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Aggregate Labor Force Participation and
Unemployment and Demographic Trends

WP 19-08

Andreas Hornstein
Federal Reserve Bank of Richmond
Marianna Kudlyak
Federal Reserve Bank of San
Francisco

Aggregate Labor Force Participation and
Unemployment and Demographic Trends*
Andreas Hornstein

Marianna Kudlyak

FRB Richmond

FRB San Francisco

March 8, 2019
Working Paper No. 19-08
Abstract
We estimate trends in the labor force participation (LFP) and unemployment rates
for demographic groups differentiated by age, gender, and education, using a parsimonious statistical model of age, cohort, and cycle effects. Based on the group trends,
we construct trends for the aggregate LFP and unemployment rate. Important drivers
of the aggregate LFP rate trend are demographic factors, with increasing educational
attainment being important throughout the sample, ageing of the population becoming
more important since 2000, and changes of groups' trend LFP rates, e.g., for women
prior to 2000. The aggregate unemployment rate trend on the other hand is almost
exclusively driven by demographic factors, with about equal contributions from an
older and more educated population. Extrapolating the estimated trends using Census
Bureau population forecasts and our own forecasts for educational shares, we project
that over the next 10 years the trend LFP rate will decline to 61.1% from its 2018 value
of 62.7% and the trend unemployment rate will decline to 4.3% from its 2018 value of
4.7%.
Keywords: Labor Force Participation Rate. Unemployment Rate. Demographic
Composition. Age Effects. Cohort Effects. Educational Attainment.

*Any

opinions expressed are those of the authors and do not reflect those of the Federal Reserve Bank

of Richmond, the Federal Reserve Bank of San Francisco, or the Federal Reserve System. E-mail addresses:
andreas.hornstein@rich.frb.org, marianna.kudlyak@sf.frb.org.

Introduction

Researchers and policymakers are very interested in decomposing the unemployment rate
and the labor force participation (LFP) rate into their long-run trends and more transitory
cyclical components. Deviations of these rates from their long-run trends serve as a signal
of the labor market’s health. Most of this discussion proceeds at an aggregate level, but
unemployment and LFP rates di¤er systematically across demographic groups de…ned by
age, gender, and education.1 Unemployment rates tend to be lower for older and more
educated workers, LFP rates tend to be lower for older and less educated workers, and
historically, men tend to have lower unemployment rates and higher LFP rates than women.
The aggregate unemployment and LFP rates are functions of population-share weighted
sums of the demographic groups’rates. Similarly, the trend in the aggregate rates depends
on the weighted sum of the trends of the groups’rates. Given the di¤erences in the rates
across demographic groups, changes in demographic composition of the population change
the aggregate trend rate, even if the trend rates of the demographic groups remain unchanged.
In this article, we estimate trends for the LFP and unemployment rates of demographic
groups de…ned by age, gender, and education, and we use these trends, together with the
groups’population shares, to construct the trends of the aggregate LFP and unemployment
rate. We estimate the groups’trends using a parsimonious statistical model of age, cohort,
and cycle e¤ects, and we de…ne the trend as the sum of the age and cohort e¤ects. The
estimated trend in the aggregate unemployment rate declined almost monotonically from
7% in 1976 to 4.7% in 2017, and the cyclical deviations of unemployment from its trend
are substantial. The decline in the trend unemployment rate is almost exclusively driven by
demographic factors, about equal contributions from an older and more educated population.
The estimated trend in the aggregate LFP rate is hump-shaped with a peak in 2000, and
cyclical deviations from its trend tend to be small. The trend LFP rate is not only driven
by demographics, with increasing educational attainment being important throughout the
sample and ageing of the population becoming more important since 2000, but also by
changes of groups’trend LFP rates, e.g., for women prior to 2000.
We construct 10-year forecasts of the unemployment and LFP rate trend using population
projections for age-gender groups and a simple cohort model of age-gender contingent educational attainment. We take the population projections from the CBO (2018) and estimate
the educational attainment model for our sample. The trend projections for the aggregate
LFP and unemployment rate depend on the assumptions made for the model. Using our
preferred model, we project that over the next 10 years the trend LFP rate will decline
1

See our illustrative example in Section 2 below.

another 1.6 ppts from its current value of 62.7 percent, and the trend unemployment rate
will decline by 0.4 ppts from its current value of 4.7 percent. If instead we …x the age-gender
contingent educational shares at their 2018 levels, the LFP rate trend projection declines an
additional 0.8 ppts, but the unemployment rate trend declines 0.2 ppts less.
Our approach, building up the trend of the aggregate LFP rate from trend estimates of
group-speci…c age-cohort models, is not new. The existing literature has used age-cohort
models of demographic groups supplemented by a large number of additional controls, e.g.,
Aaronson, et al. (2014).2 Typically, the time variation of the age-speci…c rate of a demographic group is attributed to cohort e¤ects and the age e¤ect is taken as …xed. But
age-speci…c rates vary quite a bit more than can be accounted for by cohort e¤ects. For
example, older workers participate at higher rates in the labor market now than two decades
ago; young workers, 16-24 years old, participate at a much lower rate than in the 1990s. Augmenting the model with group LFP rates that depend on additional controls, such as school
enrollment, social security payouts, and others, helps capture the evolving age e¤ects. Our
alternative approach is to allow for time variation in age e¤ects while being explicit about the
stochastic processes that drive age and cohort e¤ects. Like Montes (2018), we di¤erentiate
our demographic groups by education, rather than including educational attainment as an
additional control.
Another paper closely related to our work is Barnichon and Mesters (2018), who estimate
the trend unemployment rate.3 They emphasize that the aggregate unemployment rate is
jointly determined by the trends in group unemployment and LFP rates, and that changes
in a demographic group’s trend unemployment rate are likely related to changes in its trend
LFP rate. For this reason, Barnichon and Mesters (2018) estimate a dynamic factor model
for labor force status transition rates, which jointly determine LFP and unemployment rates.
For demographic groups de…ned by age and gender, they argue that accounting for the joint
determination of unemployment and LFP trends signi…cantly a¤ects the estimated trend for
the aggregate unemployment rate. We will argue that, despite some notable changes for
groups’trend LFP rates, changes in population shares play a larger role for the aggregate
unemployment rate trend once one also takes into account demographic trends in educational
attainment.
The rest of the paper is structured as follows. Section 2 illustrates the systematic di¤er2

Related papers that use age-cohort models of demographic groups to study the aggregate LFP rate are

Aaronson, et al. (2006), Fallick and Pingle (2007), Balleer, Gomez-Salvador and Turunen (2009), Kudlyak
(2013), and Montes (2018). Recent work on the cyclicality of the aggregate LFP rate, ignoring demographic
aspects, includes Tuzemen and Van Zandweghe (2018) and Cairó, Shigeru, and Morales-Jiménez (2019).
3
For other papers that have studied the role of demographics for the aggregate unemployment rate see,
for example, Shimer (1998) and Elsby, Hobijn, and Sahin (2010).

ences of unemployment and LFP rates for a coarse decomposition of the U.S. population.
Section 3 describes the estimation framework, including notes on the data. Section 4 describes the results for the estimates of cycle and trend of the unemployment rate and LFP
rate across demographic groups. Section 5 describes the results for the trend of the aggregate
LFP rate and unemployment rate. Section 6 provides 10-year projections of the aggregate
LFP and unemployment rate based on a cohort model of educational attainment. Section 7
concludes.

Demographics of the Labor Market, 1979 and 2018

Before we provide a formal analysis of the di¤erences in labor market outcomes across demographic groups and how they change over time, Table 1 illustrates these di¤erences for
a coarse decomposition of the U.S. population aged 25 and older. We use the micro CPS
data to calculate annual averages of unemployment and LFP rates and population shares.
We split the population by age, younger than 55 years versus 55 years and older; gender,
men versus women; and education: high school or less versus some college or more. Data are
available for the years 1976 to 2018. In order to see how group rates have changed over time
absent business cycle e¤ects, we calculate the rates and population shares for the two years,
1979 and 2018, which represent the aggregate unemployment rate troughs at the beginning
and end of our sample.
Panel (A) illustrates that the unemployment rate is lower for more educated workers and
that it tends to be lower for older workers. Over time, it appears that the unemployment
rate has increased for men and for older women, but changes have been small, less than one
percentage point for any of the demographic groups. Panel (B) illustrates that the LFP rate
is lower for less educated workers, for older workers, and for women. Over time, the LFP
rate has decreased for men and increased for women, independent of education and age, and
changes have been noticeable, between 5 and 10 percentage points.
Finally, from Panel (C) we can see that over time the U.S. population has gotten older;
the share of those older than 55 years increased by about 7 percentage points, and more
educated, the share of those with more than a high school education increased by about
30 percentage points. Holding group unemployment rates and LFP rates …xed, the shift
towards an older and more educated population lowers the aggregate unemployment rate.
For the LFP rate, these same two demographic shifts have opposing e¤ects. In what follows
we will construct trend measures of the demographic groups’unemployment and LFP rates
and then attribute changes in the aggregate trends to changes in trend group rates and
demographic shifts.
3

Framework for Trend Estimates

In this section, we describe our simple model of trend and cycle for demographic groups.
Suppose we have observations on the outcome q (LFP rate or unemployment rate) and the
population share p of demographic group i at time t for age groups a or cohorts t

Qi = fqa;i;t : t = 1; : : : ; T and a = 1; : : : Ag
Pi = fpa;i;t : t = 1; : : : ; T and a = 1; : : : Ag :
For a particular demographic group, we write the observed outcome for its age groups as
a linear function of unobserved cohort e¤ects, x, age e¤ects, y, and cycle/time e¤ects, z,
qa;i;t = xa;i;t + ya;i;t + za;i;t + "qa;i;t with iid "qa;i;t

N 0;

2
a;i;q

(1)

We assume stochastic processes for age, cohort, and cycle e¤ects that are independent across
demographic groups and will drop the group index when no confusion can arise. In particular,
we assume that the age and cohort e¤ects follow random walks
x1;t = x1;t
xa;t = xa
ya;t = ya;t

+ "x1t with iid "x1t

1;t 1
1

N 0;

2
1x

for a > 1

+ "ya;t with iid "ya;t

N 0;

2
ay

for a

The initial cohort e¤ect of a new cohort is a random variation of the initial e¤ect of the
new cohort in the previous period. We assume that the cohort e¤ect remains …xed over the
lifetime of a cohort, that is, cohort e¤ects are …xed birth-year cohort e¤ects.
There is a common cyclical e¤ect to all age groups of a demographic group, and this
cyclical e¤ect can be latent or observed. For group unemployment rates, we assume that the
cyclical e¤ect is latent and follows an AR(1) process
zt = zt

+ "zt with iid "zt

N 0;

2
z

and k k < 1:

For a group’s LFP rate, we assume that we observe a noisy signal of the cyclical e¤ect,
in particular, we take the smoothed posterior estimate of the cyclical e¤ect for the group’s
unemployment rate as the signal.
For group unemployment rates, the impact of the cyclical e¤ect on an age group is simply
za;t =
The coe¢ cients

a zt :

capture systematic age-related di¤erences in the response to the common

cyclical component, and we normalize the impact on the …rst age group,
4

1.4 For group

Alternatively, we could have normalized the variance of the innovation to the common cyclical compo-

nent,

2
z.

LFP rates, we assume that the cyclical e¤ect is a moving average of the lagged observed
cyclical unemployment e¤ects, and that there are again systematic age-related di¤erences in
the response to the common cyclical e¤ect,
za;t =

n
X

s zt s :

s=0

For this speci…cation, there is no need to normalize .
The trend of a group’s outcome is the sum of the persistent age and cohort e¤ects,
T
= xa;t + ya;t :
qa;t

We apply our model to annual averages of observable outcomes and population shares,
and we aggregate our cohorts into age groups 16-19, 20-24, 25-34, etc. Thus the observation
equation for age group g that contains ages a 2 Ag is
1 X
qg;t =
xa;t + yg;t + zg;t + "qg;t :
#Ag a2A
g

The transition equations for annual cohort e¤ects remain as they are, but the transition
equations for the age and cycle e¤ects now apply to time-averaged age groups, not individual
age groups.5
We use maximum likelihood to estimate the parameters
cycle component is not observed, and the parameters

q;g ;

g;s

;

if the

if we observe

the cycle component. We estimate the unobserved state (age, cohort, and cycle) using the
Kalman …lter conditional on parameters

. For each demographic group de…ned by gender

and education, our estimation proceeds in two steps. First, we estimate the model for the
group’s unemployment rate assuming that the cycle e¤ect ztu is not observed. Second, we
estimate the model for the group’s LFP rate, taking the smoothed posterior estimate of the
group’s cyclical e¤ect for its unemployment rate as a noisy signal of the true e¤ect. We
use this procedure since LFP rates are highly persistent and we have not been successful in
estimating a stationary cyclical e¤ect directly.6
Given the random walk nature of our cohort and age group e¤ects, we de…ne the trend
of a group as the sum of the estimated age and cohort e¤ects
X
1
T
xa;i;t + yg;i;t :
qg;i;t
=
#Ag;i a2A
g;i

We will apply our model to the levels of unemployment and LFP rates. Alternatively, we could apply

the model to the log levels of the rates, which would mean that the calculate geometric averages for the age
groups.
6
In Appendix 8.1, we provide a more detailed description of the state-space model for a demographic
group’s LFP rate.

We use the smoothed posteriors for our estimates of the age and cohort e¤ects. The trend
of the aggregate LFP rate is then the population share weighted sum of the groups’trend
LFP rates
ltT =

T
;
pg;i;t lg;i;t

(2)

g;i

and the trend of the aggregate unemployment rate is
P
T
T
g;i pg;i;t lg;i;t ug;i;t
T
ut = P
T
g;i pg;i;t lg;i;t

(3)

For this purpose, we treat the population shares of di¤erent groups as exogenous.

3.1

Data and empirical implementation

The data in the analysis are constructed from the monthly basic …les of the Current Population Survey (CPS) from January 1976 to October 2018. We use the CPS labor status
variable to classify each member of the civilian noninstitutionalized population of age 16 or
older as employed, unemployed, or out of the labor force. We aggregate the individual micro
data into age-gender-education cells using the CPS-provided sampling weights. Finally, for
each cell we construct the unemployment rate, the LFP rate, and population shares.7
The age groups are 16-19, 20-24, 25-34, 35-44, 45-54, 55-64, and 65 years and older. The
educational categories for those aged 25 and older are less than high school, high school,
some college, and college or higher. Note that we do not di¤erentiate the young, those aged
24 or less, by education. Consequently, we have 44 age-gender-education cells.
We estimate our state-space model separately for young men and women, not di¤erentiated by education, and for each gender and education group for individuals aged 25 and
older. To forecast the trend, we need a forecast of the population shares and a forecast of
the trend unemployment and LFP rates. We use our estimates of the trend to construct
groups’trend forecasts. We use population forecasts to construct population shares by age
and gender.8 We then estimate a cohort-age model of educational attainment to construct
a forecast of the age-gender shares by education.
7

We use the micro data from the CPS. For the aggregation of individual observations, we use the composite

…nal weights used to produce BLS published labor force statistics available from 1998 on and the …nal weights
otherwise. Our aggregate unemployment rate replicates the one published by the BLS for the full sample, but
there are some minor deviations, not exceeding 0.2 ppts, of our aggregate LFP rate from the one published
by the BLS for the years prior to 2002. Our data for 2018 represent the average for the months up to and
including October.
8
Speci…cally, we use the Bureau of the Census (2018) population projections based on the middle assumptions for future fertility, life expectancy and net immigration levels as of July 1 of each year. Downloaded
from Haver.

Demographics of Unemployment and LFP

We now apply our framework to the unemployment rates and LFP rates of the demographic
groups de…ned bye age, gender, and education and characterize their trend and cycle. We
…nd that group unemployment rates move together over the cycle, the least (most) educated
group is the most (least) volatile, and volatility declines with age. Group LFP rates are not
very cyclical, except for those 16-19 years old whose LFP rate is strongly procylical, and the
oldest college-educated group whose LFP rate is strongly countercyclical.
Removing the cyclical components we …nd not much of a change in the trend values
of the group unemployment rates. To the extent that group unemployment trends change
there is no uniform pattern to the contributions of age and cohort e¤ects. Turning to group
LFP rates, we …nd large and systematic changes in their trends: for those younger than 25
years, LFP rates declined for men and women alike, and for those 25 years and older, the
LFP rates of men declined and the LFP rates of women increased. Again, age and cohort
e¤ects contribute about equally to these changes, with cohort e¤ects being somewhat more
prevalent among women. While error bounds for estimates of group trend LFP rates are
quite narrow, trend unemployment rates are subject to large uncertainty.

4.1

Unemployment rates: cycle and trend

The common cyclical components of the di¤erent demographic groups’unemployment rates
move together and therefore with the aggregate unemployment rate. Figure 1 displays the
common cycle e¤ects by education for men (top panel) and women (bottom panel). With
respect to education, the least educated group (less than high school) is the most cyclically
volatile and the most educated group (college or higher) is the least cyclically volatile group.
The cyclical volatilities of the other two education groups and those younger than 25 years are
bracketed by these two groups. This characterization applies to both men and women, with
the womens’cycle e¤ects being somewhat less volatile. Finally, comparing across recession
episodes, we …nd that for all groups the cyclical unemployment factor reached a higher level
during the 2007-09 recession than in all other recessions. This is most noticeable for the
highest educated group, which has never moved much over the cycle except for the 2007-09
recession.
With respect to age, older groups are less cyclically sensitive than younger groups for
all education levels. Table 2 displays the estimated age-coe¢ cients on the common cyclical
factor by education for men (top panel) and women (bottom panel). For all groups, the
coe¢ cient on the cyclical factor declines gradually with age, independent of gender and education. For less educated men and women (less than high school) there is also a pronounced
7

step down for those aged 65 years and older.
We identify the trend unemployment rate of a group with the sum of that group’s age and
cohort e¤ects. From the 1980s to the present, trend unemployment rates tend to decline for
younger workers and increase for older workers. With few exceptions, we do not …nd large
changes in group trends. The changes we do observe are mostly less than 1 percentage point.
The exceptions are the most educated prime-age women, whose trend unemployment rate
declines by about 2 percentage points, and the least educated younger (older) males, whose
trend unemployment rate decreases (increases) by about 1.5 percentage points. Across the
di¤erent groups, age and cohort e¤ects both contribute to trend changes with no apparent
systematic pattern, except for the least and most educated prime-age women, where cohort
e¤ects seem to dominate.
In Table 3, we report changes in the groups’ trend unemployment rates from 1979 to
2018. This exercise replicates the exercise from Section 2, Table 1, with a …ner demographic
grid and a more systematic removal of cyclical e¤ects. The results from the two exercises
are broadly consistent.
For men, we …nd more increases than decreases in the trend unemployment rate across
age and education groups. Most of the changes are small, less than 1 percentage point,
except for the least educated males. For men with less than a high school education, the
trend rate declines for those between 25 and 44 years old but increases for those 55 and
older. Overall, age e¤ects seem to account for more of the trend changes, but there is no
clear pattern.
For women, we …nd the opposite than for men. There are more age-education cells where
the trend unemployment rate declines, but again, for most groups the changes are small,
except for the most educated prime-age women. For women aged 25 to 55 years with a
college education, the trend unemployment rate declined by 1 to 2 percentage points. Also,
unlike for men, cohort e¤ects seem to account for more of the trend changes across women’s
age-education groups. This is especially true for the most educated prime-age women and
for women aged less than 25 years, which we do not di¤erentiate by education.
We illustrate the role of cohort and age e¤ects in Figure 2 for the group of men with less
than a high school education. The top …ve lines plot the age e¤ects for our …ve age groups,
and the bottom line plots the cohort e¤ects.9 Clearly, age e¤ects are not constant over time.
There are short-run movements in the age e¤ects such as the increase for 25-34-year-old men
during the 1980s recession, and there are medium-run swings such as the decline and then
increase of the age e¤ect for men 65 and older. The short-run swings in age e¤ects suggest
9

We estimate age e¤ects for the duration of our sample starting in 1976, and we can infer cohort e¤ects

for those entering the sample prior to 1976.

that our estimation method does not always extract the cycle for all demographic groups.10
The medium-run swings re‡ect, in part, changes in the relative trends of di¤erent age groups.
Finally, there are also notable medium-run swings in cohort e¤ects, but movements in the
cohort e¤ects tend to be small relative to movements in age e¤ects.11 ;12 The estimates of
the age and cohort e¤ects are not very precise. The dashed lines in Figure 2 represent two
standard error bands based on the smoothed posterior variances of the unobserved states.
Note that the changes of age and cohort e¤ects over time usually stay within their initial
error bands. These wide error bands are not speci…c to the group of men with less than a
high school education but are common to all demographic groups.
The circles in Figure 2 illustrate how cohort and age e¤ects interact in the determination
of trend unemployment over the life cycle of a group that enters in 1976. Relative to those
who entered in 1960, this group has a permanently higher trend unemployment rate, about
1 percentage point. Over the next 10 years their trend rate …rst increases and then declines
with the 1980s recession. Once they turn 35 years old their trend unemployment rate declines,
but it is still about 1 percentage point higher than it was for that age group at the time the
cohort entered in 1976. At the time this cohort gets close to retirement, their age e¤ect is
about the same as it was for that age group in 1976.

4.2

LFP rates: cycle and trend

We now turn to the results for the trend in the LFP rate. In the estimation, we decompose
each groups’ LFP rate into a cyclical component, and cohort and age components. The
cyclical component is the groups’response to the estimated cyclical e¤ect from the unemployment rate model. We call LFP rates procyclical if they are negatively correlated with
the cyclical e¤ect, that is, the LFP rate increases as the cyclical unemployment rate declines.
In Table 4, we report the cyclical response of LFP rates for the di¤erent demographic
groups. The response is the sum of the coe¢ cients on the cyclical e¤ect with corresponding
standard deviations in parentheses. For almost all demographic groups, the LFP rate is procyclical. Exceptions are men older than 65 with at least some college education and women
10

We are hesitant to interpret the apparent cyclical responses in age e¤ects as persistent scarring of that

particular age group. Scarring would be better re‡ected in a change to the cohort e¤ect, but our estimation
imposes a …xed cohort e¤ect.
11
We have estimated a constrained version of our model with …xed age and cohort e¤ects, which is closer
to the approach of Aaronson et al (2014) and Montes (2018). The …t of the constrained model is signi…cantly
worse, and the inferred cohort e¤ects are extremely volatile.
12
The fact that we observe medium-run swings in age and cohort e¤ects makes us more comfortable with
not including deterministic drift terms in the laws of motion for age and cohort e¤ects.

older than 55. The response coe¢ cients tend to be small and not statistically signi…cant,
except for the 16-19 year old ones.
In Table 5, we report changes in the groups’trend LFP rates from 1979 to 2018. Like
Table 3 for the group unemployment rates, this exercise replicates the exercise from Section
2, Table 1, with a …ner demographic grid and a more systematic removal of cyclical e¤ects.
Given the limited cyclical volatility of LFP rates, it should not be surprising that the two
exercises yield similar results.
The largest trend decline of LFP rates occurs for those 16-24 years old. In particular, for
the very young, the trend LFP declines by more than 20 percentage points, most of it due
to cohort e¤ects.
For men, the trend LFP rates decline for all age and education groups, with the largest
declines among those younger than 65 and with less than a college degree. For example, for
those with a high school degree, trend LFP rates decline by about 10 percentage points. LFP
rates of men 65 and older or with a college degree decline by much less. For most groups the
age e¤ect is the largest contributor to the decline in trend LFP rates, but there are also a
number of notable cohort e¤ects among prime-age males with a high school or some college
education.
For women, the trend LFP rates increase for almost all age and education groups with
the largest increases among those with more than a high school education. For example, for
those with a college degree, LFP rates increase between 8 and 16 percentage points. Relative
to men, cohort e¤ects are more often the largest contributor to the increase in trend LFP
rates, especially for college-educated women, but even for women age e¤ects remain the
main reason for trend changes in a large number of groups. Unlike for changes in trend
unemployment rates, age and cohort e¤ects mostly work in the same direction.
Figure 3 shows the estimated cohort and age e¤ects for women with a college education.
Clearly, age e¤ects are not constant over time: they …rst increase and then plateau or
decrease for all age groups. Increasing cohort e¤ects are important for women entering prior
to the 1980s, but afterward cohort e¤ects are relatively stable. Unlike for unemployment
rates, estimates of age and cohort e¤ects for LFP rates are relatively precise. Based on the
two standard deviation error bands, the dashed lines in Figure 3, the changes in age and
cohort e¤ects over time are signi…cant. And these narrower error bands for estimated age
and cohort e¤ects of LFP rates are common to all demographic groups.
The circles in Figure 3 again illustrate how cohort and age e¤ects interact in the determination of trend LFP over the life cycle of a group that enters in 1976. Relative to those who
entered in 1960, this group has a permanently higher trend LFP rate, about 7 percentage
points. Over the next 20 years, their trend rate increases noticeably, by about 10 percentage
10

points. That is, when they turn 45 years old, their trend LFP rate is about 10 percentage
points higher than it was for that age group in 1976. As usual the LFP rate declines once
this group reaches age 55.

Aggregate Unemployment and LFP Trend

We use the groups’ population shares and our estimates of the groups’ trend unemployment and LFP rates to construct the trend for the aggregate unemployment and LFP rate.
The relative contributions of group trend rates and demographic factors to the trends of the
aggregate unemployment and LFP rate di¤er. On the one hand, trends in group LFP participation rates and changes in the demographic composition all make important contributions
to the trend of the aggregate LFP rate. On the other hand, the trend for the aggregate
unemployment rate is almost exclusively driven by demographic changes and not by changes
in group trends for unemployment and LFP rates. Finally, the cyclical component of the
aggregate LFP rate is substantially less volatile than the one of the aggregate unemployment
rate, and the two cyclical components are negatively correlated.
We …rst discuss the aggregate LFP rate, which is a simple population share weighted
average of the group LFP rates, equation (2). The aggregate LFP rate increased from 1976
on, reaching its peak just prior to 2000 and declined thereafter; Figure 4. The actual LFP
rate does not deviate much from trend; it tends to fall below trend in recessions and then
stays below trend for most of the expansion. The exceptions are the expansions following
the 1984 and 2007-09 recessions when the estimated LFP rate trend noticeably exceeded the
actual values for an extended period of time. We estimate the 2018 trend LFP rate to be
at 62.7 percent, about half a percentage point lower than the CBO (2018) estimate of the
potential LFP rate in 2018.13
We construct two counterfactuals to demonstrate how the trend of the aggregate LFP
rate depends on changes in the trend LFP rates of demographic groups and the demographic
composition of the population, Figure 4. For the …rst counterfactual, we …x the population
shares by age, gender, and education at their 2000 values, and use our estimates of the
LFP rate trends for each demographic group. The counterfactual retains the hump-shaped
path, that is, it re‡ects the increasing trend for LFP rates of women prior to 2000, and the
13

In Appendix 8.1, we consider two alternative estimators of the trend LFP rate based on two measures

for which we assume that we know the true cyclical e¤ect. The measures consist of the smoothed posterior of
the groups’cyclical unemployment e¤ect and the groups’observed average unemployment rate. The results
are very similar and well within the two standard deviation error bands of about +/-0.4 ppts around our
baseline trend.

declining trend for LFP rates of young groups post-2000, but it peaks earlier, just before
1990.
Prior to 2000, the counterfactual exceeds the trend path, which means that from 1976
to 2000 the population composition was changing towards groups with higher participation
rates. The main driver of this process was increased educational attainment, as we can see
from a comparison with our second counterfactual. For this counterfactual, we …x the educational distribution conditional on age and gender at its 2000 values, and we use the actual
population shares by age and gender and the trend group LFP rates. This second counterfactual remains close to the …rst counterfactual, that is, changes in the age distribution
alone have a minor impact on the trend aggregate LFP rate prior to 2000. Taking the actual
population shares, that is, introducing the actual educational attainment of the population,
then moves the second counterfactual to the trend. Thus, increasing educational attainment
is a major source for the increase of the aggregate LFP rate trend prior to 2000.
A similar comparison of the trend with the two counterfactuals for the post-2000 period
shows that increased educational attainment counteracted much of the widely discussed impact of population ageing on the LFP rate. Whereas the ageing of the population contributes
to an almost 3 percentage point decline of the trend LFP rate by 2018, the di¤erence between the blue and green lines, the increased educational attainment, eliminates 2 percentage
points of this gap.
We now proceed to the aggregate unemployment rate, which is a nonlinear function
of population share weighted group unemployment and LFP rates, equation (3). Figure 5
displays the actual unemployment rate and our trend estimate. Despite the apparent stability
of the trends in group unemployment rates, we observe a noticeable monotonic decline of the
trend in the aggregate unemployment rate: from 7% in 1976 to 4.6% in 2018. Relative to
estimates of group trend unemployment rates, the uncertainty associated with the estimate
of the aggregate trend unemployment rate is smaller. The two standard deviation error
bands of the trend unemployment rate estimates from the beginning and end of sample do
not overlap. We note that our estimates of the trend unemployment rate are in line with the
CBO (2018) estimates of the natural rate at the end of the sample but substantially higher
at the beginning of the sample.14
Compared to the cyclicality of the LFP rate, the cyclical deviations of the unemployment
14

The CBO now uses two di¤erent methods to estimate the natural rate of unemployment, Shakleton

(2018). For the period prior to 2005 the estimated natural rate of unemployment is based on a Philips curve,
but starting in 2005, the natural rate of unemployment is calculated as a population weighted average of
demographic group unemployment and LFP rates that are …xed at their 2005 values. The latter approach
is similar to our construction of the trend unemployment rate.

rate from its trend are large. Given the decline in the trend unemployment rate, the deviation
of the actual unemployment rate from its trend value following the 2007-09 recession is
exceptional, even when compared to the early 1980s recession. By 2016, the unemployment
rate has returned to trend, and in 2018, the unemployment rate is signi…cantly below its
trend.
In order to understand the relative contributions of changes in the trends of group unemployment and LFP rates and population shares to changes in the trend of the aggregate
unemployment rate we construct three counterfactuals, Figure 5. For the …rst counterfactual, we use our estimates of the groups’ trend unemployment rates and …x the groups’
trend LFP rates and population shares for age, gender, and education at their 2000 values.
This counterfactual is quite stable for the sample period, that is, the limited changes in the
groups’trend unemployment rates that we discussed in the previous section have only a small
impact on the aggregate trend. For the second counterfactual, we replace the …xed trend
LFP rates from 2000 in the …rst counterfactual with their estimated time path. Despite the
large changes in the trends of group LFP rates, this has only a limited impact on the trend of
the aggregate unemployment rate. For the third counterfactual, we use our estimates of the
groups’trend unemployment and LFP rates together with the actual population shares by
age and gender, but we …x the distribution of educational attainment conditional on age and
gender at its 2000 values. This third counterfactual starts out at 6.3% in 1976 and ends at
5% in 2017, that is, the ageing of the population accounts for 1.3 percentage points or about
half of the decline in the trend unemployment rate. The remaining part, the move from
the third counterfactual to trend, then re‡ects the contribution from increased educational
attainment of the population since 1976 and accounts for about two-…fths of the decline
in the trend unemployment rate. To summarize, the decline in the trend of the aggregate
unemployment rate is mainly driven by demographic factors, about half of it attributable
to the population getting older and most of the rest attributable to the population getting
more educated.15
15

Shimer (1998) has argued that changes in labor force shares of groups de…ned by education may a¤ect the

trend unemployment rates of these groups. Thus separating out the contributions coming from changes in
trend unemployment rates from the changes in labor force shares may not be possible. Our decomposition of
the trend unemployment rate suggests that this is not much of an issue. First, even with the large changes in
education shares, the estimated trend unemployment rates of these groups have not changed much. Second,
as we show in Appendix 8.2, the long-run correlations between unemployment rates and labor force shares
for groups de…ned by education are very small, mostly insigni…cantly di¤erent from zero.

Unemployment and LFP Rate Projections

Given the role that demographic trends play in the determination of the trend in the aggregate LFP rate and unemployment rate, it seems reasonable to project the future path of these
aggregate trends based on demographic projections. For this purpose we need population
projections by age and gender and projections of future educational attainment. We take the
…rst projection from the CBO (2018) and we project future educational attainment based
on an estimated simple cohort model for age-gender conditional education shares. Using our
preferred model of educational attainment, we project that over the next 10 years the trend
LFP rate will decline another 1.6 ppts from its current value of 62.7 percent, and the trend
unemployment rate will decline by 0.4 ppts from its current value of 4.7 percent.
Educational attainment is de…ned for those 25 years and older, and we model the behavior
of age-gender contingent education shares, we;g , that is, the fraction of an age-gender group
g that has education level e. We use the …ve age and four education groups consistent with
our cohort models of unemployment and LFP. We assume that the education shares for age
groups evolve according to a cohort model with no age e¤ects
we;g;t =

1 X
w
we;a;t + "w
e;g;t with iid "e;g;t
#Ag a2A

N 0;

2
w;g

we;25;t =
we;a;t =

e;0

+ we;25;t

e;g

+ we;a

+ "e25;t with iid "w
e;25;t

1;t 1

N 0;

w
+ "w
e;a;t with iid "e;a:t

N 0;

2
e;0
2
e;1

for a 2 Ag :

For each education group, we assume that there is an initial value for those who enter at
age 25. The initial cohort e¤ect of a new cohort is a random variation of the initial e¤ect of
the new cohort in the previous period. The measured education shares for age groups can
change over time, possibly due to di¤erential death rates across age groups, see, for example,
Aaronson and Sullivan (2001). The model is estimated separately for each gender-education
group using maximum likelihood and the Kalman-…lter.16
We estimate two versions of this model. First, we estimate the model with no deterministic drift,

e;j

= 0. Figure 6 displays the smoothed posterior estimates of cohort e¤ects at the

time a cohort enters the sample and at the end of the sample or at the time the cohort exits
the sample. It is apparent that the education shares display systematic drift: in a cohort,
the shares of those with more than a high school education tend to increase over time and
the shares with a high school education or less tend to decrease over time. We therefore
estimate the model allowing for nonzero drift terms,
16

e;j

6= 0, which we use for our baseline

For the projections we use the estimated models for those with a high school education or higher and

de…ne the education share for those with less than a high school education as the residual.

projection.17
Table 6 shows how the trend projections for the aggregate LFP and unemployment rate
depend on the assumptions made for the evolution of future educational attainment. The
third column displays the impact of ageing, assuming that the age-contingent education
shares remain at their 2018 values. For this assumption, the trend LFP rate is predicted
to decline by another 2.5 ppts over the next 10 years. The …rst and second column show
how predicted increases in educational attainment dampen some of that decline. The second
column shows that taking into account the built-in higher educational attainment in recent
cohorts will cut that decline by about 0.4 ppts, even if cohort education shares remain …xed.
The …rst column contains projections from our preferred baseline model. It shows that
taking into account increasing educational attainment within cohorts will cut that decline
by another 0.5 ppts. The fourth column shows that our baseline forecast predicts a smaller
decline of the trend LFP rate over the next 10 years than does the CBO (2018) forecast. As
for the trend unemployment rate, our preferred baseline model predicts a further decline by
0.3 ppts, unlike the CBO natural rate which is forecast to remain unchanged. Taking into
account the predicted increase in educational attainment increases the predicted decline over
the next 10 years.

Conclusions

We estimate trends for the LFP and unemployment rates of demographic groups de…ned by
age, gender, and education, and we use these trends, together with the groups’population
shares, to construct the trends of the aggregate LFP and unemployment rate. We characterize a group’s LFP and unemployment rate using a parsimonious statistical model of age,
cohort, and cycle e¤ects, and we de…ne the trend as the sum of the age and cohort e¤ects. In
contrast to alternative approaches, our model of group-speci…c trends features time-varying
age e¤ects, which we estimate using standard data …ltering techniques.
The estimated trend in the aggregate unemployment rate declines almost monotonically
from 7% in 1976 to 4.7% in 2018, and is almost exclusively driven by demographic factors with
roughly equal contributions from an older and more educated population. The estimated
trend in the aggregate LFP rate is hump-shaped with a peak in 2000. In contrast to the
trend unemployment rate, the trend LFP rate is not only driven by demographics, with
increasing educational attainment being important throughout the sample and ageing of the
population becoming more important since 2000, but also by changes of groups’trend LFP
17

Even though the estimates for the drift terms tend to be not signi…cant, the drift terms capture the
systematic movements in the education shares. The coe¢ cient estimates are in Appendix 8.3, Table 7.

rates, e.g., for women prior to 2000.
We construct 10 year projections of the aggregate trends, using a cohort model of agegender contingent educational attainment. The cohort model predicts an increase in educational attainment in the next 10 years. Combining Census Bureau population forecasts and
our forecasts for educational attainment, we project that over the next 10 years the trend
LFP rate will decline to 61.1% from its 2018 value of 62.7%, and the trend unemployment
rate will decline to 4.3% from its 2018 value of 4.7%.

References
[1] Aaronson, Daniel, and Daniel Sullivan. 2001. Growth in Worker Quality. Economic
Perspectives, Federal Reserve Bank of Chicago, 2001 Q4.
[2] Aaronson, Stephanie, Tomaz Cajner, Bruce Fallick, Felix Galbis-Reig, Christopher
Smith, and William Wascher. 2014. Labor Force Participation: Recent Developments
and Future Prospects. Brookings Papers on Economic Activity, Vol. 2014: 197-275.
[3] Aaronson, Stephanie, Bruce Fallick, Andrew Figura, Jonathan Pingle, and William
Wascher. 2006. The Recent Decline in the Labor Force Participation Rate and Its Implications for Potential Labor Supply. Brookings Papers on Economic Activity, Spring
2006, 69-134.
[4] Balleer, Almut, Ramón Gómez-Salvador, and Jarkko Turunen. 2009. Labor Force Participation in the Euro Area: a Cohort Based Analysis, European Central Bank, Working
Paper Series, No. 1049.
[5] Barnichon, Regis, and Geert Mesters. 2018. On the Demographic Adjustment of Unemployment, The Review of Economics and Statistics, 100(2): 219-231.
[6] Congressional Budget O¢ ce. 2018. An Update to the Economic Outlook: 2018 to 2028.
https://www.cbo.gov/publication/54318
[7] Bureau of the Census. 2018. Population Projections.
https://www.census.gov/programs-surveys/popproj.html
[8] Cairó, Isabel, Shigeru Fujita, and Camilo Morales-Jiménez. 2019. Elasticities of Labor
Supply and Labor Force Participation Flows. FRB Philadelphia Working Paper 19-03.
[9] Daly, Mary C., Osborne Jackson, and Robert G. Valetta. 2007. Educational Attainment,
Unemployment, and Wage In‡ation. FRBSF Economic Review 49-61.
[10] Elsby, M., Hobijn, B. A. Sahin. 2010. The Labor Market in the Great Recession. Brooking Panel on Economic Activity, April 2010
[11] Kudlyak, Marianna. 2013. A Cohort Model of Labor Force Participation, Federal Reserve Bank of Richmond Economic Quarterly 99(1): 25–43.
[12] Montes, Joshua. 2018. CBO’s Projection of Labor Force Participation Rates, Congressional Budget O¢ ce, Working Paper 2018-04.
17

[13] Müller, Ullrich, and Mark Watson. 2018. Long-Run Covariability. Econometrica 86,
775–804.
[14] Shackleton,
Using

CBO’s

Robert.

2018.

Forecasting

Estimating
Growth

and

Model.

Projecting
CBO

Working

Potential

Output

Paper

2018-03.

https://www.cbo.gov/publication/53558
[15] Shimer, Robert. 1998. Why Is the U.S. Unemployment Rate so Much Lower? NBER
Macroeconomics Annual, vol. 13, 1998, pp. 11-61.
[16] Tuzemen, Didem, and Willem Van Zandweghe. 2018. The Cyclical Behavior of Labor
Force Participation. FRB Kansas City Working Paper No. 18-08.

Appendix

8.1

Cyclical e¤ects for the LFP rate

The state space model for a demographic group’s LFP rate is characterized by the measurement equations
qg;t

1 X
=
xa;t + yg;t +
#Ag a2A
g

z~t = zt + "zt~ with iid "zt~

n
X

s zt s

+ "qg;t with iid "qg;t

N 0;

2
g;q

s=0

N 0;

2
z~

;

where z~ is a noisy signal of the cyclical e¤ect, and the state transition equations
x1;t = x1;t
xa;t = xa
yg;t = yg;t
zt =

We estimate the parameters
cyclical e¤ect ( ;

2
z)

+ "x1t with iid "x1t

1;t 1

2
1x

N 0;

for a > 1

+ "yg;t with iid "yg;t

+ "zt with iid "zt
2
g;q ;

2
1x ;

2
gy ;

N 0;
N 0;

2
gy

for g

2
z

and take the estimated parameters for the

from the group’s unemployment rate model as given. Furthermore, the

noisy signal for the cyclical e¤ect is the smoothed posterior estimate for the group’s cyclical
unemployment e¤ect, and we take the average variance of the smoothed posterior as the
variance of the noise term

2
z~.

As a robustness check we consider two alternative models of the cyclical e¤ect for the
LFP rates. The implied estimates for the aggregate LFP rate are displayed in Figure 7. The
…rst alternative assumes that the smoothed posterior mean estimate of the group’s cyclical
unemployment e¤ect represents the true cyclical e¤ect without noise. The implied trend for
the aggregate LFP rate is almost the same as for our baseline estimate, but unsurprisingly
the standard error band is smaller. For the second alternative, we note that the groups’
average unemployment rates are highly correlated with our estimated cyclical e¤ects for the
groups’unemployment rates. We therefore take the groups’average unemployment rates as
the observed true cyclical e¤ect for the groups’LFP rates. The LFP rate trend implied by
this alternative model tends to be close to the trend of the baseline model but is slightly
higher than the baseline trend for the most recent years.

8.2

Long-run correlation of unemployment rate and labor force
shares

Shimer (1998) argues that in the long run the unemployment rates of demographic groups
may be correlated with the labor force shares of these groups. If this is correct, then decomposing changes in the aggregate trend unemployment rate into changes coming from
group trend unemployment rates and changes coming from the labor force shares of the
groups are a pure accounting exercise and should not be interpreted as causal. He argues
that this is especially true for groups de…ned by education decomposition. For example, if
employers care about relative education or education is contaminated by unobserved quality,
then changes in education shares can a¤ect education contingent unemployment. In the end,
this is an empirical issue, and Daly et al. (2007) argue that there is no correlation between
unemployment rates and labor force shares for groups de…ned by age, gender, and education.
We extend the analysis of Daly et al. (2007) for our sample and calculate the long-run
correlations between unemployment rates and labor force shares using the approach of Müller
and Watson (2018). In Figure 8, we plot the posterior medians, and 67% and 90% con…dence
intervals for the long-run correlation between unemployment rates and labor force shares for
demographic groups de…ned by education, age, and gender. Most of the median correlations
are close to zero, and there is no group for which zero is not included in the 90% con…dence
interval.

8.3

A cohort model for education

Figure 9 illustrates the role of di¤erent assumptions on the dynamics of education shares for
medium-term projections of these shares. Here we plot the actual and predicted shares of
male high school (HS) graduates for the …ve age groups using our two models for the evolution
of education shares, together with the simple assumption that the education shares of agegender groups remain …xed at their last observed values. Clearly the predictions are quite
di¤erent. The evolution of education shares in the model without drift can be understood as
follows. Since prior to 2018 the HS share among the 25-34-year-olds was increasing, the HS
share of entering cohorts must have been increasing. Since the forecast applies the share of
the last cohort that entered to all future entering cohorts, the average share of the age group
is forecast to increase. Since prior to 2018 the HS share of the 35-44-year-olds was lower than
that for the 25-34-year-olds, and going forward the cohorts in the 35-44-year-olds are being
replaced with cohorts from the 25-34-year-olds, the average share of the age group 35-44 is
forecast to increase. By an analogous argument, the average HS share of the 45-54-year-olds
is decreasing, since prior to 2018 that group’s HS was higher than for the 35-44-year-olds.
20

And similar arguments apply to the remaining age groups. Allowing for nonzero drift in the
education shares can amplify (25-34, 45-54, 55-64), dampen (65-79), or completely reverse
(35-44) these patterns.

Figure 1: Common Unemployment Cycle by Demographic Group

Note: Estimated cyclical e¤ect for the age group 16-24 (not di¤erentiated by education)
and the demographic groups de…ned by gender and education. Dashed lines denote two
standard error bands. The black line with circles is the aggregate unemployment rate.

Figure 2: Cohort and Age Effects for Unemployment Rate of Males with
Less Than High School Education

Note: Estimated cohort and age e¤ects for groups aged 25-79 years. The circles mark
the life cycle of a group that enters in 1976. Dashed lines denote two standard error
bounds based on the smoothed posterior estimates from the Kalman …lter.

Figure 3: Cohort and Age Effects for LFP Rate of Females with College
Education

Figure 4: Labor Force Participation Rate Trend

Note: The red line shows the estimated trend in the aggregate LFP rate. The blue
line …xes the population distribution by age, gender, and education at its 2000 values
and allows for variation of the LFP rate trend of each demographic group. The green
line …xes the education distribution conditional on age and gender at its 2000 values
and allows for variation of the LFP rate trend of each demographic group, and the
population shares by age and gender. Dashed lines denote two standard error bounds
based on the smoothed posterior estimates from the Kalman …lter.

Figure 5: Unemployment Rate Trend

Note: The dark blue line …xes the trend LFP rate and the population shares by age,
gender, and education at their 2000 values and allows for variation of the unemployment rate trend of each demographic group. The green line …xes the population shares
at their 2000 values and allows for variation of the unemployment rate and LFP rate
trends of each demographic group. The light blue line …xes the education distribution
conditional on age and gender at its 2017 values and allows for variation of the unemployment rate and LFP rate trends and the population shares of each demographic
group. The red line is the trend and allows for variation in the trend values of the
unemployment rate and LFP rate and the population shares of demographic groups.
The red dotted line is the CBO natural rate estimate. The dashed red lines denote
a two standard deviation error band for the trend based on the smoothed posterior
estimates from the Kalman …lter.

Figure 6: Cohort Effects for Education Shares

Note: Solid lines denote the education share at the time a cohort enters the sample
and dashed lines denote the education share at the end of the sample or at the time
the cohort exits the sample.

Figure 7: Trend LFP Rate with Alternative Cyclical Indicators

Note: Solid colored lines represent estimates of the trend LFP rate using di¤erent
models of the cyclical e¤ect correction. The light dashed lines represent the two standard error bands. The cyclical e¤ects are de…ned speci…c to gender-education groups.
The blue line uses a demographic group’s average unemployment rate as the CI, and
the green and red lines use the estimated CI for the group’s trend unemployment rate
model. The green line takes the CI as known, and the red line assumes that the CI is
a noisy signal of the true CI.

Figure 8: Long-Run Correlations

Note: Posterior median (circle) and 67% (thick bar) and 90% (thin whisker) con…dence
intervals for the long-run correlation between a demographic group’s unemployment
rate and its labor force share.

Figure 9: Projections of Education Shares for Males with a High School
Education

Note: Solid lines prior to 2019 denote the actual education shares of the di¤erent age
groups. The light solid lines denote projections for future education shares assuming that the education shares remain unchanged at their 2018 values or they evolve
according to the cohort model without (+) or with (o) deterministic drift.

Table 1: Unemployment, Labor Force Participation, and Demographics
(1)

(2)

(3)

(4)

Men, 25-54 Men, 55+ Women, 25-54 Women, 55+
(A) Unemployment Rate
1979
HS or less

4.4

3.4

6.4

3.4

More than HS

2.1

3.9

2.8

2018
HS or less

4.5

4.1

5.5

3.2

More than HS

2.5

2.7

2.8

3.2

(B) LFP Rate
1979
HS or less

93.0

42.9

58.6

21.7

More than HS

96.4

60.5

70.3

30.7

2018
HS or less

84.3

40.3

63.3

25.9

More than HS

92.1

50.3

80.6

41.7

18.1

12.0

22.5

16.2

More than HS

13.3

3.4

11.0

3.5

2018
HS or less

11.1

8.2

9.2

10.1

More than HS

17.3

11.5

19.9

12.8

Note: Table shows data for 1979 and 2018, years with unemployment troughs at the
beginning and end of sample; population 25 years and older.

Table 2: Cyclical Response of Unemployment Rates
(1)
(2)
(3)
(4)
(5)
All

HS <COL COL+

<HS

Male
20-24

0.75
(0.04)

35-44

0.91

45-54

0.75

0.80

0.95

(0.06) (0.04)

(0.04)

(0.08)

0.67

0.81

0.95

(0.06) (0.04)

(0.04)

(0.08)

0.64

0.73

0.91

(0.05) (0.04)

(0.04)

(0.10)

0.33

0.61

0.74

(0.06) (0.04)

(0.08)

(0.13)

0.77

0.91

(0.07) (0.05)

(0.04)

(0.08)

0.65

0.70

0.88

(0.06) (0.04)

(0.05)

(0.08)

0.60

0.73

0.85

(0.05) (0.04)

(0.06)

(0.09)

0.43

0.72

0.73

(0.05) (0.06)

(0.08)

(0.13)

0.82

55-64

0.69

65+

0.28

Female
20-24

0.66
(0.03)

35-44
45-54
55-64
65+

0.85
0.73
0.48
0.27

Note: The age groups 16-24 are not di¤erentiated by education. The cyclical response
of age groups 16-19 and 25-34 is normalized to one. Standard deviations in parenthesis.

Table 3: Change of Trend Unemployment Rates from 1979 to 2018
(1)
(2)
(3)
(4)
(5)
All

<HS

<COL

COL+

Male
16-19

0.1
(-0.0, 0.1)

20-24

-0.0
(0.0, -0.0)

25-34
35-44
45-54
55-64
65-79

-1.8

-0.3

-0.7

-0.5

(-0.9, -0.8)

(-0.0, -0.3)

(-0.4, -0.3)

(-0.0, -0.5)

-0.8

0.4

0.2

-0.1

(-0.7, -0.1)

(-0.0, 0.4)

(-0.3, 0.5)

(-0.0, -0.1)

0.5

0.0

0.4

(-0.1, 0.6)

(0.0, 0.5)

(-0.3, 0.3)

(-0.0, 0.4)

1.6

0.6

0.2

0.6

(0.6, 1.0)

(0.0, 0.6)

(-0.0, 0.2)

(0.0, 0.6)

1.4

0.4

0.1

0.8

(0.5, 0.9)

(0.0, 0.4)

(0.3, -0.1)

(0.0, 0.8)

Female
16-19

-0.6
(-0.7, 0.1)

20-24

-0.9
(-0.8, -0.2)

25-34
35-44
45-54
55-64
65-79

-1.0

-0.4

-1.0

-2.2

(-0.9, -0.1)

(-0.0, -0.4)

(-0.1, -0.8)

(-1.6, -0.5)

-0.6

0.3

-0.0

-1.7

(-0.9, 0.3)

(-0.0, 0.3)

(-0.1, 0.1)

(-1.5, -0.2)

0.0

0.1

-0.2

-0.7

(0.1, -0.1)

(-0.0, 0.1)

(-0.1, -0.2)

(-0.9, 0.2)

0.6

0.1

0.3

(1.1, -0.5)

(0.0, 0.1)

(-0.0, 0.4)

(-0.3, 0.6)

1.2

0.2

0.9

0.3

(0.6, 0.6)

(0.0, 0.2)

(0.0, 0.9)

(0.2, 0.1)

Note: For each demographic group, we calculate the percentage point change in the
trend unemployment rate from 1979 to 2018. The …rst (second) number in parentheses
denotes the contribution from the cohort (age) e¤ect. The age groups 16-24 are not
di¤erentiated by education. The sample period
32 is 1976-2018.

Table 4: Cyclical Response of LFP Rates
(1)
(2)
(3)
(4)
(5)
16-24

<HS

HS <COL COL+
Male

Sum of CE
20-24

-0.55

-0.18

-0.29

-0.30

-0.66

(0.11) (0.10) (0.09)

(0.12)

(0.27)

0.54

0.49

0.18

(0.72) (0.40)

(0.38)

(0.31)

0.68

1.04

0.41

(0.91) (0.44)

(0.55)

(0.33)

2.00

1.32

0.05

(0.96) (0.69)

(0.67)

(0.50)

0.56

-0.32

-1.00

(0.42) (0.43)

(0.47)

(0.66)

-0.33

-0.46

-0.01

(0.13) (0.13) (0.14)

(0.23)

(0.20)

0.61

0.73

-0.35

(0.35) (0.30)

(0.58)

(1.35)

0.40

0.35

1.53

(0.30) (0.29)

(0.60)

(2.89)

0.86

-0.31

-1.00

(0.28) (0.35)

(0.52)

(3.70)

0.14

-0.39

1.98

(0.20) (0.25)

(0.49)

(4.30)

0.43
(0.16)

35-44

0.98

45-54

1.65

55-64

1.69

65-79

0.07

Female
Sum of CE
20-24

-0.58

-0.41

0.32
(0.16)

35-44
45-54
55-64
65-79

0.58
0.61
0.32
0.10

Note: For each demographic group, we take the estimated cyclical e¤ect (CE) from
the cohort model of the unemployment rate of that group as a noisy signal of the
underlying CE. The response is proportional to the weighted sum of the current and
two lags of the CE. The …rst row displays the sum of the coe¢ cients on the CE with
corresponding standard deviations in parenthesis. The remaining rows display the
response coe¢ cients of the di¤erent age groups in a demographic group. The response
of the youngest group in each demographic group is normalized to one. The age group
16-24 is not di¤erentiated by education. The
33 sample period is 1976-2018.

Table 5: Change of Trend LFP Rate from 1979 to 2018
(1)

(2)

(3)

(4)

(5)

16-24

<HS

<COL

COL+

Male
16-19

-28.4
(-19.2, -9.2)

20-24

-13.3
(-16.5, 3.2)

25-34
35-44
45-54
55-64
65-79

-10.0

-9.3

-5.8

-2.7

(-1.9, -8.2)

(-6.1, -3.3)

(-3.7, -2.1)

(-0.0, -2.7)

-6.1

-9.1

-5.9

-2.5

(-1.3, -4.8)

(-5.4, -3.6)

(-3.2, -2.7)

(-0.0, -2.5)

-10.1

-9.9

-6.5

-3.1

(-1.6, -8.5)

(-3.9, -6.1)

(-1.9, -4.7)

(-0.0, -3.1)

-6.6

-9.0

-8.2

-4.0

(-2.3, -4.3)

(-2.3, -6.7)

(-1.1, -7.1)

(-0.0, -4.0)

-1.0

-4.6

-2.1

-1.8

(-1.7, 0.6)

(-1.3, -3.3)

(-0.4, -1.7)

(0.0, -1.8)

Female
16-19

-21.2
(-9.7, -11.4)

20-24

-1.2
(-6.6, 5.5)

25-34
35-44
45-54
55-64
65-79

0.9

4.2

9.0

8.3

(-1.2, 2.1)

(-5.4, 9.5)

(-0.8, 9.8)

(1.6, 6.6)

-0.6

1.6

9.5

10.5

(1.0, -1.6)

(-0.1, 1.6)

(3.8, 5.7)

(5.1, 5.4)

4.0

7.2

13.8

11.2

(2.5, 1.5)

(6.0, 1.2)

(8.0, 5.8)

(7.8, 3.5)

2.8

8.2

11.9

16.0

(2.2, 0.6)

(7.4, 0.8)

(8.5, 3.4)

(8.3, 7.7)

0.9

1.2

5.9

11.8

(1.0, -0.1)

(3.7, -2.5)

(4.8, 1.1)

(5.1, 6.7)

Table 6: The LFP and Unemployment Rate Trend Projections, 2019-2028
(1)

(2)

(3)

(4)

Education forecasted, Education forecasted, Education …xed CBO (2018)
model with drift

model with no drift

at 2018

projections

LFP Rate Trend
2018

62.7

63.1

2019

62.5

62.4

62.9

2020

62.3

62.2

62.1

62.8

2021

62.1

62.0

61.8

62.6

2022

61.9

61.8

61.6

62.4

2023

61.8

61.5

61.3

62.2

2024

61.6

61.3

61.1

61.9

2025

61.5

61.1

60.8

61.7

2026

61.3

60.9

60.6

61.5

2027

61.2

60.8

60.4

61.3

2028

61.1

60.6

60.2

61.1

Unemployment Rate Trend
2018

4.7

4.6

2019

4.6

2020

4.6

2021

4.5

4.6

2022

4.5

4.6

2023

4.5

4.6

2024

4.4

4.5

4.6

2025

4.4

4.5

4.6

2026

4.4

4.5

4.6

2027

4.3

4.5

4.6

2028

4.3

4.4

4.5

4.6

Note: All projections of the aggregate LFP and unemployment rate use the CBO
medium-fertility projections for the population size of age-gender groups. We project
education shares of age-gender groups using (1) the cohort model with nonzero drift,
(2) the cohort model with no drift, and (3) the …xed 2018 education shares. The
fourth column represents the CBO (2018) projections for the potential LFP rate and
the long-run natural rate of unemployment.

Table 7: Education Share Drifts
(1)
(2)
(3)
(4)
HS <COL COL+

<HS

Male
Age 25
Age 26-34
Age 35-44
Age 45-54
Age 55-64
Age 65-79

-0.21

-0.17

0.06

0.34

(0.18) (0.27)

(0.28)

(0.22)

0.66

0.15

0.34

(0.56) (0.85)

(1.06)

(0.65)

-1.13

-0.06

0.57

(0.46) (0.70)

(0.86)

(0.53)

0.56

0.28

-0.06

(0.37) (0.56)

(0.69)

(0.43)

-0.66

-0.03

0.33

(0.30) (0.46)

(0.56)

(0.35)

0.14

0.17

0.06

(0.16) (0.25)

(0.31)

(0.19)

-0.71
0.25
-0.48
0.11
-0.22

Female
Age 25
Age 26-34
Age 35-44
Age 45-54
Age 55-64
Age 65-79

Note: The drift terms

-0.20

-0.50

0.04

0.69

(0.06) (0.28)

(0.39)

(0.24)

-0.17

0.11

0.69

(0.31) (1.01)

(1.30)

(0.62)

-0.63

0.17

0.30

(0.25) (0.82)

(1.05)

(0.51)

-0.04

0.12

0.36

(0.20) (0.66)

(0.85)

(0.41)

-0.37

0.16

0.02

(0.17) (0.54)

(0.69)

(0.33)

-0.13

0.06

0.11

(0.09) (0.30)

(0.38)

(0.18)

-0.26
-0.14
-0.20
-0.01
0.06

are estimated for the entering cohort at age 25 and for the age

groups of continuing cohorts. The coe¢ cients are de…ned with respect to percentage
shares, with standard deviations in parenthesis.

Full text of Working Papers (Federal Reserve Bank of Richmond) : Aggregate Labor Force Participation and Unemployment and Demographic Trends, Working Paper 19-08 : Working Paper

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