Employment growth: cyclical movements or structural change?
Rissman, Ellen R.
Introduction and summary
The Federal Reserve, in its policy analysis, must carefully weigh
incoming data and evaluate likely future outcomes before determining how
best to obtain its twin goals of employment growing at potential and
price stability. It is tempting to regard high or rising unemployment as
a sign of a weak economy. And, normally, a weak economy is one with
little inflationary pressure and, therefore, room for expansionary
monetary policy to stimulate growth. But unemployment is influenced by
more than simply aggregate conditions. in a dynamic economy that
responds to changing opportunities, some industries are shrinking while
others are growing. Labor must flow from declining industries to
expanding ones. This adjustment takes time. it takes time for employees
in declining sectors to learn about new opportunities in other
industries, acquire necessary skills, apply for job openings, and
potentially relocate. And during this period of adjustment, the
unemployment rate rises as waning industries lay off workers. Thus, the
unemployment rate may increase or decrease, even though the aggregate
state of the economy remains stable, simply because the labor market
adjusts to shifting patterns of production.
For policymakers, it is essential to decipher what portion of a
rising unemployment rate is due to a cyclical slowdown in which many
sectors of the economy are simultaneously affected, as opposed to a
structural realignment in production in which particular sectors of the
economy are affected. The two factors ideally should result in different
policy responses. If unemployment is rising because of a weak economy,
the textbook response is for the Fed to take a more accommodative policy
stance. If, instead, the unemployment rate is rising because of
underlying compositional shifts in employment, an easing of monetary
policy may discourage declining industries from contracting by keeping
them marginally profitable, impeding the adjustment process.
Furthermore, this policy may also encourage inflation as employers
across a broad spectrum of industries compete for scarce labor
resources. Thus, comprehending the underlying sources of movements in
the unemployment rate is more than just a theoretical exercise: It has
practical implications for monetary policy.
As a first step toward evaluating the role of structural change, I
need to be able to measure it. Lilien (1982) suggests a dispersion
measure that is a weighted average of squared deviations of industry
employment growth rates from aggregate employment growth. Abraham and
Katz (1986) argue that Lilien's measure does not properly account
for cyclical shifts in employment across industries, instead conflating
cyclical variation with structural change. When aggregate economic
conditions are weak, certain sectors are affected more than others
because demand for their products is more cyclically sensitive, but as
soon as economic conditions improve, these sectors will also recover
more quickly. The Lilien measure more accurately captures both cyclical
variation in employment responses and structural changes in the
composition of employment across industries, making it impossible to
disentangle the importance of the two effects on the measure of
dispersion.
The sectoral shifts hypothesis has been revisited more recently by
Phelan and Trejos (2000) and Bloom, Floetotto, and Jaimovich (2009).
Phelan and Trejos (2000) calibrate a job creation/job destruction model
to data from the U.S. labor market to suggest that permanent changes in
sectoral composition can precipitate aggregate economic downturns.
Bloom, Floetotto, and Jaimovich (2009) examine the effect of what they
term "uncertainty shocks" on business cycle dynamics, arguing
that increases in uncertainty lead to a decline in economic activity in
affected industries, followed by a rebound. Increasing uncertainty, in
their view, causes firms to be more cautious in their hiring and
investment decisions and impedes the reallocation of capital across
sectors. Thus, structural change and recessions are simultaneous events,
implying that distinguishing structural change from cyclical downturns
is problematic.
As noted by Bloom, Floetotto, and Jaimovich (2009), structural
realignment (in other words, sectoral reallocation) may be concurrent
with economic downturns. Businesses on the brink ofdownsizing or
disappearing altogether may find that they are tipped over the edge
during a recession. To the extent that whole industries are affected,
the downturn will then occur at the same time as sectoral reallocation.
Recessions are followed by expansions, whereas sectoral reallocation
tends to have a long-term impact on the composition of employment.
Therefore, shifts in production that are cyclical in nature tend to be
transitory, but those that are the result of structural realignment are
more long lasting.
Previous studies, including Loungani, Rush, and Tave (1990) and
Rissman (1993), have employed a variety of techniques to distinguish
between sectoral shifts that are driven by structural change and those
that are driven by cyclical swings. Loungani, Rush, and Tave (1990), for
example, suggest that stock market prices efficiently reflect the future
stream of business profits. They employ measures based on stock prices
to create a dispersion measure that reflects structural shifts rather
than short-term cyclical fluctuations. In Rissman (1993), I note that
structural change is long lasting, whereas cyclical swings are of a
shorter duration. I use this observation to distinguish between
compositional shifts in employment that are due to cyclical
fluctuations, which are short term, and those that are due to structural
realignment, which are long term. Rissman's (1993) measure cannot
be produced in real time because current changes in employment patterns
may be either temporary or permanent. Thus, this measure offers little
guidance for policymakers who need to make decisions based on current
information. In contrast, the Loungani, Rush, and Tave (1990) measure
has the benefit of being based on stock price data that are available at
high frequency. However, stock prices are noisy, and it may be difficult
to disentangle the persistence of shocks from them. In particular, a
given decline in a stock price may be a reflection of short-run factors
or may instead be interpreted as a small permanent decline in an
industry's fortunes. Having a supplementary employment-based
measure that does not require the use of leading data, in contrast to
Rissman (1993), would provide a useful benchmark.
This problem of optimally inferring the current state has been
widely studied in economics and in related statistical literature. Stock
and Watson (1989) employ the Kalman filter to create an index of
coincident economic indicators. They formally operationalize the idea
that the business cycle "refers to co-movements in different forms
of economic activity, not just fluctuations in GNP [gross national
product]." (1) Stock and Watson (1989) examine several different
economic time series, including employment, and try to extract a common
factor. I use the same approach here to identify a common factor in the
labor market based on how it affects employment in different industries.
This common factor is permitted to have different loadings in each
industry, giving some context to the notion that some sectors are more
cyclically sensitive than others. This framework has the added benefit
of creating a common factor that can be interpreted as a measure of the
employment cycle, focusing only on the industry cross section of
employment growth. This is particularly relevant, since it is widely
thought that the labor market typically lags the business cycle. Thus, a
measure of the business cycle based only on cross-sectional employment
growth helps clarify the relationship between more traditional measures
of the cycle, such as real gross domestic product (GDP) growth, and
employment growth. This measure of the cycle may help shed light on the
phenomenon of the jobless recoveries that we have experienced during the
two most recent expansions following the contractions ending in 1991:Q1
and 2001:Q4. Furthermore, the model is based upon quarterly data, giving
policymakers a more timely tool for evaluating the relative importance
of cyclical and structural factors to the labor market than other
measures. There is little reason why the model cannot be estimated on a
monthly basis as well. Finally, the model provides some insight into the
sources and magnitude of structural change in the economy.
To summarize the results, most industries exhibit cyclical
employment growth, which accounts for the majority of the variation in
employment in those industries. However, structural shifts are also
important and account for most of the variation in employment growth in
the finance, insurance, and real estate (FIRE) sector and in the
government sector. Perhaps not surprisingly, given the well-chronicled
declines in the housing market, the construction industry has undergone
a structural reduction in employment after a notably long period of
structural expansion. Recent structural employment declines in finance,
insurance, and real estate are particularly large when compared with
past episodes. Careful measurement of structural change suggests that
sectoral reallocation may have been on the rise in the past few
quarters. However, structural realignment cannot account for much of the
recent increase we have observed in the unemployment rate.
In the next section, I examine employment growth for nine
industries comprising most of total nonfarm employment. Then, I
introduce the estimation framework. I present my results using this
framework. Finally, I develop a measure of sectoral reallocation and
investigate its impact on the unemployment rate.
Industry employment growth
The U.S. Bureau of Labor Statistics collects detailed industry
employment data for workers on nonfarm payrolls. Over the years the
industry classification system has changed to reflect the changing
industrial composition of the economy. Because of this, it is difficult
to compare earlier industry data, which were collected using the
Standard Industrial Classification (SIC) System, with more recent
industry data, which were collected using the North American Industry
Classification System (NAICS). For example, nine new service sectors and
250 new service industries are recognized in the NAICS data, but they
are not in the SIC data. The problem of comparability over time is less
of an issue with the broadest industry aggregates. Earlier estimates of
sectoral reallocation were computed using SIC data. To facilitate
comparison with earlier work, the NAICS data were converted as closely
as possible to be consistent with SIC classifications.
Figure 1 shows annualized quarter-to-quarter employment growth from
1950 through the second quarter of 2009 for the following nine sectors:
construction; durable manufacturing; nondurable manufacturing;
transportation and utilities; wholesale trade; retail trade; finance,
insurance, and real estate; services; and government. (2) Business cycle
contractions, as determined by the National Bureau of Economic Research
(NBER), have been shaded for reference. The figure also shows the
average annual industry employment growth rate over this period.
Given the current focus on the housing market as the source of some
of our economic problems, it is interesting to examine employment in the
construction sector. Employment growth in construction is highly
volatile and, not surprisingly, quite cyclical as well. Construction
employment growth appears to decline in advance of business cycle peaks
and reaches its bottom at or just past the trough of a recession.
Although employment growth in construction was above average during the
most recent expansion, which peaked in December 2007, the strong
employment growth does not appear abnormally large in comparison with
earlier recoveries. Nonetheless, the most recent quarters show a very
strong drop in construction employment, surpassing even the large
declines of the mid-1970s. It is an open question as to what part of
this observed decline in construction is structural in nature and what
part is cyclical (and will therefore rebound when aggregate conditions
improve).
The finance, insurance, and real estate sector tells a somewhat
different story. Like most industries, FIRE experiences reduced
employment growth during recessions. Yet, while FIRE's employment
growth has dipped below average during recessions, historically,
employment in this sector has very rarely declined. The steep drop in
employment in the early 1990s seems to be the harbinger of a change in
employment growth in this sector, with average employment growth falling
below the 3 percent growth of earlier decades. Furthermore, the steep
job losses of the past few quarters are unprecedented in the past 60
years. The key question is whether the sharp employment declines are
cyclical, with employment likely to rebound as the economy moves into
the expansionary phase of the business cycle, or structural and,
therefore, likely to linger. Later, I will show that employment growth
in this industry tends to be highly persistent, suggesting that these
declines are likely to last for quite a while. Yet, these job losses in
FIRE may not transfer directly into increased unemployment. Since
workers in FIRE may have skills that are more easily transferred to
other areas, they may be more likely to find employment in expanding
sectors; therefore, the adjustment out of this sector may not involve
much of an increase in the unemployment rate.
The services sector is also interesting to consider. At one time,
this sector was thought to be the engine of employment growth, as can be
seen by the high average employment growth rates since the 1950s. Yet,
more recently, employment growth here has been weak as well. And
employment growth in services over the past couple of quarters is the
lowest it has been since the late 1950s.
Taken as a whole, these data suggest several important facts.
First, average growth rates differ across industries, with some sectors
of the economy barely growing at all, such as durable and nondurable
manufacturing, and others exhibiting more robust growth, such as FIRE
and services. Second, some industries are far more volatile than others.
Construction, durable and nondurable manufacturing, and transportation
and utilities have wide swings in employment growth compared with the
other industries. Third, unsurprisingly, employment growth is highly
cyclical, dropping during contractions and rising during expansions.
However, some industries appear more cyclically sensitive than others.
Focusing on the period since the onset of the current recession in the
fourth quarter of 2007, employment has declined precipitously in most
industries. If most of the recent declines in employment growth are
cyclical, then employment growth should rebound and return to normal as
the economy moves into the expansionary phase of the business cycle.
However, a portion of the recent declines in employment growth may be
the result of other factors such as structural realignment in the
economy. If this is indeed the case, then it may indicate that some
industries will likely experience more permanent reductions in
employment or employment growth. An accurate assessment of whether
employment data are driven by the business cycle or structural change is
important for formulating policy and for projecting the future path of
employment growth.
[FIGURE 1 OMITTED]
Table 1 shows the same employment growth data for the entire sample
in the first row and divided into ten-year increments in the subsequent
rows. (3) Construction employment has averaged 2.0 percent annualized
quarterly growth over the entire sample period. However, over the past
decade the average quarterly growth in construction employment has been
-0.42 percent. Durable and nondurable manufacturing have experienced
large declines in employment over the past decade, with job losses or
stagnant growth since the late 1970s. Employment growth has been weak
for the past decade in transportation and utilities, as well as in
wholesale and retail trades. In fact, all sectors have exhibited weaker
average employment growth over the past decade than they have averaged
over the past 60 years. (4)
A model of industry employment growth
The discussion in the previous section suggests that industry
employment growth, in addition to having a tong-term average, can be
described by two additional components: a cyclical component and an
idiosyncratic component that reflects other noncyclical factors. Let
1) [g.sub.it] = [a.sub.i] + [C.sub.it] + [X.sub.it],
where g,, is employment growth in sector i at time t, i - l ..., 1,
and t - 1 ..., T; [a.sub.i], is average employment growth in the
industry; [C.sub.it], is the cyclical portion of industry employment
growth (and it varies across time and industry); and [X.sub.it], is the
idiosyncratic part of industry employment growth (and it also varies
across time and industry). This construction is similar to the problem
analyzed by Stock and Watson (1989), in which they noted that individual
aggregate time series depend upon a common cyclical component and an
idiosyncratic component.
As currently specified, equation 1 cannot be estimated because
there is no way to distinguish between the cyclical and idiosyncratic
components. To address this issue, I assume that the cycle is a common
component affecting all industries. However, the cycle may have a
differential impact across sectors. Specifically,
2) [C.sub.it] = [b.sup.1.sub.i] [C.sub.t] + [b.sup.2.sub.i]
[C.sub.t-1],
where [b.sup.1.sub.i] and [b.sup.2.sub.i] are parameters indicating
the sensitivity of the i-th sector to current and lagged values of the
business cycle. Furthermore, it is assumed that the cycle itself follows
a second-order autoregressive process with:
3) [C.sub.t] = [[phi].sub.1] [C.sub.t-1] _ [[phi].sub.2]
[C.sub.t-2] + [u.sub.t].
Here [u.sub.t] is independent and identically normally distributed
with unit variance. The [[phi].sub.1] and [[phi].sub.2] are unknown
parameters that are to be estimated. Setting [[sigma].sup.2.sub.u] = 1
determines the scale of the business cycle. For example, an alternative
estimate of the cycle [C.sup.*.sub.t] = [delta] [C.sub.t], would result
in estimates of the b, values scaled by 1/[delta]. Two sets of estimates
are possible, both [C.sub.t], and -[C.sub.t], depending upon the initial
values of the parameters. For ease of interpretation, it is assumed that
the business cycle has a positive impact on durable manufacturing
employment growth.
The idiosyncratic component of industry employment growth
[X.sub.it], is assumed to follow an AR (1) process. Specifically,
4) [X.sub.it] = [[gamma].sub.i] [X.sub.it 1] + [[epsilon].sub.it]
where [[gamma]sub.i] , is a sector-specific parameter that
indicates the degree of persistence of sectoral shocks. It is assumed
that the [[epsilon].sub.it], values are uncorrelated over time and
across industries. Note that E([[epsilon].sub.it]) = 0 and E
[[epsilon].sup.2.sub.it] = [[sigma].sup.2.sub.i] for all i, t.
Furthermore, the [[epsilon].sub.it] values are assumed to be
uncorrelated with the cyclical shock [u.sub.t], for all i, t. This
specification allows for a common unobserved cycle that has a
differential impact across industries. It also permits structural change
to occur through the idiosyncratic component [X.sub.it]. Thus, changes
in an industry's employment growth are due to either cyclical
factors or factors that are specific to that particular industry.
Estimation is accomplished using the Kalman filter, details of
which are discussed in box 1. The state vector [[z.bar].sub.t], is given
by [[z.bar].sub.t], = [C.sub.t], [C.sub.t-1], [C.sub.t-2], [C.sub.1t],
[X.sub.2t], ..., [X.sub.It]'. The Kalman filter algorithm enables
estimates of the state vector [[z.bar].sub.t], and the underlying
parameters to be estimated. These parameters include the values for
[a.sub.i], [b.sup.1.sub.i], [b.sup.2.sub.i], [[gamma].sub.i],
[[sigma].sub.i], and [[phi].sub.1] and [[phi].sub.2]. The shocks
[u.sub.t] and [[epsilon].sub.it] can also be obtained for i = 1 ..., I
and t = 1, ..., T.
The Kalman filter is a way of optimally updating the underlying
state vector as new information becomes available each quarter. A Kalman
smoothing algorithm is used to optimally backcast for final estimates of
the state vector and model parameters.
Estimation results
The estimate of the cycle [[??].sub.t], obtained from the Kalman
filter exercise is shown in figure 2. (5) The 2x standard error bands
are also shown. These standard error bands indicate whether the estimate
is significantly different from zero. Defining a recession as the period
during which the estimated employment cycle is significantly below zero,
the estimate indicates that we are currently in the midst of a deep
recession. The cyclical point estimate in 2009:Q1 measures the recession
to be the most severe since 1950. However, because of parameter
uncertainty, this point estimate is not significantly worse than earlier
recessions in a statistical sense. The estimate for 2009:Q2 indicates
that aggregate employment continues to deteriorate, albeit at a slower
pace.
Employment failed to rebound as quickly as other sectors of the
economy during the two most recent recoveries following the NBER-dated
recessions of 1990-91 and 2001. This lack of improvement in the labor
market, termed the "jobless recovery," drew commentary from
both the popular press and economists. As computed here, the
employment-based measure of the cycles indicates that the contractions
lasted seven and eleven quarters, respectively--significantly longer
than the length of the NBER's contractionary periods of three and
four quarters, respectively--indicating that the labor market
experienced a delayed recovery relative to other measures of economic
activity that the NBER's Business Cycle Dating Committee examines
in determining business cycle peaks and troughs. Shortly after the 2001
recession, Groshen and Potter (2003) suggested that the abnormally slow
recovery was the result of sectoral reallocation (in other words,
structural factors) rather than cyclical factors. The evidence provided
here shows that the slow growth in employment was likely attributable to
weak cyclical activity. (6) Using a similar methodology, Aaronson,
Rissman, and Sullivan (2004) reach a similar conclusion. Furthermore,
findings presented in the next section regarding the role of [X.sub.it]
appear to show that sectoral shocks do not play a major role in
accounting for unemployment. Recall that the employment cycle is defined
by co-movement in employment growth rates across many industries
simultaneously. As such, the model interprets the lengthy employment
contraction during these two episodes as broad-based; that is, a wide
spectrum of industries are negatively affected, and the contraction is
not concentrated in only a few industries, as would be the case if
sectoral reallocation were the underlying cause of low aggregate
employment growth.
BOX 1
The Kalman filter
The Kalman filter is a statistical technique that is useful in
estimating the parameters of the model specified in equations 1-4
(pp. 44-45). In addition, the Kalman filter enables the estimation
of the processes [u.sub.t], and [[epsilon].sub.it], and the
construction of the unobserved cyclical variable C, and the
idiosyncratic components [X.sub.it]. The Kalman filter consists of
a state equation and a measurement equation. The state equation
describes the evolution of the possibly unobserved variable(s) of
interest, [[z.bar].sub.t], while the measurement equation relates
observables g, to the state. The vector [[g.bar].sub.t], is related
to the m x 1 state vector, [[z.bar].sub.t], via the measurement
equation:
B1) [[g.bar].sub.t] = B [[z.bar].sub.t] + D [[[eta].bar].sub.t] + H
[[w.bar].sub.t],
where t = 1, ..., T; B is an N x m matrix; [[[eta].bar].sub.t], is
an N x 1 vector of serially uncorrelated disturbances with mean
zero and covariance matrix [I.sub.N]; and [[w.bar].sub.t], is a
vector of exogenous (possibly predetermined) variables with H and D
being conformable matrices.
In general, the elements of [[z.bar].sub.t], are not observable. In
fact, it is this very attribute that makes the Kahnan filter so
useful to economists. Although the [[z.bar].sub.t], elements are
unknown, they are assumed to be generated by a first-order Markov
process as follows:
B2) [[z.bar].sub.t]= A [[z.bar].sub.t-1] + F [[u.bar].sub.t] + G
[[w.bar].sub.t],
for t = 1 ..., T, where A is an m x rn matrix, F is an m x p
matrix, and [[u.bar].sub.t], is a p x 1 vector of serially
uncorrelated disturbances with mean zero and covariance matrix
[I.sub.g]. This equation is referred to as the state or transition
equation.
The definition of the state vector [[z.bar].sub.t], for any
particular model is determined by construction. In fact, the same
model can have more than one state-space representation. The
elements of the state vector may or may not have a substantive
interpretation. Technically, the aim of the state-space formulation
is to set up a vector [[z.bar].sub.t], in such a way that it
contains all the relevant information about the system at time t
and that it does so by having as small a number of elements as
possible* Furthermore, the state vector should be defined so as to
have zero correlation between the disturbances of the measurement
and transition equations, [[u.bar].sub.t] and [[[eta].bar].sub.t].
The Kalman filter refers to a two-step recursive algorithm for
optimally forecasting the state vector [[z.bar].sub.t], given
information available through time t - 1, conditional on known
matrices B, D, H, A, F, G. The first step is the prediction step
and involves forecasting [[z.bar].sub.t], on the basis of
[[z.bar].sub.t-1]. The second step is the updating step and
involves updating the estimate of the unobserved state vector
[[z.bar].sub.t], on the basis of new information that becomes
available in period t. The results from the Kalman filtering
algorithm can then be used to obtain estimates of the parameters
and the state vector [[z.bar].sub.t], by employing traditional
maximum likelihood techniques.
The model of employment growth proposed here can be put into
state-space form, defining the state vector [[z.bar].sub.t], =
[[C.sub.t], [C.sub.t-l], [C.sub.t-2], [X.sub.1t], [X.sub.2t], ...,
[X.sub.It]'. The Kalman filter technique is a way to optimally
infer information about the parameters of interest and, in
particular, the state vector [[z.bar].sub.t], which in this case is
simply the unobserved cycle, [C.sub.t], and its two lags and the
unobserved structural components [X.sub.it]. The cycle, as
constructed here, represents that portion of industry employment
growth that is common across the industries while allowing the
cycle to differ in its impact on industry employment growth in
terms of timing and magnitude through the parameters
[b.sup.1.sub.i] and [b.sup.2.sub.i]. The model is very much in the
spirit of Burns and Mitchell's (1946) idea of cycles entailing
co-movement, but the estimation technique permits the data to
determine which movements are common and which are idiosyncratic.
(2)
(1) The interested reader may obtain further details in Harvey
(1989) and Hamilton (1994).
(2) Stock and Watson (1989) employ the Kalman filter in
constructing leading and current economic indicators.
Table 2 provides parameter estimates with associated standard
errors. Focus on the coefficient estimates of the [b.sup.1.sub.i] values
(second column): All sectors of the economy are affected by cyclical
variation, as constructed here. However, the degree of cyclical
sensitivity varies across industries, with durable manufacturing
employment being the most contemporaneously cyclically sensitive,
followed by construction. The estimated intercept term [[??].sub.i]
(first column) is not significantly different from zero in construction,
durable manufacturing, nondurable manufacturing, and transportation and
utilities. The estimated parameter [[??].sub.i] (fourth column) gives
the degree of persistence of the idiosyncratic component. There is a
great deal of variation in the persistence of these idiosyncratic shocks
[[epsilon].sub.i], with finance, insurance, and real estate exhibiting
the most persistence.
Shocks to both services and transportation and utilities are not
statistically persistent. Furthermore, variation in these shocks differs
across industries, reflecting in part the variation in employment growth
noted in figure 1 (p. 43). Shocks to the idiosyncratic portion of
industry employment growth are more variable in construction, durable
manufacturing, and transportation and utilities than in other sectors of
the economy (fifth column).
[FIGURE 2 OMITTED]
BOX 2
Calculating the variance
Rewriting the model as a vector AR(1) process,
define
B3) [[y.bar].sub.t] = [[g.sub.1t],[g.sub.2t], ..., [g.sub.1t],
[C.sub.t],[C.sub.t-1],[C.sub.t-2],[X.sub.1t],[X.sub.2t], ...,
[X.sub.1t]]'.
Then
B4) [[y.bar].sub.t] = [PI][[y.bar].sub.t-1], + [[v.bar].sub.t],
which has a variance
B5) [OMEGA] = [PI][OMEGA][PI]' + [SIGMA].
This can be solved as:
B6) vec([OMEGA]) = [[I - [PI] [cross product] [PI]].sup.-1]vec
([summation]),
where [cross product] is the Kronecker product of [PI] with itself
and vec(x) is the vector constructed by stacking the
columns of an n x m matrix into a single column
vector. The matrix [PI] is given by
B7) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],
and the submatrices are given by
B8) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],
B9) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],
and
B10) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
The error term [[v.bar].sub.t] is given by
B11) [[v.bar].sub.t] = [[[epsilon].sub.1t],[[epsilon].sub.2t], ...,
[[epsilon].sub.1t],[u.sub.t],0,0,[[epsilon].sub.1t],[[epsilon].sub.2t],
..., [[epsilon].sub.1t]]'.
Using the model, it is straightforward to calculate the portion of
the variation in an industry's employment growth that is
attributable to cyclical activity and that which is attributable to
industry-specific factors. Details of the calculations are found in box
2, and the results are presented in table 3. As noted previously, some
industries exhibit much more variation in employment growth than others.
Construction and durable manufacturing are the two most volatile sectors
of the economy, exhibiting large swings in employment growth. By
comparison, the variance of employment growth in nondurable
manufacturing and transportation and utilities is about one-fifth that
of the most volatile industries, and the least volatile sectors have
about one-tenth the variance. The model attributes this volatility to
either cyclical variation or the idiosyncratic structural component.
Within construction, for example, about half the total variance in
employment growth stems from the structural component and half is the
result of cyclical variation. The cyclical component accounts for most
of the variation in employment growth in durable manufacturing,
nondurable manufacturing, transportation and utilities, wholesale trade,
retail trade, and services. In contrast, the structural component
carries the most weight in two sectors--FIRE and government.
In addition to examining the estimated cycle, it is also useful to
consider the idiosyncratic portion of employment growth. Figure 3 shows
the idiosyncratic component [X.sub.it] for each of the nine industries
from 1950:Q1 through 2009:Q2. Positive values suggest that employment
growth is stronger in these industries than explained by either normal
cyclical variation [C.sub.it] or long-term averages [a.sub.i]. Note that
the scale differs from one industry to the next. Upon closer inspection
of the construction sector (figure 3, panel A), the estimates suggest
that employment growth in this industry was higher than could be
explained from the business cycle or sectoral trends over most of the
1990s through the first half of 2006, when the trend abruptly reversed,
reflecting the unfolding crisis in the housing market. The sharp drop in
[X.sub.it], shows that construction employment seems to be taking a
bigger hit in the current episode than can be explained based on the
usual prior cyclical patterns for this sector. Perhaps even more
noteworthy is the recent experience in finance, insurance, and real
estate (figure 3, panel G) that shows a marked decline in recent years,
suggesting this sector is in the midst of a restructuring that is
unexplained by either the normal cyclical pattern or long-term trends.
How this downsizing of FIRE affects the unemployment rate is an open
question.
As table 1 (p. 44) suggested, the parameters of the model may
change over time. A test of parameter stability can be done using a
likelihood ratio test. The test statistic compares the log likelihood of
the model estimated using the full sample, from 1950:Q1 through 2009:Q2,
with the sum of the log likelihoods from the model estimated on two
smaller samples--the 1950:Ql-1983:Q4 period and the 1984:Q1-2009:Q2
period. The resulting test statistic is distributed [X.sup.2](46), and
its value is 498.22, rejecting the hypothesis that at normal confidence
levels the parameter vector is the same for the two smaller sample
periods.
Table 4 presents parameter estimates from the 1984:Q1-2009:Q2
sample period. In comparing the estimates found in table 2 (p. 47) and
table 4, there is some evidence of "The Great Moderation," (7)
with most of the coefficients on the contemporaneous estimate of the
cycle, [[??].sup.1.sub.i], being smaller in magnitude for the
1984:Q1-2009:Q2 sample period than for the entire sample. For example,
in the full sample a one standard deviation increase in the cycle
increased durable manufacturing employment growth by 3.7 percent per
annum, whereas in the 1984:Q1-2009:Q2 sample, the impact was a much
smaller 1.2 percent (see second row, second column of tables 2 and 4,
respectively). Furthermore, generally, estimates of the variance of the
idiosyncratic shocks in each industry, [[??].sub.i], are much smaller
for the 1984:Q1-2009:Q2 sample, with the exception of finance,
insurance, and real estate (compare the fifth column in tables 2 and 4).
For example, the estimate of the standard deviation in the shock to
construction is 20.2 for the entire sample, but a much smaller 4.3 for
the 1984:Q1-2009:Q2 sample. There is also evidence that for the
1984:Q1-2009:Q2 sample, industry shocks are more persistent, as can be
seen by comparing the estimated [[??].sub.i] values for the entire
sample and those for the 1984:Ql-2009:Q2 sample, with government being a
notable exception (see the fourth column in tables 2 and 4).
Nonetheless, the interpretation of the results seems to hold. In
particular, when estimated on the 1984:Q1-2009:Q2 sample, [X.sub.it] in
construction shows the run-up in construction employment starting in the
mid-1990s and the abrupt decline in 2006 that cannot be explained by the
typical cyclical patterns of the past. The estimated [X.sub.it] values
are shown in figure 4 for the two samples.
Sectoral reallocation
In his original paper, Lilien (1982) presented a dispersion measure
as a way to quantify the degree of sectoral reallocation occurring in
the economy at any given time. His measure is given by
5) [[sigma].sub.Lt] [equivalent to]
[[[summation].sub.i][s.sub.it][([g.sub.it] -
[g.sub.t]).sup.2]].sup.1/2],
where [s.sub.it] is industry i's employment share at time t;
[g.sub.it] is employment growth in i at time t; and [g.sub.t] is total
employment growth at time t. Abraham and Katz (1986) demonstrate that
this dispersion measure will increase even if no sectoral reallocation
is present, simply because some industries are more cyclically sensitive
than others.
[FIGURE 3 OMITTED]
Keep in mind the Abraham and Katz (1986) criticism that
Lilien's (1982) dispersion measure reflects cyclical movements: The
framework presented previously provides a way to eliminate the impact of
the cycle on employment shares, industry employment growth, and
aggregate employment growth so as to create a dispersion measure that is
purged of cyclical variation. This measure is given by
6) [[??].sub.t] [equivalent to]
[[[summation].sub.i][[??].sub.it][([[??].sub.it] -
[[??].sub.t]).sup.2]].sup.1/2],
where [??] indicates that the variable x is purged of the cycle. To
create the purged series, first, let [[??].sub.it], = [X.sub.it]. Then,
assuming that the cycle was zero in some reference year, taken here to
be 1964, it is simple to calculate [[??].sub.it],
[[??].sub.t],[[??].sub.it, and [[??].sub.t], where [[??].sub.it], is
noncyclical employment in industry i at time t and [[??].sub.t] is total
noncyclical employment at time t. Figure 5 shows the results of these
calculations. The red line is Lilien's (1982) measure as given in
equation 5, and the black line is calculated as in equation 6. The
noncyclical measure of dispersion is far less volatile than the original
measure, as Abraham and Katz (1986) argued. Nonetheless, there has been
a modest uptick in this measure of structural realignment over the past
couple of quarters. Figure 6 shows the noncyclical measure in panel A
and another measure that is based only on the shocks [[epsilon].sub.it]
in panel B. In this figure you can see the recent uptick more clearly.
The most recent quarter shows a decline in these dispersion measures,
reflecting industry shocks that are smaller in magnitude than those of
the previous few quarters. However, while it suggests a potential role
for industrial realignment in explaining recent increases in
unemployment, this simple summary measure may not be too informative in
explaining recent changes in the unemployment rate. To put it more
succinctly, structural realignment in and of itself may have little
impact on the unemployment rate. Workers laid off in one sector may be
readily absorbed into other industries, particularly if real wages
adjust to encourage the flow of workers from declining industries to
expanding ones.
[FIGURE 4 OMITTED]
[FIGURE 5 OMITTED]
In order to determine whether the structural component of
employment growth plays a role in unemployment dynamics, I ran
regressions of the following form:
7) [DELTA][ur.sub.t] = [alpha](L)[DELTA][ur.sub.t-1] +
[delta](L)[Cycle.sub.t] + [lambda](L)[[summation].sub.t], + c[W.sub.t] +
[v.sub.t],
where [alpha](L), [delta](L), and [lambda](L) are polynomials in
the lag operator L; [DELTA][ur.sub.t] is the change in the unemployment
rate at time t; Cycle is a measure of the cycle at time t;
[[summation].sub.t] is a measure of sectoral reallocation at time t.
including the constructed dispersion measures or, more broadly, the
individual estimated [X.sub.it] and [[epsilon].sub.it] values; and
[W.sub.t] is other variables that potentially influence changes in the
unemployment rate. The variable [v.sub.t] is a random shock assumed to
be independent and identically normally distributed.
Two separate measures of the cycle were examined, namely,
deviations of real GDP growth from its long-term average ([gGDP.sub.t] -
gGDP) and [[??].sub.t]. Several different measures of
[[summation].sub.t] were considered, including the two noncyclical
measures computed as in equation 6, as well as the estimated [X.sub.it]
values and the [[epsilon].sub.it] values individually. Regression
results are shown in table 5. Three lags of changes in the unemployment
rate are included in each regression, as is a demographic variable that
is calculated as the change in the female labor force participation rate
of white women aged 20 and above. (Other demographic variables that
reflected changes in the age, race, and sex composition of the labor
force were also investigated but were statistically insignificant and
are not reported in these results.) Of the two cyclical variables
considered, the measure of the employment cycle [[??].sub.t] performed
better than deviations of real GDP growth from its long-term average, in
that those regressions had higher [[bar.R].sup.2] values. Generally, the
two dispersion measures of sectoral reallocation did poorly in
explaining changes to the unemployment rate. The third and fourth
columns examine the impact of adding dispersion measures of sectoral
reallocation to the regressions. These dispersion measures are
statistically significant, but enter with the opposite sign anticipated
by the sectoral reallocation hypothesis; that is, increasing
reallocation, as measured here, tends to reduce the unemployment rate.
(8) The last two regressions omit the cyclical variable, [C.sub.t], and
include the two dispersion measures. Only in the results of the sixth
column, in which the cyclical variable is omitted, does dispersion enter
significantly positive. The weak results suggest that sectoral
reallocation as measured here may be positively associated with changes
in the unemployment rate. However, once cyclical effects are properly
accounted for, the impact disappears or changes sign.
[FIGURE 6 OMITTED]
One possibility is that these dispersion measures, being summary
statistics, are not very good at capturing the effects of reallocation
in the labor market. The dispersion measure treats all employment shifts
of the same magnitude as identical, regardless of the industry. This
ignores the possibility that human capital may differ across industries,
suggesting that unemployment responses should differ across sectors as
well. Specifically, some industries may require industry-specific human
capital. Sectoral reallocation away from those industries will take time
and cost more for those who have become displaced. To examine this
possibility, 1 have entered the idiosyncratic components both
individually and together. The results are found in tables 6 and 7,
which differ only in their sample periods. Table 6 provides results for
the period from 1954:Q2 through 2009:Q2, and table 7 provides results
from 1984:Q1 through 2009:Q2. (9)
The first two columns of table 6 examine the effect of including
each idiosyncratic component separately in a regression having both
cyclical and demographic variables. The [[bar.R].sub.2] values are
reported from each of these regressions in the second column. The
sectors of the economy in which the idiosyncratic component of
employment growth is statistically significant are construction, durable
manufacturing, transportation and utilities, retail trade, services, and
government. The signs of these effects are also interesting to consider.
Specifically, as noncyclical employment grows above trend in
construction, durable manufacturing, and transportation and utilities,
it reduces the unemployment rate. However, it has the opposite effect in
retail trade, services, and government, in that shifts toward these
industries tend to raise the unemployment rate. The third column reports
the coefficients from a single regression in which all idiosyncratic
industry components are included, in addition to current and lagged
employment cycle and demographic variables. Noncyclical shifts in
construction, durable manufacturing, and government are still
statistically significant, entering with the same sign as in the single
variable regressions. However, transportation and utilities, retail
trade, and services are no longer statistically significant.
The fourth, fifth, and sixth columns of table 6 repeat the
regression exercise but instead employ idiosyncratic shocks
[[epsilon].sub.it] as explanatory variables. The results are consistent
with the results using [X.sub.it]. Shocks to construction and durable
manufacturing tend to reduce unemployment, whereas shocks to retail
trade, services, and government tend to raise unemployment (fourth
column). The transportation and utilities industry does not meet the 5
percent significance criterion. However, its marginal significance level
is close to 10 percent. Table 7 reestimates the equations of the
preceding table, but with the 1984:Q1-2009:Q2 sample period. Most of the
results disappear for this sample period.
To obtain estimates of the effect of sectoral reallocation on the
unemployment rate, I assume that the economy was in equilibrium in
2007:Q4, with an unemployment rate of 4.8 percent. Furthermore, I assume
that the cycle is set equal to its expected value from 2007:Q4 through
2009:Q2. In this analysis, that implies that [C.sub.t] = 0. l also
assume that there are no demographic changes in the female labor force
participation rate over this period.
Table 8 provides estimates of the effect of [X.sub.it] on the
civilian unemployment rate as estimated from the equation used in the
third column of table 7, using the 1984:Q1-2009:Q2 sample period. The
first column gives the estimated total effect of the [X.sub.it], on the
unemployment rate, given the assumptions in the preceding paragraph. The
impact of sectoral reallocation in this model is negligible. The
remaining columns compute the impact on the equilibrium unemployment
rate of having idiosyncratic employment growth shocks in the specified
industry given by the estimated shocks. For example, although
equilibrium employment remained largely unchanged, by 2009:Q2 the shocks
to construction raised the unemployment rate by approximately 25 basis
points (see the notes in table 8). This rise was offset by declines
elsewhere.
As a whole, these models suggest that idiosyncratic shifts in
industry employment growth account for very little of the observed
increase in the unemployment rate over the past several quarters. On its
own, this would imply that there is room for accommodative policy as a
response to the current increase in unemployment, but bringing to bear
additional evidence on dispersion would help us gain a better sense of
whether the conclusions implied by the empirical model discussed here
are robust. There is a great deal of uncertainty surrounding the
estimates presented here. As noted before, the parameters of the
state-space model appear to differ between the 1950:Q1-1983:Q4 period
and the 1984:Q1-2009:Q2 period. Because of parameter and model
uncertainty, these estimates of the impact of sectoral reallocation on
the unemployment rate must be viewed somewhat skeptically. To underscore
this fact, results of the same exercise that estimate the unemployment
equation using the full sample suggest a decline in unemployment since
2008:Q1 attributable to sectoral reallocation.
Conclusion
The labor market appears to have a cycle that is well described by
co-movements in employment growth. The estimate of the employment cycle
that results from my model seems to agree with anecdotal evidence about
jobless recoveries. The model also does a good job of capturing turning
points in the business cycle, suggesting that it may be a useful tool
for understanding labor market dynamics and may help in predicting
future employment. The idiosyncratic component that the methodology
yields may also provide some additional insight into the impact of
structural realignment on changes in the unemployment rate. Structural
change favoring construction, durable manufacturing, and transportation
and utilities seems to be associated with decreasing unemployment; this
suggests that there may be some impediments to displaced workers in
these sectors finding jobs in other industries. Even with the downsizing
of finance, insurance, and real estate, the overall impact on the
unemployment rate is not statistically significant. One possibility is
that employees from finance, insurance, and real estate are better able
to find alternative employment in other sectors of the economy because
the skills they possess are more readily transferable to employment in
other industries. Conversely, employees in construction, durable
manufacturing, and transportation and utilities may be less readily
absorbed into other sectors.
REFERENCES
Aaronson, Daniel, Ellen R. Rissman, and Daniel G. Sullivan, 2004,
"Can sectoral reallocation explain the jobless recovery?,"
Economic Perspectives, Federal Reserve Bank of Chicago, Vol. 28, No. 2,
Second Quarter, pp. 36-49.
Abraham, Katharine G., and Lawrence E Katz, 1986, "Cyclical
unemployment: Sectoral shifts or aggregate disturbances?," Journal
of Political Economy, Vol. 94, No. 3, part 1, June, pp. 507-522.
Bloom, Nicholas, Max Floetotto, and Nir Jaimovich, 2009,
"Really uncertain business cycles," Stanford University,
mimeo, January, available at
http://aida.econ.yale.edu/seminars/macro/mac09/
bloom-floetottojaimovich-090219.pdf.
Burns, Arthur F., and Wesley C. Mitchell, 1946, Measuring Business
Cycles, New York: National Bureau of Economic Research.
Groshen, Erica L., and Simon Potter, 2003, "Has structural
change contributed to a jobless recovery?," Current Issues in
Economics and Finance, Federal Reserve Bank of New York, Vol. 9, No. 8,
August, pp. 1-7.
Hamilton, James D., 1994, Time Series Analysis, Princeton, NJ:
Princeton University Press, pp. 372-408.
Harvey, Andrew C., 1989, Forecasting, Structural Time Series
Models, and the Kalman Filter, Cambridge, UK, and New York: Cambridge
University Press.
Lilien, David M., 1982, "Sectoral shifts and cyclical
unemployment," Journal of Political Economy, Vol. 90, No. 4,
August, pp. 777-793.
Loungani, Prakash, Mark Rush, and William Tave, 1990, "Stock
market dispersion and unemployment," Journal of Monetary Economics,
Vol. 25, No. 3, June, pp. 367-388.
Phelan, Christopher, and Alberto Trejos, 2000, "The aggregate
effects of sectoral reallocations," Journal of Monetary Economics,
Vol. 45, No. 2, April, pp. 249-268.
Rissmau, Ellen R., 1993, "Wage growth and sectoral shifts:
Phillips curve redux," Journal of Monetary Economics, Vol. 31, No.
3, June, pp. 395-416.
Stock, James H., and Mark W. Watson, 1989, "New indexes of
coincident and leading economic indicators," in NBER Macroeconomics
Annual 1989, Olivier J. Blanchard and Stanley Fischer (eds.), NBER
Macroeconomics Annual, Vol. 4, Cambridge, MA: National Bureau of
Economic Research, pp. 351-394.
NOTES
(1) Stock and Watson (1989), p 353.
(2) The services sector includes information services, professional
and business services, education and health services, leisure and
hospitality, and other services Mining has been omitted from the
analysis for two reasons First, because of the incidence of strikes,
employment growth in this industry is quite volatile Second, mining
accounts for a small fraction of total employment.
(3) Averages for the current decade are based on data through
2009:Q2.
(4) The only exception, unreported here, is the mining sector.
(5) The hat symbol (^) indicates an estimate.
(6) There is another notable discrepancy when comparing the NBER
business cycle recession dates with those estimated here The two NBER
recessions in the early and mid-1970s were longer by two and three
quarters, respectively, than those proposed here Instead, the
employment-based measure of the cycle shows a labor market that was
quick to return to more normal activity during those times.
(7) The Great Moderation is a term used to describe the period
usually thought to have begun in 1984 and lasting through the present,
during which many economic time series exhibited less volatility than in
previous years The validity of this concept as a permanent shift has
been called into question by the recent financial crisis.
(8) The coefficients reported here are for contemporaneous measures
of dispersion. Including a number of leads and lags did not
substantively change the results Altering the specification so that the
dispersion measure was in changes or log changes had no bearing on the
results either.
(9) The lull sample period is slightly shortened by starting in
1954:Q2 because earlier data for female labor force participation were
not available.
Ellen R. Rissman is an economist in the Economic Research
Department at the Federal Reserve Bank of Chicago. The author thanks
Gadi Barlevy for helpful comments and suggestions and Zachary Seeskin
for his valuable research assistance.
TABLE 1
Average annualized quarterly employment growth, in total and by decade
Durable Nondurable Transportation
Construction manufacturing manufacturing and utilities
(--percent--)
Total 2.00 0.37 -0.40 1.00
2000s -0.42 -3.82 -3.41 -0.29
1990s 2.42 -0.04 -0.78 1.76
1980s 1.63 -0.90 -0.25 1.32
1970s 2.64 0.98 0.09 1.30
1960s 2.08 2.50 1.23 1.30
1950s 3.54 3.31 0.58 0.52
Finance,
insurance,
Wholesale Retail and real
trade trade estate Services Government
(--percent--)
Total 1.63 2.06 2.53 3.00 2.29
2000s -0.41 -0.18 0.18 1.16 1.04
1990s 1.20 1.44 1.56 3.24 1.28
1980s 1.57 2.52 2.97 3.72 1.13
1970s 2.97 3.33 3.59 3.62 2.65
1960s 2.42 3.03 3.38 3.70 4.15
1950s 1.93 2.08 3.37 2.45 3.41
Note: Data are seasonally adjusted.
Source: Author's calculations based on data from the U.S. Bureau
of Labor Statistics from Haver Analytics.
TABLE 2
Parameter estimates, 1950:Q1-2009:Q2
[[??].sup.1. [[??].sup.2.
[[??].sub.i] sub.i] sub.i]
Construction 1.8435 1.8695 *** 1.5357 ***
(1.1963) (0.3407) (0.4730)
Durable manufacturing 0.2714 3.7417 *** 0.8463
(1.5350) (0.3549) (0.6397)
Nondurable manufacturing -0.4657 1.5231 *** 0.4054
(0.6295) (0.1537) (0.2385)
Transportation 0.9105 1.2185 *** 0.7769 **
and utilities (0.5921) (0.2354) (0.3036)
Wholesale trade 1.5546 *** 0.8004 *** 0.6365 ***
(0.4448) (0.1135) (0.1888)
Retail trade 1.9921 *** 1.2430 *** 0.2449
(0.4377) (0.1589) (0.2255)
Finance, insurance, 2.3220 *** 0.2073 * 0.2340 ***
and real estate (0.6162) (0.0913) (0.0862)
Services 2.9343 *** 1.0738 *** 0.3221
(0.4061) (0.0994) (0.1661)
Government 2.2712 *** 0.0890 0.1438
(0.3532) (0.1280) (0.1031)
[[??].sub.i] [[??].sub.i]
Construction 0.4240 *** 20.1902 ***
(0.0741) (1.8060)
Durable manufacturing 0.612 *** 9.9197 ***
(0.0552) (0.9951)
Nondurable manufacturing 0.6461 *** 1.9574 ***
(0.0479) (0.2371)
Transportation 0.0933 3.8068 ***
and utilities (0.0883) (0.4611)
Wholesale trade 0.5516 *** 1.2072 ***
(0.0673) (0.1134)
Retail trade 0.1727 * 1.7845 ***
(0.0818) (0.2004)
Finance, insurance, 0.8978 *** 0.7583 ***
and real estate (0.0361) (0.0786)
Services 0.1728 0.4891 ***
(0.1119) (0.0804)
Government 0.5748 *** 2.9139 ***
(0.0639) (0.2494)
* Significant at the 5 percent level.
** Significant at the 2 percent level.
*** Significant at the 1 percent level.
Note: Standard errors are in parentheses.
Source: Author's calculations based on data from the U.S. Bureau
of Labor Statistics from Haver Analytics.
TABLE 3
Effect of cyclical anti structural components on variation,
1950: Q I-2(109: Q2
of total
of total variance
Total variance due to
variance due to C [X.sub.i]
Construction 46.9245 0.4754 0.5246
Durable manufacturing 58.7445 0.7300 0.2700
Nondurable manufacturing 10.8692 0.6909 0.3091
Transportation and utilities 11.5470 0.6674 0.3326
Wholesale trade 5.7097 0.6961 0.3039
Retail trade 6.3833 0.7119 0.2881
Finance, insurance,
and real estate 4.2831 0.0874 0.9126
Services 4.4125 0.8857 0.1143
Government 4.4569 0.0236 0.9764
Source: Author's calculations based on data from the U.S. Bureau
of Labor Statistics from Haver Analytics.
TABLE 4
Parameter estimates, 1984:Q1-2009:Q2
[[??].sup.1 [[??].sup.2.
[[??].sub.i] .sub.i] sub.i]
Construction 1.1703 2.0239 *** 0.1505
(5.8890) (0.4471) (0.7041)
Durable manufacturing -2.0404 1.2233 *** 0.9706 ***
(5.8171) (0.3697) (0.3687)
Nondurable manufacturing -1.7455 0.6885 *** 0.3827
(2.8657) (0.2296) (0.2630)
Transportation and 0.9551 0.6666 * 0.4383
utilities (2.8641) (0.3072) (0.3680)
Wholesale trade 0.5980 0.7366 *** 0.2876
(2.6710) (0.1784) (0.2258)
Retail trade 1.0153 0.7983 *** 0.1708
(2.5684) (0.2299) (0.3379)
Finance, insurance, 1.1042 0.2289 0.2021
and real estate (1.5869) (0.1927) (0.1860)
Services 2.5218 0.6012 *** 0.2775
(2.2840) (0.1699) (0.1683)
Government 1.3070 *** -0.1437 0.2893
(0.4682) (0.2637) (0.2858)
[[??].sub.i] [[??].sub.i]
Construction 0.7837 *** 4.3028 ***
(0.1066) (1.5117)
Durable manufacturing 0.7809 *** 1.4940 ***
(0.1028) (0.3755)
Nondurable manufacturing 0.7261 *** 0.8580 ***
(0.1025) (0.2103)
Transportation and 0.0793 2.0082 ***
utilities (0.1213) (0.3299)
Wholesale trade 0.7551 *** 0.6228 ***
(0.0807) (0.1714)
Retail trade 0.3190 * 1.0826 ***
(0.1487) (0.2504)
Finance, insurance, 0.8818 *** 0.9104 ***
and real estate (0.0883) (0.2466)
Services 0.0339 0.3434 ***
(0.2188) (0.0882)
Government 0.2061 * 1.4475 ***
(0.1003) (0.2520)
* Significant at the 5 percent level.
** Significant at the 2 percent level.
*** Significant at the 1 percent level.
Note: Standard errors are in parentheses.
Source: Author's calculations based on data from the U.S. Bureau
of Labor Statistics from Haver Analytics.
TABLE 5
Regression results: Dependent variable is Durr, 1984:Q1-2009:Q2 sample
1 2 3
3 lags [DELTA]ur.sub.t-1 Yes Yes Yes
Current and two lags -0.0433 *** -- --
of [gGDP.sub.t] - gGDP (0.0074)
Current and two lags -- -0.1674 *** -0.1771 ***
of [C.sub.t] (0.0264) (0.0264)
Change in female 0.1126 0.0690 0.1240
participation rate (0.0749) (0.0652) (0.0696)
[??] based on [[??].sub.it] -- -- -0.0131 *
-0.0065
[??] based on [[??].sub.it] -- -- --
[bar.[R.sup.2]] 0.6714 0.7904 0.7970
4 5 6
3 lags [DELTA]ur.sub.t-1 Yes Yes Yes
Current and two lags -- -- --
of [gGDP.sub.t] - gGDP
Current and two lags -0.1980 *** -- --
of [C.sub.t] (0.0291)
Change in female 0.1270 0.0639 0.0362
participation rate (0.0686) (0.0950) (0.0911)
[??] based on [[??].sub.it] -- 0.0073 --
(0.0077)
[??] based on [[??].sub.it] -0.0175 * -- 0.0182 *
(0.0077) (0.0079)
[bar.[R.sup.2]] 0.7993 0.5987 0.6162
* Significant at the 5 percent level.
** Significant at the 2 percent level.
*** Significant at the 1 percent level.
Notes: Estimating over the full sample did not materially change
the results. The full sample was estimated from 1954:Q2 through
2009:Q2, since the female labor force participation rate data are
not available prior to 1954:Q2. The estimate of the employment
cycle employed in the analysis is from the 1950:Q1-2009:Q2 Kalman
filter exercise. Standard errors are in parentheses.
Sources: Author's calculations based on data from the U.S. Bureau
of Labor Statistics and U.S. Bureau of Economic Analysis from Hover
Analytics.
TABLE 6
Effect of idiosyncratic components and shocks on changes
in the unemployment rate, 1954:Q2-2009:Q2
[X.sub.it]
Coefficient Coefficient
and standard [bar. and standard
error [R.sup.2]] error
Construction -0.0111 *** 0.7910 -0.0117 ***
-0.0025 -0.0027
Durable manufacturing -0.0174 *** 0.7876 -0.0191 ***
-0.0044 -0.0045
Nondurable manufacturing -0.0022 0.7718 -0.0013
-0.0076 -0.0082
Transportation and utilities -0.0146 * 0.7770 -0.0041
-0.0065 -0.0070
Wholesale trade 0.0161 0.7743 0.0180
-0.0104 -0.0103
Retail trade 0.0242 ** 0.7781 0.0108
-0.0098 -0.0103
Finance, insurance, 0.0001 0.7718 0.0031
and real estate -0.0074 -0.0072
Services 0.0596 *** 0.7799 0.0228
-0.0212 -0.0252
Government 0.0126 * 0.7761 0.0146 **
-0.0062 -0.0059
[bar.[R.sup.2]] = 0.8179
[[epsilon.sub.it]
Coefficient Coefficient
and standard [bar. and standard
error [R.sup.2]] error
Construction -0.0093 *** 0.7836 -0.0093 ***
(0.0027) (0.0027)
Durable manufacturing -0.0156 ** 0.7818 -0.0102
(0.0050) (0.0062)
Nondurable manufacturing 0.0010 0.7718 0.0074
(0.0105) (0.0129)
Transportation and utilities -0.0119 0.7756 -0.0043
(0.0062) (0.0064)
Wholesale trade 0.0159 0.7735 0.0166
(0.0125) (0.0126)
Retail trade 0.0212 * 0.7766 0.0132
(0.0099) (0.0111)
Finance, insurance, 0.0171 0.7734 0.0201
and real estate (0.0139) (0.0130)
Services 0.0508 *** 0.7790 0.0448
(0.0192) (0.0243)
Government 0.0224 *** 0.7806 0.0227 ***
(0.0076) (0.0072)
[bar.[R.sup.2]] = 0.8064
* Significant at the 5 percent level.
** Significant at the 2 percent level.
*** Significant at the 1 percent level.
Notes: Dependent variable is [DELTA][ur.sub.t]. Also included in
the regressions are three lags of the dependent variable, one
current and two lags of the estimated employment cycle, and changes
in the labor force participation rate of white women aged 20 and
above. See the text for further details.
Source: Author's calculations based on data from the U.S. Bureau
of Labor Statistics from Haver Analytics.
TABLE 7
Effect of idiosyncratic components and shocks on changes
in the unemployment rate, 1984:Q1-2009:Q2
[X.sub.it]
Coefficient Coefficient
and standard [bar. and standard
error [R.sup.2]] error
Construction -0.0101 * 0.7990 -0.0129 *
-0.0045 -0.0063
Durable manufacturing -0.0025 0.7884 -0.0054
-0.0070 -0.0087
Nondurable manufacturing 0.0130 0.7919 0.0031
-0.0101 -0.0145
Transportation and utilities -0.0254 *** 0.8048 -0.0272 **
-0.0090 -0.0108
Wholesale trade 0.0108 0.7987 -0.0001
-0.0113 -0.0137
Retail trade 0.0252 * 0.7981 0.0206
-0.0117 -0.0143
Finance, insurance, -0.0048 0.7892 -0.0043
and real estate -0.0070 -0.0079
Services 0.0025 0.7882 0.0102
-0.0305 -0.0376
Government 0.0087 0.7997 0.0019
-0.0099 -0.0099
[bar.[R.sup.2]] = 0.8153
[[epsilon].sub.it]
Coefficient Coefficient
and standard [bar. and standard
error [R.sup.2]] error
Construction -0.0085 0.7935 -0.0125 *
-0.0055 -0.0059
Durable manufacturing -0.0128 0.7912 -0.0123
-0.0110 -0.0132
Nondurable manufacturing 0.0152 0.7898 0.0139
-0.0175 -0.0208
Transportation and utilities -0.0246 *** 0.8050 -0.0243 **
-0.0086 -0.0094
Wholesale trade 0.0007 0.7881 -0.0024
-0.0162 -0.0172
Retail trade 0.0239 0.7966 0.0221
-0.0121 -0.0146
Finance, insurance, 0.0130 0.7901 0.0107
and real estate -0.0139 -0.0137
Services 0.0003 0.7881 0.0149
-0.0274 -0.0346
Government 0.0005 0.7881 -0.0023
-0.0101 -0.0099
[bar.[R.sup.2]] = 0.8104
* Significant at the 5 percent level.
** Significant at the 2 percent level.
*** Significant at the 1 percent level.
Notes: Dependent variable is [DELTA][ur.sub.t]. Also Included in
the regressions are three lags of the dependent variable, current
and two lags of the estimated employment cycle, and changes in the
labor force participation rate of white women aged 20 and above.
See the text for further details.
Source: Author's calculations based on data from the U.S. Bureau
of Labor Statistics from Haver Analytics.
TABLE 8
Estimated impact of idiosyncratic industry employment growth
on unemployment, 1984:Q1-2009:Q2
All Durable Nondurable
[X.sub.it] Construction manufacturing manufacturing
(--percent--)
2007:Q4 4.80 4.80 4.80 4.80
2008:Q1 4.79 4.84 4.78 4.80
2008:Q 4.76 4.89 4.76 4.81
2008:Q3 4.71 4.91 4.73 4.81
2008:Q4 4.69 4.94 4.70 4.82
2009:Q1 4.73 5.01 4.68 4.81
2009:Q 4.82 5.06 4.68 4.82
Transportation Wholesale Retail
and utilities trade trade
(--percent--)
2007:Q4 4.80 4.80 4.80
2008:Q1 4.76 4.80 4.79
2008:Q 4.72 4.80 4.75
2008:Q3 4.69 4.80 4.73
2008:Q4 4.68 4.80 4.69
2009:Q1 4.64 4.80 4.70
2009:Q 4.63 4.80 4.71
Finance,
insurance,
and real
estate Services Government
(--percent--)
2007:Q4 4.80 4.80 4.80
2008:Q1 4.82 4.80 4.80
2008:Q 4.83 4.79 4.80
2008:Q3 4.85 4.79 4.80
2008:Q4 4.87 4.79 4.79
2009:Q1 4.90 4.79 4.79
2009:Q 4.94 4.79 4.79
Notes: Results are for the regression in table 7, third column.
Calculations assume that the equilibrium unemployment rate was
equal to its value of 4.8 percent in 2007:Q4 and that the
employment cycle is in equilibrium from 2007:Q4 through 2009:Q2, so
that [X.sub.it] = 0 from 2007:Q4 through 2009:Q2. The first column
calculates the unemployment rate that would have occurred had the
industry idiosyncratic components been as estimated from 2007:Q4
through 2009:Q2 and the employment cycle been in equilibrium. The
second through tenth columns reflect the impact of the
idiosyncratic components in each of the individual industries. For
example, in the second column the estimated impact of idiosyncratic
shifts in construction on the unemployment rate in 2009:Q2,
assuming all other industry components to be as given by the
estimated [X.sub.it] values, is to raise the unemployment rate by
0.24 percentage points (calculated by subtracting the value in the
last row, first column, from the value in the last row, second
column, 5.06 -4.82). Results differ if the unemployment rate
regression is estimated using the entire sample period.
Source: Author's calculations based on data from the U.S. Bureau
of Labor Statistics from Haver Analytics.
