25–54 interacted
with marital status and the presence of children under five years old).
Technically, we use sampling weights in our logit regression analysis.
Consequently, the standard likelihood ratio (LR) test or the Akaike
information criterion (AIC)—methods of measuring the relative
quality of a statistical model—cannot be used. Instead, we apply
these tests to an unweighted version of our baseline model, which
turns out to give nearly identical estimates as the weighted version.
We find that for all ten sex-education-level groups, the LR test can
strongly reject the restrictions imposed by the pooled model (with
p-value < 0.001). Moreover, the AIC also favors the less restricted
three-age-group (baseline) model across all sex-education-level groups.
39
Adjusting the natural rate of unemployment for changes in the
educational distribution of the labor force is somewhat controversial.
Summers (1986) argues that such adjustments imply counterfactually
high unemployment rates in earlier years. Shimer (1999) builds a
model in which workers’ relative levels of education signal ability
to employers, but average absolute levels of education do not affect
unemployment. However, we see fairly modest empirical support
for education signaling models. Altonji and Pierret (2001) show
that employers use education level as a proxy for unobserved productivity among job applicants but that this signaling effect fades
once firms learn new information about the productivity of their
hires. Lange (2007) builds a model to quantify the speed of employer learning about new workers and shows that, under his preferred specification, only 10 percent of the workers’ return to
schooling can be ascribed to education signaling. Clark and Martorell
(2014) provide direct evidence that education signaling may not
matter to wages in the case of high school diplomas. Shimer (1999)
also notes that endogenous choice of schooling levels might bias
upward the effects of education on unemployment if more-able people
choose to get more education. That said, research on the effects of
education on wages using plausible instrumental variables or twinsbased designs does not produce estimates notably below those obtained from ordinary least squares; see, for example, Card (1999).
Our preferred interpretation of the impact of schooling on
unemployment is that increased education has indeed been pushing
down unemployment for many decades, but that its effects have
been offset by other factors. However, given that there is uncertainty
over whether adjustments for education are warranted, we note that
changes in the age distribution of the labor force alone lower the
natural rate of unemployment by 0.34 and 0.16 percentage points
relative to what it would have been in the third quarter of 2014 if
the age composition of trend LFP had remained the same as in 2000
and 2007, respectively. Similarly, changes in the distribution of
educational attainment of the labor force alone lower the natural
rate of unemployment by 0.40 and 0.23 percentage points relative
to what it would have been if the composition of trend LFP had
remained the same as in 2000 and 2007, respectively. Changes in
the gender composition have no impact. Together, changes in the
age distribution, gender composition, and the distribution of educational attainment reduce the natural rate of unemployment by 0.61
and 0.32 percentage points relative to what it would have been if
the composition of trend LFP had remained the same as in 2000
and 2007, respectively.
40
As mentioned earlier, the CBO’s short-run NAIRU accounts for
temporary factors, such as unemployment insurance extensions,
that boosted the natural rate after 2007. The long-run NAIRU does
not include these transitory factors.
41
Specifically, we adjust this hypothetical natural rate of
unemployment by uthypo + ( utCBO _ LR − 5.0 ) for t ≥ 2008.
∧
43
The trend employment-to-population ratio e = p∧ × (1 − u∧ ) ,
42
∧
pop
∧
where p is trend LFP and u is the natural rate of unemployment.
4Q/2014, Economic Perspectives
the Hodrick–Prescott (HP) filter to isolate a trend component. To
avoid the standard end-of-sample problem with the HP filter and
because the U.S. Census Bureau’s projection of trend population is
superior to a statistical estimate from an HP filter, we replace the
HP-filtered trend with the U.S. Census Bureau’s projections after 2015.
For the last constructed measure, note that payroll employment is
the employment reported in the BLS’s Current Employment Statistics
survey, which is also referred to as the payroll or establishment survey. Household employment is from the CPS. For further details on
these two different measures of employment, see www.bls.gov/
web/empsit/ces_cps_trends.pdf.
44
As with population growth, we use the HP filter to estimate the
trend of the ratio of payroll to household survey employment.
46
Both the historical data and projections for the civilian noninstitutional population aged 16 and older are from the U.S. Census Bureau.
We use the U.S. Census Bureau’s national Quarterly Intercensal
Noninstitutional Civilian Population files (1982:Q1–1990:Q1) and
the Monthly Postcensal Noninstitutional Civilian Population estimates
(1990:Q2–2013:Q4). The U.S. Census Bureau’s 2013–20 population projections are from the 2012 National Population Projections,
which were released on December 12, 2012. Historical data are found
at www.census.gov/popest/data/historical/index.html and the projections
at www.census.gov/population/projections/data/national/2012/
downloadablefiles.html. Discontinuities between the two series are
smoothed. We also smooth the data to adjust for revisions produced
by decennial censuses. We adjust for the seasonal pattern in population shares by using a four-quarter moving average. We then use
45
The increase and subsequent decline in the ratio of payroll to
household survey employment is evident even when using the
payroll-concept-adjusted household employment series. This series
is a research series created by the BLS to make the household employment series more comparable to the payroll employment series
(see note 44); for details, see U.S. Bureau of Labor Statistics (2012).
47
The final trend employment growth series is smoothed using a
four-quarter moving average.
48
APPENDIX
FIGURE A1
Labor force participation rate, 1948–2014
percent
68
66
64
62
60
58
56
1948 ’51
’54
’57
’60 ’63
’66 ’69
’72
’75 ’78
’81
’84
’87 ’90
’93
’96 ’99 2002 ’05 ’08 ’11
’14
Notes: The figure plots official quarterly data over the period 1948:Q1–2014:Q3. The shaded bars indicate recessions as defined by the
National Bureau of Economic Research.
Source: U.S. Bureau of Labor Statistics, Current Population Survey, from Haver Analytics.
Federal Reserve Bank of Chicago
133
APPENDIX (continued)
FIGURE A2
Additional employment-related and demographic data series used as controls
for estimating the statistical models, 1982–2020
A. Marital rates with or without young child
percent
100
90
80
70
60
50
40
30
20
10
0
1982 ’84
’86
’88
’90
’92
’94
’96
’98
2000
’02
’04
’06
’08
’10
’12
Not married with young child
Married with young child
Not married with no young child
Married with no young child
’14
’16
’18
’20
B. Unemployment gap
percentage points
5
4
3
2
1
0
−1
1982 ’84
’86
’88
’90
’92
’94
’96
’98
2000 ’02
’04
’06
’08
’10
’12
’14
’16
’18
’20
’88
’90
’92
’94
’96
’98
2000 ’02
’04
’06
’08
’10
’12
’14
’16
’18
’20
C. Minimum wage
dollars per hour
9.00
8.50
8.00
7.50
7.00
6.50
6.00
5.50
5.00
1982 ’84
134
’86
4Q/2014, Economic Perspectives
APPENDIX (continued)
FIGURE A2 (continued)
Additional employment-related and demographic data series used as controls
for estimating the statistical models, 1982–2020
D. Youth-to-adult wage ratio
percent
68
66
64
62
60
58
56
1982
’84
’86
’88
’90
’92
’94
’96
’98 2000
’02
’04
’06
’08
’10
’12
’14
’16
’18
’20
’88
’90
’92
’94
’96
’98 2000
’02
’04
’06
’08
’10
’12
’14
’16
’18
’20
E. Life expectancy
age
90
88
86
84
82
80
1982
’84
’86
Male
Female
Notes: For panel A, a young child is a child under age five. For panel B, the state-level unemployment gap (that is, the difference between
the actual unemployment rate and the CBO’s short-run natural rate of unemployment explained in the text) is a four-quarter moving average
with no lag. For panel C, the state minimum wages are deflated by the BLS’s Consumer Price Index for All Urban Consumers and then averaged. For panel D, youth are aged 16–24 and adults are aged 25–54. For panel E, the life expectancy plotted is that averaged for all ages
16 and older. All the panels plot quarterly data over the period 1982:Q1–2020:Q4. Methods for obtaining projections after the current quarter
are described in the text.
Sources: Authors’ calculations based on data from the U.S. Bureau of Labor Statistics (BLS), Current Population Survey, from Haver Analytics;
Congressional Budget Office (CBO) from Haver Analytics; U.S. Bureau of Labor Statistics, January issues of the Monthly Labor Review;
U.S. Department of Labor (www.dol.gov/whd/state/stateminwagehis.htm); and Bell and Miller (2005).
Federal Reserve Bank of Chicago
135
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4Q/2014, Economic Perspectives
Interest rates and asset prices: A primer
Robert Barsky and Theodore Bogusz
Introduction and summary
Economic commentators often assert that major asset
price booms and busts are closely associated with variations in the terms of borrowing to fund risky asset
purchases. One important narrative focuses on changes
in borrowing costs arising from variation in the riskless interest rate, which may result from a variety of
causes—notably central bank policy actions in the
short run and changes in world saving and associated
capital flows over a longer horizon. For example, Allen
and Gale (2000) contend that so-called bubble episodes
typically begin with “financial liberalization or a conscious decision by the central bank to increase lending.”
After a period of perhaps several years, these authors
continue, the central bank’s policy stance tightens, interest rates rise, and the bubble collapses.1 Greenspan
(2010) also notes a connection between interest rates
and asset prices but stresses the role of global savings
patterns and other determinants of long-term rates
rather than the short-term policy rates that are most
closely connected to the actions of central bankers.2
What does economic theory have to say about the
extent to which exogenous changes in short-term and/or
long-term riskless rates ought to affect asset prices, and
by what channels? In this article, we examine the implications of three key theoretical models of asset booms
and busts, focusing on a variety of channels through
which interest rates might affect real asset prices.
After providing a bit of empirical motivation via
a brief look at data from Japan’s stock and land price
boom and bust of 1985–91, we study implications of the
central model of traditional asset pricing, in which price
is simply expected discounted future dividends. Here
the focus is on the way in which the riskless interest
rate affects the fundamental value of assets. Leverage
does not play a central role because of the celebrated
Modigliani–Miller theorem, which says that the total
value of titles to an asset’s payoffs is independent of
Federal Reserve Bank of Chicago
how they are divided into debt and equity claims. Using
first the simple Gordon formula, and then Campbell
and Shiller’s log-linearized dynamic Gordon model, we
derive quantitative implications for the effects of innovations in the short-term rate on an asset that could be
thought of as land or the stock of an unlevered firm.
The key result of this perfect markets model is
that the extent to which increases in the riskless interest rate lower fundamental asset values is an increasing function of the persistence of short-term interest
rates and a decreasing function of the risk premium.
This observation has important implications for debates
over whether or not central banks are likely to cause
Robert Barsky is a senior economist and research advisor and
Theodore Bogusz is a senior associate economist in the Economic
Research Department of the Federal Reserve Bank of Chicago.
© 2014 Federal Reserve Bank of Chicago
Economic Perspectives is published by the Economic Research
Department of the Federal Reserve Bank of Chicago. The views
expressed are the authors’ and do not necessarily reflect the views
of the Federal Reserve Bank of Chicago or the Federal Reserve
System.
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President and Director of Research; Spencer Krane, Senior Vice
President and Economic Advisor; David Marshall, Senior Vice
President, financial markets group; Daniel Aaronson, Vice President,
microeconomic policy research; Jonas D. M. Fisher, Vice President,
macroeconomic policy research; Richard Heckinger, Vice President,
markets team; Anna L. Paulson, Vice President, finance team;
William A. Testa, Vice President, regional programs; Lisa Barrow,
Senior Economist and Economics Editor; Helen Koshy and
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Economic Perspectives articles may be reproduced in whole or in
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ISSN 0164-0682
139
FIGURE 1
Japanese discount rate and real stock price
percent
6.4
index
550
6.0
500
5.6
450
5.2
400
4.8
350
4.4
300
4.0
250
3.6
200
3.2
150
2.8
100
50
2.4
1985
’86
’87
’88
’89
’90
’91
Nikkei 225 index deflated by consumer price index, all items except food and energy (right axis)
Nominal discount rate (left axis)
Source: Haver Analytics.
large cycles in real asset prices by varying policy rates.
In order to have such effects in this standard model,
central bankers must be able to create highly persistent
changes in real policy rates—put differently, they must
exert major effects on real long-term interest rates.
Monetary theory, however, suggests that the ability of
central banks to effect permanent changes in real rates
is limited (Shiller, 1980).3 These two observations in
combination suggest that central banks also have limited
ability to create booms and busts in real asset markets.
While traditional asset-pricing theory focuses on
fundamentals—discounted future real cash flows—
there are alternative theories in which market imperfections play an important role. One such model,
originating with Allen and Gale (2000) and developed
more fully in Barlevy (2014), is based on the idea that
“speculators” borrow (without sufficient collateral)
from “banks” in order to buy risky assets. Banks are
unable to differentiate between “entrepreneurs” that
are safe to lend to and speculators that default if the
payoff from the asset is disappointing. In this model,
the price is pushed above its (social) fundamental value
because of the default option. We introduce a borrowing limit (a “haircut” in finance terminology) and show
that its magnitude impacts the size of the bubble. In
140
the one-period model we sketch explicitly, the interest
rate affects both the fundamental value and the size
of the bubble, but the channel for the latter is essentially the same as that for the fundamental value.
In the Allen–Gale–Barlevy model—unlike the
fundamental valuation model—leverage is absolutely
essential; there is no Modigliani–Miller theorem. Further,
the model’s indispensable constraint on short sales
makes it a model of “limits to arbitrage,” in the sense
of Shleifer and Vishny (1997). We consider another
model in this class—the “natural buyers” model, based
in our case (as in Miller, 1977; Geanakoplos, 2010; and
Simsek, 2013) on heterogeneous beliefs, the natural
buyers being those most optimistic about the dividend
payout of the asset. In general, the natural buyers borrow
in order to leverage their purchases of the asset. Increasing the effective demands of the natural buyers
raises the equilibrium price, an effect that may be
limited by high interest rates and possible credit constraints. This results in an asset price that is determined
by a combination of beliefs, interest rates, and borrowing limits. In particular, we use a simple model from
Barsky and Bogusz (2013) to illustrate the channels
through which the interest rate can affect the asset
price in this sort of model. The significant new interest
4Q/2014, Economic Perspectives
FIGURE 2
Yearly interest rate changes
label
2
1
0
–1
–2
–3
1985
’86
’87
’88
’89
’90
’91
Change in Bank of Japan discount rate
Change in long-term real bond yields
Change in long-term nominal bond yields
Sources: Barsky (2011), table 2.1, and sources cited therein.
rate channel that this sort of model adds to the mix is
what might be called an “affordability” effect. Higher
borrowing costs may make it impossible for collateralconstrained natural buyers to fully roll over loans used
to buy the asset, and the resulting drop in “cash in the
market” necessitates a lower level of the asset price.4
A key question is whether the models incorporating limits to arbitrage might produce larger effects of
temporary interest rate changes on asset prices than
are seen in the perfect markets model. Though we by
no means rule out that possibility, the simple examples
that we construct do not have this property. In the imperfect markets models we present, the effects of interest rates on asset prices never exceed the effects on
fundamental value.
Empirical motivation: Japanese stock prices,
1985–90
Figure 1 is a time-series plot of the raw monthly
data on the Bank of Japan’s nominal discount rate
and the Nikkei 225, perhaps the best-known index of
Japanese stock prices, divided by the core consumer
price index (all items, except food and energy). The
Federal Reserve Bank of Chicago
plot shows that the discount rate halved between late
1985 and early 1987. As the discount rate fell from 5 to
2.5, the Nikkei 225 increased by 50 percent. From
March 1987 until April 1989, the interest rate remained
constant at 2.5 percent, its lowest level prior to the deep
recession that followed the Nikkei’s collapse. During
this period, the Nikkei 225 increased a further 50 percent. From one perspective, this suggests the possibility
that the low interest rate environment was fueling an
asset boom. An alternative perspective might emphasize the fact that stock prices continued to rise rapidly
without a further lowering of the discount rates. For a
period of several months in 1989, the interest rate and
asset price rose together, an indication that the relationship between interest rates and asset prices is complex
and inconsistent with unidimensional causality in
either direction. As the discount rate rose by a further
1.75 percentage points between late 1989 and the
middle of 1990, stock prices declined by more than a
third. These rate increases in 1989 and 1990 correspond rather closely with the collapse of the Nikkei.
In particular, we see from figure 1 that the sharp rise
in the discount rate from 4.25 percent to 5.25 percent
141
in February 1990 corresponds to a drop of 14 log points
in the real Nikkei that same month. This, compounded
by subsequent drops in the Nikkei—as well as in various
indexes of land and housing prices—earned Yasushi
Mieno (rightly or wrongly) the distinction of being called
the “governor who pricked Japan’s bubble economy.”5
From mid-1991 through the middle of the subsequent year, the discount rate fell steadily as the stock
price continued to decline. Thus, figure 1 illustrates
the Allen–Gale notion of a so-called bubble that begins
in an environment of falling policy rates and ends in a
period characterized by sharp rate increases, but it also
indicates that the relationship between interest rates
and real asset prices is complex and requires a theoretical framework to facilitate meaningful discussions
regarding causality. We turn now to the question of
what theories might be relevant and what they might
teach us.
How do interest rates affect fundamentals?
As noted in the introduction, the long-term rate
features heavily in discussions of interest rate effects
on asset prices. While only the discount rate is under
the direct control of the central bank, figure 2 illustrates via a bar graph the association in annual data
between changes in the basic discount rate, nominal
and real long-term rates, and the Nikkei. In 1986, the
Bank of Japan (BOJ) cut its discount rate by 200 basis
points. In 1987, the discount rate was reduced by another 50 basis points. The discount rate was increased
sharply in 1989 and 1990. Figure 2 shows that BOJ
alterations of the nominal discount rate were associated
with changes in both nominal and real long-term bond
yields. We now turn to a consideration of several models
that might shed light on the effect of short- and longterm interest rates on asset prices.
The most orthodox account of the impact of interest rate changes on asset prices focuses on the effect
on the fundamental value of the asset—the expectation
of the asset’s stream of future cash flows discounted
by an appropriate discount factor that we will call ρ.
For now, we assume this is constant over time, though
we will relax this later. More precisely, if Pt is the
fundamental real asset price at time t and Dt+i is the
real dividend or service flow received by the asset
holder at time t + i, then
∞
Pt = Et ∑
i =1
Dt + i
.
(1 + ρ)i
Because of the uncertain nature of the cash flows
from real assets, they should be discounted not at the
riskless interest rate r, but at a higher rate that includes
142
a risk premium that we will call θ.6 Thus, the full discount rate ρ is the sum of the riskless interest rate r
(which is the primary focus of this article) and the
risk premium
ρ = r + θ.
It is both convenient and revealing to represent
the present value formula heuristically in a compact
form known universally as the Gordon formula,
Dt
= ρ − g , or in terms of the asset price,
Pt
Pt =
Dt
Dt
=
. 7 The Gordon formula is deρ− g r +θ− g
rived when ρ and g are constant over time, but what
we are interested in, of course, is the effect of changes
in r. Differentiating the Gordon formula will give the
correct answer for the effect of unanticipated and permanent changes in r. If, on the other hand, r follows
a stochastic process other than a random walk, a
somewhat more complicated approximate formula is
required (see below).
Let us begin with the effect on Pt of a permanent
change in the riskless rate r. We have
d log(Pt )
1
=−
.
drt
r +θ− g
This derivative becomes large as g gets close to r + θ.
Thus, the presence of the risk premium θ puts a damper on the extent to which a change in r can affect the
fundamental asset price. Since θ has historically been
quite large (Mehra and Prescott, 1985), the dampening
effect due to the presence of the risk premium is quantitatively important, and it will substantially reduce
the effect of changes in the interest rate.
So far, we have focused on permanent changes
in r. When r follows a stochastic process that renders
interest rate changes less than permanent, it remains
true that the presence of the risk premium reduces the
effect on asset prices of changes in the riskless rate.
In addition, however, the effect on the fundamental
value of a shock to r is further reduced relative to the
case when r is shocked permanently.8 A way to see
this is to work with the log-linear approximation to the
Gordon formula that holds when required rates of return and dividend growth rates are nonconstant over
time but follow stationary stochastic processes (the
Campbell–Shiller “dynamic Gordon growth model;”
see Campbell, Lo, and MacKinlay, 1997, pp. 260–267).
4Q/2014, Economic Perspectives
The formula reads
pt ≅
where γ =
∞
k
+ Et ∑ γ i[(1 − γ )dt +1+ j − rt +1+ j ] ,
1− γ
j =0
1
and μd–p is the population
1 + exp(µ d − p )
mean of the log dividend–price ratio. Here, the lowercase pt refers to the log of the price. Because our
concern is with the role of the interest rate, it will
∞
prove useful to define prt ≡ ∑ γ irt +1+ j , the part of
j =0
this expression for the log-linearized asset price that
depends on current and expected future short-term
interest rates.
Campbell, Lo, and MacKinlay (1997) offer as an
example the special case in which Et [rt +1 ] = r + xt
with xt = φxt −1 + ξt . In this instructive example, we
have
prt =
x
r
+ t .
1 − γ 1 − γφ
This provides a satisfying framework in which to
discuss the role of the persistence of interest rate disturbances. We see immediately that the effect of an
interest rate shock on the fundamental price is increasing
in the persistence parameter ϕ and the discount factor γ
(in fact they appear completely symmetrical). Note that
ϕ measures the persistence of innovations in the interest rate. As ϕ goes to one, we effectively replicate the
permanent shocks to r associated with the simple Gordon
formula shown at the beginning of this section.9
The intuition for the importance of interest rate
persistence is rather straightforward. The asset is presumed to be long lived, yielding cash flows for many
years to come. A highly persistent increase in the interest rate raises the rate at which even cash flows that
are expected to arrive far in the future are discounted,
reducing significantly the present value of the sum total of expected future cash flows. A transitory increase
in the interest rate, on the other hand, affects only the
present value of cash flows expected to arrive in the
near future. How about the role of the risk premium?
Since the discount factor γ is inversely related to the
mean dividend price ratio (which in turn is increasing
in the average risk premium), this can be regarded as
the reappearance in the dynamic context of the earlier
point that a large risk premium puts a damper on the
effect of an interest rate innovation on the asset price.
The intuitive reason is that a higher baseline required
Federal Reserve Bank of Chicago
return shortens the duration of the asset and reduces the
importance of interest rates in the more-distant future.
How persistent would interest rate shocks have
needed to be to rationalize the rise in the Nikkei between
1985 and 1986 entirely in terms of the drop in the discount rate? Translating the persistence parameter ϕ
into the half-life of the interest rate response to an exogenous shock of the appropriate magnitude and loosely
calibrating to the Japanese financial data from this period
suggest that the required degree of persistence corresponds to a half-life of about 13 years. If the change
in the interest rate came from a monetary policy shock,
this half-life is far too large to be plausible. If instead
of a shock to the policy rate we were dealing with a
drop in interest rates due to long-term capital flows,
13 years might be a quite reasonable half-life. Thus it
matters a great deal where interest rate shocks come
from. Contrary to first impressions, in the perfect markets present value model with rational expectations
monetary policy does not seem to be a good candidate
for explaining the large swings in the Nikkei during
this period.
Limits-to-arbitrage models with a nontrivial
role for leverage
Risk-shifting models
In the previous section, we examined the effect
of interest rates on fundamentals. Our analysis shows
that large fluctuations in asset prices due to exogenous interest rate movements cannot be explained entirely through fundamentals. However, a number of
asset-pricing models deviate from the standard Gordon
model. One such model is the monetary bubble model
we dismissed in the introduction. In this section, we
will examine two asset-pricing models that may yield
more dramatic results. In both the risk-shifting and
heterogeneity models, the price depends not only on
fundamentals, but also on the ability of agents to borrow funds. It seems plausible that interest rates may
have a larger effect in these models.
We sketch here a simple one-period version of a
model proposed by Allen and Gale (2000) and analyzed
in a much richer context by Barlevy (2014). This variety
of model arises from the moral hazard that is induced
when some agents are able to buy risky assets largely
with borrowed money and default in one or more lowpayout states, shifting the risk to lenders. In these
models, there is typically a kind of “bubble,” in the
sense that the price of the risky asset rises above its
social valuation due to the subsidy implicitly received
by the borrower as a result of the option to default. One
question we will ask is whether a sufficiently high
riskless interest rate can “pop the bubble.”
143
Suppose that there is a good state that occurs with
probability q, in which the asset pays a high liquidating
dividend of H at the end of the period. With probability
1 ̶ q, a bad state occurs in which the asset pays nothing
at all. In the benchmark model, the asset is purchased
by agents that we will call “speculators,” entirely with
funds borrowed from agents that we will call “banks.”
Speculators pay back the loan in the good state and
default in the bad one. Banks cannot identify speculators because they are pooled with a third set of agents
that we (following Barlevy, 2014) call “entrepreneurs.”
Though they would not lend to recognizable speculators, in the pooling equilibrium these risk-neutral banks
earn an expected return just high enough to compensate
for the “riskless rate” r yielded by an outside activity.
The one element we add to the existing models
is a borrowing limit measured in terms of a margin
or “haircut” h, so that speculators can borrow only
B = (1 – h) P per unit of the risky asset priced at P.
The (social) fundamental value F of the asset is
qD / (1 + r). With free entry to the pool of speculators,
the price of the asset will be this fundamental value
plus the expected value of the subsidy (1 – q) B. Thus
we have the equilibrium condition
P=
qD
+ (1 − q )(1 − h) P.
(1 + r )
The solution for the asset price, therefore, is
P=
qD
1
].
[
1 + r 1 − (1 − q )(1 − h)
Not surprisingly, in the case in which the entire
asset purchase can be funded by borrowing (that is, when
h = 0), this collapses to P =
D
. The speculator
(1 + r )
is willing to pay up to the full present value of the
dividend in the good state, because in the bad state the
purchase price is effectively refunded. This captures
the intuition in the popular description of moral-hazardfilled financial transactions as “heads I win, tails
you lose.”
Note that in this zero-haircut case, the level of
D
D
, that is, the price
1+ r
(1+ r )
qD
minus the fundamental
. Although one might
1+ r
the bubble is (1 − q )
imagine that a sufficiently high interest rate would deter
potential speculators and cause the price to revert to
144
its fundamental level, this is not the case in the model
described. These expressions show that a rise in the
interest rate lowers the magnitude of the bubble component in exactly the same proportion that it lowers
the fundamental value. However, there is another—
somewhat unexpected—channel by which a rise in
the interest rate can burst the bubble. Recall that the
speculator is able to borrow only because in the context of a pooling equilibrium lenders cannot distinguish
him from a productive entrepreneur. If the interest rate
rises above the marginal efficiency of investment, the
entrepreneurs will drop out of the loan market, revealing the identities of the speculators to the banks and
leaving them unable to borrow.
Natural-buyer (heterogeneous beliefs) models
Another way to analyze the possible role of leverage in major asset price fluctuations is with a model in
which agents have heterogeneous beliefs about fundamentals. Optimists face collateral constraints limiting
their ability to borrow, and pessimists face short-sales
constraints limiting their ability to sell the risky asset
to the optimists. Here, we examine a simple and highly stylized one-period model of heterogeneous beliefs
borrowed from Barsky and Bogusz (2013).
The model incorporates two types of agents, optimists and pessimists, and two goods, a final consumption good called “coconuts” and a coconut-yielding
asset called “trees.” Optimists and pessimists each receive an endowment of coconuts and trees. In equilibrium, optimists buy trees from the pessimists using
coconuts, some of which are borrowed from the pessimists. At the end of the period, trees yield coconuts
and agents consume. Optimists and pessimists differ
in their beliefs about the number of coconuts that trees
will yield at the end of the period, and pessimists—
which might be thought of as money market funds
that cannot afford to “break the buck”—additionally
have a particular concern with avoiding the downside
risk associated with defaults on loans that they make.
Aside from purchasing trees, agents can always store
coconuts to earn a riskless return f. They can also take
out loans at the interest rate r.
We define the following variables: Si is agent i’s
storage; bi is the amount borrowed; qi is the quantity of
trees purchased (negative if the trees are sold); Et(Y)
refers to agent i’s expected yield of trees at the end of
the period; and Ti refers to agent i’s initial endowment
of trees. The optimistic agents (i = 1), which might be
thought of as hedge funds, are risk neutral and thus have
expected utility U1 = s1(1 + f) ̶ b1(1+r)+E1[Y](qi + Ti).
The “money market” agents are principally concerned
with avoiding losses resulting from their lending and
4Q/2014, Economic Perspectives
FIGURE 3
Interest rate shock
price
Vb
1+ r
Vs
1+ r
quantity
will charge haircuts sufficient to render the loans riskless. Thus, in addition to the budget constraint and the
nonnegative storage constraint faced by both kinds of
agents, the borrower faces the collateral constraint
bi ≤
L j (Ti + qi )
1+ r
, where Lj is the worst state of the world
from the pessimists’ point of view. Since even in the
worst state of the world the lender is paid in full, loans
are entirely riskless, and this ensures that the return on
storage will be equal to the interest rate in equilibrium.
There are two channels through which movements
in the interest rate affect asset prices in this model. Which
channel the interest rate innovation operates through
depends on what set of constraints are binding. The
first way a rise in the interest rate affects the price is by
reducing the fundamental value of both the optimists
and the pessimists, since the perceived fundamental
can be written as Ei (Y ) . This channel is relevant in
1+ r
two different scenarios. The first is the case in which
the short-sales constraint binds for the pessimists but
the collateral constraint does not bind for the optimists.
In this scenario, the price of the asset will be the optimists’ fundamental value. The other scenario is when
the short-sales constraint doesn’t bind, but the collateral
Federal Reserve Bank of Chicago
constraint does bind. In this scenario, the price of the
asset will be the pessimists’ fundamental value.
With the right constraints, however, interest rate
movements can have rich effects in a heterogeneity
model through an entirely different mechanism. When
collateral constraints bind alongside short-sales constraints, a scenario we refer to as “cash in the market,”
the rise in the interest rate tightens the borrowing
constraint shown above and reduces the affordability
of the asset to the optimists. Since the optimists are
able to borrow less than they were before the interest
rate increase, the equilibrium asset price must fall. It
follows that no matter what combinations of constraints
are binding, a rise in the interest rate will reduce the
asset price. Figure 3 illustrates the response equilibrium
price to an exogenous interest rate shock.
Here, the red line corresponds to the optimists’
demand curve and the blue line corresponds to the
pessimists’ supply curve. Note that the optimists can
afford to pay their full valuation up to a certain quantity of the risky asset. This makes their demand curve
horizontal. At a certain point, the collateral constraint
begins to bind, and the optimists’ demand curve is bent
downward. The supply curve has a similar structure.
As long as the pessimists are the marginal holders of
the risky asset, the price will be their valuation and
the supply curve is horizontal. However, once the
145
pessimists hit their short-selling constraint and no
longer hold any of the risky asset, the trees can sell at
a price above the pessimists’ beliefs about the trees’
fundamental value.
The dashed line corresponds to the supply and
demand curves under a higher interest rate than before.
Looking at the buyers’ demand curve, we see there
are two effects of the interest rate. First, it lowers
fundamentals, since the optimists’ valuation is E (Y ) .
1+ r
However, there is an additional effect of increasing
the interest rate, which is to lower the amount of lending the pessimists are willing to do.
Note that while leverage is a sine qua non for nontrivial results in Allen and Gale (2000) and Barlevy
(2014), the natural-buyers model has content even in
its absence. When the binding constraints are such
that the equilibrium price is one of the agents’ full
valuation of the asset, there need not be any leverage
at all. However, changes in the degree of leverage make
the natural-buyers model a rich framework for studying large credit-induced movements in asset prices.
Cash-in-the-market pricing is, of course, a result of
leverage and the forces constraining it, and here the
degree to which the optimist is able to lever himself
has a crucial role to play.
In the cash-in-the-market region, we can also derive an expression for the effect (in logs) of a change
in the interest rate on the asset price when the buyer
is collateral constrained:
1
d ln(p)
=−
.
n(1 + r)
dr
(
+ 1)(1 + r)
b
n
Here,
is the ratio of risk capital to borrowing, which
b
in this model is the inverse of a measure of leverage.
This says the effect of an interest rate change on price
is increasing in leverage. Not surprisingly, the effect
of interest rate movements on asset prices is larger
when a greater fraction of the asset is paid for with
borrowed funds.
Thus, the heterogeneity model is suggestive of
two ways that exogenous interest rate movements
might cause fluctuations in asset prices: one through
146
fundamentals and another through the affordability
channel. It is sometimes argued that the “fire sales”
resulting from the sudden inability of natural buyers
to roll over the loans needed to fund their positions
can cause drops in asset prices that greatly exceed
fundamentals, and Geanakoplos (2010) constructs a
rather complex edifice with this property. In our oneperiod model, however, it is not hard to see that the
effect of the interest rate on market price never exceeds its effect on the fundamental value as perceived
by either the optimists or pessimists. For example, in
the cash-in-the-market region, the effect on the market price approaches the fundamental effect only as
the haircut approaches zero and the asset is funded
entirely through borrowing.
Conclusion
We have discussed several models in which exogenous changes in the riskless interest rate, collateral
constraints, or both have potentially major effects on
real asset prices. We began with models in which credit
constraints are absent and riskless interest rates impact
asset prices through their effects on fundamental value.
We found that in order to have large effects on fundamental real asset prices, large changes in the short-term
interest rate have to be highly persistent. In addition,
we showed that the presence of a substantial risk
premium also puts a damper on the effects of interest
rate changes on fundamentals.
We then moved to models with limits to arbitrage,
in which the extent to which agents are able to purchase
risky assets on margin is a key determinant of asset
prices. The simple models we studied did not suggest
that the asset price effects of interest rate changes are
substantially larger in this context than in the classic
model based on fundamentals. Geanakoplos (2010),
in the elaborate fire-sales model mentioned earlier, is
able to generate collapses in asset prices in excess of
those justified by worsened fundamentals in response
to certain sequences of bad news that necessitate
deleveraging. It appears possible, but by no means
certain, that some of the same considerations could
rationalize large responses of asset prices to changes
in interest rates. We are investigating this further in
ongoing research.
4Q/2014, Economic Perspectives
NOTES
We use the term “bubble” as it appears in popular discourse without necessarily adopting the academic criterion that asset prices
depart from fundamentals during these episodes.
1
Similar arguments appear in a number of speeches by former
Federal Reserve Board Chair Ben Bernanke, available on the
website of the Board of Governors of the Federal Reserve System,
www.federalreserve.gov.
2
Shiller’s paper is now 35 years old. Yet his “hypothesis 3” (that
there is a policy effectiveness interval beyond which anticipated
monetary policy cannot force real interest rates to depart from the
natural rate) is fully consistent with current New Keynesian dynamic stochastic general equilibrium (DSGE) models. The length
of this interval depends on the degree of price and wage rigidity
and can be as short as a few months or as long as several years. See
also Stanley Fischer’s introduction to the volume in which Shiller’s
paper is found (Fischer, 1980).
3
An additional alternative theory of asset pricing that warrants
mention, but is not taken up further in this article, is the standard
model of “rational bubbles.” The simplest textbook version describes an asset with no fundamental value that trades at a positive
price only because of the self-fulfilling rational expectation that the
asset can be resold to someone else in the future. The only restriction on the asset price is that it must offer the market return by
growing at the expected rate of interest. Thus, these models determine only the growth rate of the asset price, not its level, a point
4
Federal Reserve Bank of Chicago
acknowledged but unfortunately underplayed in a prominent recent
paper by Galí (2014). Galí argues—unconvincingly in our view—
that raising interest rates may well exacerbate rather than mitigate
bubbles. Since a satisfactory resolution of this and other policy
questions requires determining asset price levels, we do not discuss
this model further.
Mayumi Otsuma, 2012, “Mieno, governor who pricked Japan’s
bubble economy, dies,” Bloomberg, April 18, available at
www.bloomberg.com/news/2012-04-18/mieno-governor-whopricked-japan-s-bubble-economy-dies-at-88.html.
5
This premium, which compensates for systematic risk, is typically
represented as a covariance between the asset’s ex post return and
the return on a broad index, such as the market portfolio or aggregate consumption.
6
Note that it is necessary that ρ > g, or the above present value will
be infinite. There is an extensive technical literature about possible
worlds in which this condition does not hold.
7
The remainder of this paragraph, as well as the next one, draws
heavily on Barsky’s (2011) chapter on the Japanese bubble.
8
To see this, note that
9
dprt
d log( Pt )
1
1
1
=
≈
=
=−
.
dxt 1− γ exp(μ d − p ) ρ − g
drt
147
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