FEDERAL RESERVE BANK OF SAN FRANCISCO
WORKING PAPER SERIES

Dissecting Aggregate Real Wage Fluctuations:Individual Wage Growth and theComposition EffectMary C. Daly
Federal Reserve Bank of San Francisco
Bart Hobijn
Federal Reserve Bank of San Francisco,
VU University Amsterdam and Tinbergen Institute
Theodore S. Wiles
The Analysis GroupMay 2012
Working Paper 2011-23
http://www.frbsf.org/publications/economics/papers/2011/wp11-23bk.pdf

The views in this paper are solely the responsibility of the authors and should not beinterpreted as reflecting the views of the Federal Reserve Bank of San Francisco or the
Board of Governors of the Federal Reserve System.

Dissecting Aggregate Real Wage Fluctuations:Individual Wage Growth and the Composition Effect
MARY C. DALY
Federal Reserve Bank of San Francisco

1

BART HOBIJN

THEODORE S. WILES

Federal Reserve Bank of San Francisco,
VU University Amsterdam,
and Tinbergen Institute

The Analysis GroupMay 16, 2012

Using data from the Current Population Survey from 1980 through 2011 we examine what drives the variationand cyclicality of the growth rate of real wages over time. We employ a novel decomposition technique thatallows us to divide the time series for median weekly earnings growth into the part associated with the wage
growth of persons employed at the beginning and end of the period (the wage growth effect) and the partassociated with changes in the composition of earners (the composition effect). The relative importance of these
two effects varies widely over the business cycle. When the labor market is tight job switchers get large wage
increases, making them account for half of the variation in median weekly earnings growth over our sample.
Their wage growth, as well as that of job-stayers, is procyclical.

During labor market downturns, thisprocyclicality is largely offset by the change in the composition of the workforce, leading aggregate real wages tobe almost non-cyclical. Most of this composition effect works through the part-time employment margin.
Remarkably, the unemployment margin neither accounts for much of the variation in nor much of the cyclicalityof median weekly earnings growth.

Keywords: Business cycle, labor market dynamics, wage growth.

JEL-codes: E24, J3, J6.

1

We are grateful to Alessandro Barbarino, Marianne Bitler, Michael Elsby, Thomas Lemieux, Ayşegül Şahin, Eric Swanson, andseminar participants at the New York, St. Louis, and San Francisco Federal Reserve Banks, the NBER Labor Studies group, theRiksbank, OECD, and Tinbergen Institute for useful suggestions and comments. The views expressed in this paper solely reflect
those of the authors and not necessarily those of the Federal Reserve Bank of San Francisco, nor those of the Federal Reserve
System as a whole. Corresponding author: Bart Hobijn, bart.hobijn@sf.frb.org.

1

Dissecting Aggregate Real Wage Fluctuations

1. Introduction
The muted and inconsistent fluctuations of aggregate real wage growth have been a perennial
puzzle of macroeconomics. Aggregate real wages exhibit less variability over time than mostmacroeconomic models predict and movements that do take place appear only modestly related tothe business cycle.2 Both of these patterns are apparent in Figure 1 which plots the growth in real
median weekly earnings along with the unemployment rate.
As the figure shows, aggregate real wage growth varies much less than the unemployment rate,a standard measure of business cycle movements.3 In addition, and in contrast to most models,there is no apparent single pattern of comovement between wage growth and the unemployment
rate over time.4 For example, in the 1980s aggregate real wage growth looks slightly procylical,
falling during the deep recessions of the first part of the decade and rising when the unemployment
rate declined in middle of the decade. From the late 1980‟s through the mid 1990‟s, real wage
growth appears countercyclical, increasing at the same time that the unemployment rate rose. The
relationship between real wage growth and unemployment seemed to vanish altogether during thesecond half of the 1990s as the unemployment rate hovered near its structural level and wages grew
rapidly, statistically producing an acyclical relationship.

Finally, in the most recent severerecession, real wage growth remained high while unemployment increased, suggesting that
aggregate real wages responded countercyclically.
In contrast to the movements of aggregate real wage growth, real wage fluctuations ofindividuals consistently have been found to be procyclical, rising as the unemployment rate falls
and falling as the unemployment rate rises. Moreover, in keeping with standard macro theory, thesize of the response is non-trivial. For example, several authors including Bils (1985), Solon,
Barsky, and Parker (1994), and Devereux, (2001) find that a one percent increase in the2

Several authors have concluded that wages are modestly tied to business cycle conditions: for example, Lucas (1977); Mankiw(1989); and Christiano and Eichenbaum (1992). See Abraham and Haltiwanger (1995) for a survey of empirical studies of realwage growth over the business cycle.
3
The limited variability of aggregate real wage growth fails the predictions of a variety of macro models including real businesscycle models (Hansen 1985) and models of frictional unemployment (Shimer 2005). The flipside of this is that unemployment,
employment, and hours tend to move more than these models predict, suggesting that most of the adjustments in the labor market
come through quantities rather than prices.
4
While most models expect wages to exhibit some cyclicality the direction depends on the model. For example, Kydland andPrescott (1982), Barro and King (1984), Rotemberg and Woodford (1992), and Bartelsman et al (1994) all posit procyclical real
wages while a countercyclical relationship is predicted by Keynesian with sticky wages. See Swanson (2007) for a brief review ofthese issues.

2

Daly, Hobijn, and Wiles

unemployment rate reduces real-wage growth of individuals by about 1.3 percentage points. Thispattern holds across decades and for various subpopulations of the labor market.
To reconcile the different views coming from aggregate and individual real wage fluctuations
researchers have noted that movements in aggregate real wages reflect the net result of two separate
effects. The first, which we will term the wage growth effect, captures the responsiveness of
individual wages, or, wages of comparable worker groups, to fluctuations in the economy. In
simple terms, if a rising tide lifts all boats, the wage growth effect measures by how much (Hines,
Hoynes, and Krueger 2001). The size of the wage growth effect at any point in the business cycle isdetermined by the efficiency of markets, which is itself determined by wage setting practices, wage
norms, and government policy. Efficiency wage models, implicit contract models, and insideroutsider models as well as the long literature on nominal wage rigidities all focus on understanding
the wage growth effect.5 Models of wage bargaining have frequently been used to explain why
aggregate wages adjust much less than employment or hours; nominal rigidities are pointed to as areason for limited cyclical responsiveness of wages in downturns.
The second effect, termed the composition effect, denotes the impact that changes in thecomposition of the workforce over the business cycle can have on aggregate wage fluctuations. If
hiring or layoffs are not randomly distributed across all types of workers, composition bias canobscure the true relationship between wages and economic conditions. Returning to the boats
metaphor, this is the idea that in economic downturns some boats sink; the composition effectmeasures the impact of the sinking boats on aggregate real wage movements. Previous studies haveshown that employment losses during economic downturns disproportionately occur workers withlower than average wages (Hines, Hoynes, and Krueger, 2001, for example). This “upskilling”
implies less variation in aggregate real wages than would be implied by models where workers arehomogeneous and wages adjust uniformly (Altonji and Devereux, 2000). Research has shown that
controlling for composition bias, wages are highly procyclical.6
Although these micro studies indicate that aggregate real wage growth reflects both wage
growth and composition components and that controlling for composition bias makes wages much

5

Empirical research has focused on nominal wage rigidities (e.g. Card and Hyslop, 1997, Lebow, Saks, and Wilson, 2003, Dickens
et al., 2007, and Barratieri, Basu, and Gottschalk, 2010) as well as the relative size of wage fluctuations for job-stayers and jobswitchers (e.g. Bils, 1985, Devereux, 2001). See Pissarides (2009) and Kudlyak (2010) for two useful overviews.
6
Perry (1972), Bils (1985), and Solon, Barsky, and Parker (1994).

3

Dissecting Aggregate Real Wage Fluctuations

more procyclical, variation in data used, years analyzed, and methods applied have made it difficult
for the micro evidence to fully illuminate the drivers of aggregate real wages over time and whether
their contributions change over the business cycle.7 As such, most modern macro theory continues
to struggle with the challenges of the data presented in Figure 1—small and inconsistent
responsiveness of wages to the business cycle.
In this context, the aim of our paper is to provide a unified framework in which to examine how
the wage growth and composition effects have interacted over time to produce the aggregate real
wage fluctuations shown in Figure 1. Our paper develops a strategy for netting out these effects andtracking their importance over time for both the variance of aggregate real wage growth and for
aggregate real wage cyclicality.

The findings are revealing and provide useful guidance forthinking about how macroeconomic fluctuations affect aggregate real wage growth.
The key conclusions are as follows.

The relative importance of the wage growth andcomposition effects varies considerably over the business cycle. The wage growth effect is strongly
procyclical and accounts for the bulk of the variance of real wage growth over time; the wage
growth effect is dominated by changes in wages among job switchers. In business cycle downturns,
the composition effect rises in importance, offsetting more than half of the procyclicality of thewage growth effect. Much of the composition effect comes through the part-time employment
margin. This was especially important in during the Great Recession. Somewhat surprisingly,
given its central placement in a variety of macroeconomic models of wage fluctuations, theunemployment margin is relatively unimportant for the variance and cyclicality of real wage
growth.
The remainder of the paper is structured as follows. In Section 2 we describe the data we use:
the Current Population Survey (CPS) for 1980 through 2011. In Section 3 we introduce a novel
percentile decomposition technique that allows us to decompose the change in median wages into
tractable components while avoiding issues of top coding present in most publically available
individual-level data on earnings in the U.S.8 We then show how this technique allows us to focus
on movements in the earnings distribution related to different groups (those who enter and exit theworkforce and those who stay employed) and to specifically identify the relative contributions of
7

Another reason for this is that most of the empirical work has focused on tying down one aspect of the puzzle (e.g., wage growth ofparticular groups, composition bias) or been restricted to aggregate or individual data with little ability to reconcile the two pieces.
8
Our decomposition is closely related to, but different from, the one introduced in DiNardo, Fortin, and Lemieux (1996).

4

Daly, Hobijn, and Wiles

the composition and wage growth effects that drive changes in each of the percentiles of theearnings distribution. In Section 4, we present the results of our decomposition of real median
weekly earnings growth in the U.S. from 1980 through 2011. We conclude with Section 5. Two
appendices follow: one with the details on the CPS data and the other detailing the mathematicalderivations of our percentile decomposition.

2. Studying Wage Growth using the Current Population Survey
For our analysis we use data from the Current Population Survey (CPS). The CPS is uniquely
suited to our project since it is the only publically available, long-standing, nationally
representative, high-frequency, micro data source on labor market status and earnings for the U.S.
It also has the important advantage of being a key source of information on aggregate U.S. wage
growth.9 The most commonly quoted aggregate measure of wages derived from the CPS, and theone we focus on in our analysis, is Median Usual Weekly Earnings (MWE) of full-time wage andsalary workers.10 MWE is published at a quarterly frequency. Usual Weekly Earnings are defined
as “…earnings before taxes and other deductions and include any overtime pay, commissions, or
tips usually received (at the main job in the case of multiple jobholders).”11
To show how the CPS data on aggregate real wage growth compares with alternative aggregate
wage measures, especially those used in other empirical studies, Figure 2 plots Average Hourly
Earnings (AHE) of production and non-supervisory workers in the private sector, Compensation Per
Hour (CPH) in the nonfarm business sector, and the Employment Cost Index (ECI) along with

9

Previous research on the drivers of aggregate wage dynamics relied on smaller panel surveys which provide detailed data on
individuals. For example, Bils (1985) uses the National Longitudinal Survey of Youth (NLS/Y). Solon, Barsky, and Parker(1994), Devereux (2001), and Hagedorn and Manovskii (2010) use the Panel Study of Income Dynamics (PSID). Gertler andTrigari (2009), Barattieri, Basu, and Gottschalk (2010) use data from the Survey of Income and Program Participation (SIPP). Cardand Hyslop (1997), like we do here, use data from the Current Population Survey (CPS).
10
The focus on full-time wage earners still means that MWE is affected by fluctuations in overtime, overtime pay, as well as a trend
in the average work week for full-time workers (See Perry, 1972, for a discussion of these issues)
11
The CPS survey questions related to usual weekly earnings have evolved over time: “Prior to 1994, respondents were asked how
much they usually earned per week. Since January 1994, respondents have been asked to identify the easiest way for them toreport earnings (hourly, weekly, biweekly, twice monthly, monthly, annually, other) and how much they usually earn in thereported time period. Earnings reported on a basis other than weekly are converted to a weekly equivalent. The term "usual" is as
perceived by the respondent. If the respondent asks for a definition of usual, interviewers are instructed to define the term as morethan half the weeks worked during the past 4 or 5 months” (BLS, 2011).

5

Dissecting Aggregate Real Wage Fluctuations

MWE from the CPS from 1980 through 2011.12 All measures of nominal wages are deflated by the
Personal Consumption Expenditures Price Index so that the figure shows growth in real wages.
As the figure shows, all of these measures are highly correlated and exhibit similar cyclicalpatterns. The correlation of real wage growth measured by MWE with the other three measures is
0.6 or higher.

Importantly for our work the MWE series appears to capture the coincident

movements of the competing series very well. Visual inspection shows that MWE is rarely an
outlier across the series in terms of fluctuations in growth.13 Of the four measures of real wage
growth in Figure 2, MWE, which is based on the CPS, is the only one for which underlying
individual level data is available that covers both the level of earnings of workers as well as theirlabor market status.
The micro data underlying the CPS aggregates can be used cross-sectionally or, with someeffort, to construct short panels of individual respondents. To explain the type of information
contained in each of these short panels it is necessary to briefly review the CPS survey design andinterview structure. The CPS is a dwelling-based survey in which households are included for 16
months. Over this period, individuals are interviewed monthly for the first four months, notinterviewed for the next eight months, and then interviewed monthly again for the remaining fourmonths before being retired from the sample.14 As such, we have eight monthly surveys for eachmember of our panel.
The CPS survey and interview structure are illustrated in Table 1 (rows 1-2). The regularmonthly surveys collect very basic information about labor market status but no information about
earnings. Earnings information along with other details of jobs are collected twice during the CPS
survey interval, once in survey month 4 (interview month 4) and again in survey month 16(interview month 8) (Table 1, rows 3-4).15 Earnings and job information are collected only for
individuals who are employed at the time of the interview. Following other researchers, we rely
most heavily on the information collected in these survey months and use the additional information
12

For example, Gertler and Trigari (2009) focus on AHE for the empirical analysis in their paper while Galí (2011) focuses on CPH
for his estimate of the New-Keynesian Wage Phillips Curve. Lebow, Saks, and Wilson (2003) analyze the National Compensation
Survey data on which the ECI is based.
13
The exception to this statement is 1994, when MWE rose much more rapidly than the other series. This coincides with the CPS
redesign and the way the survey was changed to determine whether someone is a part-time or full-time employee.
14
Because the CPS is a dwelling-based survey, individuals who change residences are dropped from the sample.
15
Survey months 4 and 16 (interview months 4 and 8) are commonly referred to as the outgoing rotation groups since they are
individuals temporarily moving off the sample frame or permanently retiring from the survey. The matched samples of theseoutgoing rotation groups are known as the MORG files.

6

Daly, Hobijn, and Wiles

collected in other survey months to refine our labor market status measures as described below. To
match individuals across surveys we follow Madrian and Lefgren (1999) and Nekarda (2009). The
details are provided in Appendix A.16
In any quarter, the published aggregate MWE statistic is based on respondents who are either inthe fourth or eighth month of the CPS survey tenure (see Table 1). This means that the 4-quarter
growth rate of published MWE is based on a changing sample of individuals. To consider wagechanges of a group of individuals, we instead need a matched sample for our analysis. Using theshort individual panels, we compute an aggregate “Matched MWE”. This “Matched MWE”
measures the growth in median wages for those individuals who are in survey month 16 and were in
survey month 4 a year ago. Figure 3 plots our matched MWE against the published aggregate,
shown earlier in Figures 1 and 2. The two measures of MWE are very similar with a correlation of
0.79. As such, we conclude that the measure of MWE growth we use for our decomposition has thesame main characteristics of interest as the published MWE growth. Our data cover 1980 through2011.17Subgroups used in decomposition
Having settled on a wage series, we next turn to organizing our data into groups relevant for thedecomposition. Since our goal is to understand which labor market groups drive fluctuations inaggregate real wages we divide individuals based on reported labor market status in survey months
4 and 16 (interview months 4 and 8). We are able to distinguish five distinct states: (1) full-time
employed in the same job in both periods, (2) full-time employed in a different job from one period
to the next, and (3), (4), and (5) transitions to or from part-time employment, unemployment, or notin the labor force, respectively. 18 See Table 2 for a visual accounting of these groups.

16

One concern about using the CPS to track individuals over time is that the sample may not be representative of the population.
Since the CPS is a housing unit survey, when individuals change residences they are dropped from the sample and the newoccupants of the unit are interviewed. While this does not alter the cross-sectional representativeness of the CPS, it can potentiallyinterfere with representativeness of the individual-based short panels, especially if moving is related to the variables being
analyzed. However, work by Nekarda (2009) and Kim (2009) which carefully corrects for this type of sample attrition finds thatthe biases introduced are empirically modest. Thus, we use the raw CPS matched data as our baseline for analysis.
17
Due to the scrambling by the Census Bureau of identifiers that we use to match individuals across months, we are unable toperform this matching for two sub-periods of our sample, namely October 1985 through September 1986 and September 1995
through August 1996.
18
We do not differentiate between individuals in any of these subgroups based on their observable characteristics. Hence, ourcomposition effect is not measured based on efficiency units, as is done in Bowlus, Liu, and Robinson (2002). They, however, do
not aim to decompose aggregate wage fluctuations but focus on the sensitivity of parameter estimates to composition bias.

7

Dissecting Aggregate Real Wage Fluctuations

Although most of these states can be directly measured from the CPS survey data, we need tomake an imputation to fill out the data matrix displayed in Table 2. It regards the fraction of fulltime workers who stay in the same job versus change jobs over the sample. This distinction isimportant given the evidence that wage growth of persons who remain in the same job is lesscyclical than that of persons who switch jobs. See, for example, Bils (1994), Devereux (2001),
Martins, Solon, and Thomas (2010), and Hagedorn and Manovskii (2010). To impute the fractionof full-time employed individuals who stay in the same job we use the methods developed and usedby Card and Hyslop (1997), Fallick and Fleischman (2004), and Nagypál (2008). We provide fulldetails of our imputation in Appendix A.
Subgroups as share of full-time wage and salary earners
The final columns of Table 2 report the average shares (1980-2011) of wage earners who are ineach of our five categories at the beginning and end of the period (survey months 4 and 16;
interview months 4 and 8). The vast majority (over 89 percent) of wage earners are full-time
employed at both the beginning and the end of our individual sample frame. About 40 percent ofworkers in our sample are full-time employed in the same job; about 49 percent are full-time
employed but in different jobs in the first and second periods. Of the remaining wage earners, 2.7
percent of full-time employed at the beginning of the year end up unemployed at the end of it.
Conversely, 2.6 percent of those full-time employed at the end of the year were unemployed at the
beginning. There are slightly larger numbers of workers moving in and out of the labor market andinto or out of part-time or self-employment to or from full-time employment.
Earnings levels of subgroups
The fact that continuously full-time employed workers account for, on average, about 90 percent
of all wage earners suggests that they are likely to drive most of the movements in aggregate wages.
In our nomenclature this would suggest that aggregate real wage fluctuations are largely determinedby the wage growth effect. However, as previous researchers have noted, during periods of labormarket upheaval, such as recessions and recoveries, those exiting from (entering into) full-time
employment might also influence movements in aggregate wages, even though on average they
make up only a small share of overall wage earners. To show the potential of this type of effect we
examine from where in the wage distribution flows into and out of full-time employment are8

Daly, Hobijn, and Wiles

typically drawn. Specifically, we consider the share of each of our five labor market status groups
that comes from below the median wage computed across all workers. The results are reported inTable 3.
Looking first at the margin most commonly associated with the composition effect (transitions
into and out of unemployment), the data show that on average about 64.0 percent of full-timeworkers who become unemployed were making less than median earnings before entering
unemployment (Row 4, Column I). An even larger fraction (72.8 percent) of those making thereverse transition, from unemployment to full-time employment, make below median earnings(Row 4, Column II). The difference between the 64.0 and 72.8 percent in part reflects that thedisplacement penalty associated with unemployment spells, documented by Farber (1997, 2005).
Row 4 of Table 3 shows that, on average, the incidence of unemployment occurs
disproportionately below median earnings. As a result, if unemployment goes up, workers making
below median earnings lose their jobs in greater numbers than other workers. Holding wages ofother workers constant, this change in the composition of the workforce serves to increase medianaggregate wages. This is one example of the composition effect.
The part-time and self-employed (Row 3 of Table 3) as well as those who move into and out of
the labor force (Row 5) contribute to the composition effect in a similar way. Most of their flows
into and out of full-time employment occur below the median. Thus, when exits from full-time
employment to part-time employment or self-employment and not-in-the-labor-force increase,
median aggregate wages tend to rise. Finally, it is worth noting that since wages for those in thesame job and NISJ (Rows 1 and 2) tend to grow over time, fewer of them earn below the median at
the end of the period than at the beginning.
These results illustrate the potential for both wage growth and composition effects to matter for
aggregate real wage growth. To accurately quantify the importance of these effects and track theirrelative contributions over time we need a more formal accounting strategy that allows for a flexible
decomposition of aggregate wage movements into component parts. We turn to this in the next
section.

9

Dissecting Aggregate Real Wage Fluctuations

3. Wage Growth and Composition Effects: Percentile decomposition
Decompositions of movements in economic aggregates are commonly used to quantify the various
influences on these aggregates. The most common type of decomposition is a shift-share analysis
which can be easily applied when the aggregate being examined is a mean.19 We, however, areinterested in decomposing the growth rate (log change) of the median of the wage distribution; assuch, we cannot apply a conventional type of shift-share analysis. As an alternative, we introduce a
percentile decomposition that functions like a conventional shift-share analysis but works with
distribution functions rather than means.
Our percentile decomposition is similar in spirit to the one introduced by DiNardo, Fortin, andLemieux (1996). Our method differs in that it does not require the calculation of counterfactual
percentiles. Instead, it relies on the application of the mean-value theorem to translate shifts in the
distribution function into shifts in percentiles. This difference makes our method more directlycomparable to a conventional shift-share analysis as well as somewhat easier to implement than
DiNardo, Fortin, and Lemieux (1996). The difference between the two methodologies is explained
in detail in Appendix B.
We introduce our decomposition in three steps. First, we illustrate how changes in percentiles
are related to shifts in the underlying distribution function. Second, we show that changes in the
distribution function can be decomposed into separate parts which in our case map to thecomposition and wage growth effects we are interested in.

We conclude the section with a

discussion of how we implement the decomposition to track the dynamics of MWE growth.
Relating changes in percentiles to changes in distribution functions
To understand how our percentile decomposition follows and differs from the traditional shiftshare analysis it is useful to refer to Figure 4. The figure plots two log-earnings distributionfunctions, ( ) and( ). The -th percentiles associated with these two distribution functions

are given byrespectively. To illustrate the relationship between changes in percentiles

andand changes in the underlying distribution functions we assume, without loss of generality, that19

See Juhn and Potter (2006) for an example related to the labor force participation rate and Bartelsman, Haltiwanger, andScarpetta (2004) for an application to labor productivity growth.

10Daly, Hobijn, and Wiles

there is positive growth in the percentile over the period and that

. These percentiles

satisfy
(

)

(

).

(1)

Our decomposition works as follows. We apply a shift-share type decomposition to the changes inthe distribution functions.

(That is we decompose

)

(

) and

(

)

(

) intocontributions by the different groups we identify. We then apply the mean value theorem totranslate these contributions, measured along the vertical axis in Figure 4, into changes in earnings
along the horizontal axis, i.e.

. This is what yields the decomposition of the change in thepercentile of log earnings.
As we show in Appendix B, rearranging (1) allows us to write
. (

)

(

)/

. (

)

(

)/

. (

)

(

)/

. (

)

(

)/.

(2)

This result implies that the sum of the changes in each of the distribution functions evaluatedbetweenandandequals the sum of the difference in the value of the distribution functions in. In the figure, the vertical lines I and II correspond to the left-hand side terms of (2) while

the lines A and B correspond to the right-hand side terms.
The left-hand side terms in the above equation can be translated into changes in the percentile
by the application of the mean value theorem. If the distribution functions
continuously differentiable, then there exists a
. (

)

(

)/

. (

)

, such that
(

, (

)/

( ) and( ) are

, and
)

(

)-(

).

(3)

This allows us to express the change in the percentile from the beginning to the end of the period,(( ) to), in terms of shifts in the distribution function from( ). In particular, we

can write
(

)

(

)

(

)

{. (

)

(

)/

. (

This generalizes to the case in which the population from which

)

(

)/}.

(4)

is drawn is made up of various

subgroups. In that case we can apply a shift-share type decomposition to the right-hand side of theabove equation.
11

Dissecting Aggregate Real Wage Fluctuations

Decomposing changes in distribution functions by subgroup
Equation (1) can be rewritten in terms of conditional distribution functions as∫ ( ) (| )∫ ( ) (

| )

.

(5)

As we derive in detail in Appendix B, this can be rearranged to obtain a generalization of equation(2) of the form
∫ ( ){ (

| )

(

| )}

∫ ( ){ (

| )

(

| )}

∫ ( ){ (

| )

(

| )}

∫ ( ){ (

| )

(

| )}

}-* ( )

( )+

∫,{ (

| )

}

{ (

| )

(6)

Similar to equation (2), the left-hand side of the above equation is expressed in terms of the changes
in each of the conditional distribution functions evaluated between

and. The first two termson the right-hand side of (6) are similar those on the right-hand side of (2) in that they reflectchanges in the distribution functions at

and. The final term on the right-hand side captures

the effect of the changes in the shares of the different sub-groups.
Just like in the example in the previous subsection, we can use the mean value theorem totranslate the left-hand side into changes in the percentile. That is, there exists a, such that

, and
∫ ( ){ (| )(∫ ( ){ (

| )}

| )

(

| )}
(7)

[∫ ( ) (| )∫ ( ) (

| )

](

)

This then allows us to express the change in the percentile, ((){∫ ( ){ (

| )

(

| )}

(

)

), as

∫ ( ){ (

| )

(

| )}

}
(8)

{∫[{ (

| )

}

{ (

| )

}]* ( )( )+}Thus, we are able to decompose the change in the percentile in terms of (i) a part that is due to shifts
in the distribution functions for each of the subgroups that make up the population and (ii) a partdue to the changes in the shares of these subgroups in the population.

12

Daly, Hobijn, and Wiles

However, these shifts and shares parts do not directly correspond to the composition and wage
growth effects that are the focus of our analysis. Extracting these two effects requires an additional
reshuffling of the right-hand side terms of (8). In order to disentangle the composition effect fromthe wage growth effect, we have to divide the population of wage earners into three types ofsubgroups. The first type consists of those who earn a wage both at the beginning and end of theperiod. They are subgroups that are part of. The two subgroups in this set are those who are in

the same job and who are NISJ. The second type consists of individuals who are full-time wage andsalary workers at the beginning of the year and who flow out of these jobs and become either parttime or self employed, unemployed, or drop out of the labor force. These groups are exiters fromfull-time employment, denoted by the set. . The final type consists of those who flow into full-time wage and salary jobs and were either part-time or self employed, unemployed, or not in thelabor force at the beginning of the period. These groups of entrants into full-time jobs are part of. By explicitly defining who enters and exits the group of full-time wage earners we are able torewrite (8) as
(

)

{∫

( ){ ({∫| )(( )[{ (

| )

| )}

∫

}

{ (

( ){ (
| )

}]

| )

(

| )}

}

}
(9)

{∫
{∫

[{ (

( )[{ (
| )

| )
}

{ (

}

{ (
| )

| )
}]* ( )

}]

}
( )+

}

The right-hand side of (9) consists of four terms. The first term captures the effect of the shift in theearnings distribution for those who are full-time employed both at the beginning and at the end of
the period on the change in the percentile. The first part of this term quantifies how much thepercentile would have changed if the distribution of the population over different groups inremained fixed at the one that prevailed at the beginning of the period, i.e. at( ). The second part

captures the same effect, but instead holding the distribution constant at the one observed at the endof the period, ( ). Putting the two parts together, the first term on the right-hand side quantifies
how much the percentile changed because of the wage growth of the individuals who were observed
working in both periods. This is the wage growth effect. If, for all groups in
13

,

(

| )

Dissecting Aggregate Real Wage Fluctuations(| ) as well as (| )(| ), then, just like in Figure 4, there has been a rightward shift

in the distribution of weekly earnings of those employed at both the beginning and end of the period
and this contributes positively to the change in the percentile of weekly earnings. In that case, thewage growth effect would be positive.
The second term on the right-hand side of (9) measures the effect of flows out of full-time
employment on the change in the percentile. Two things contribute to this effect. The first is whatfraction of full-time wage and salary workers who flow out of full-time employment, measured by( ) for. The second is where in the earnings distribution these exiters were before leaving

their jobs. If a disproportionate share of exiters come from below the examined percentile, such
(

that

| )

and

(

| )

, their exit will cause the percentile to rise. This is the exit

component of the composition effect.
The third term on the right-hand side of (9) measures the effect of flows into full-time
employment on the change in the percentile. As for the second term, two things contribute to thiseffect. The first is the fraction of full-time wage and salary workers at the end of the period who are
newly employed, measured by ( ) for. The second is where in the earnings distribution the

newly employed locate. Similar to the exit term, if a disproportionate share of newly employedworkers locate below the examined percentile, such that

(

| )

and

(

| )

, the

percentile itself declines. This is the entry component of the composition effect.
As for the last term, if there is more exit than entry, then there is no full replacement ofoutflows. As a result, the share of those inis higher at the end of the period than at the beginningof the period. For example, if those inare disproportionately making more than a given

percentile, such that (

| )

and (

| )

for

, then the shortfall of replacement ofoutflows leads to an increase in the percentile since the shortfall is effectively replaced by stayers
whose earnings are relatively high. This mechanism is captured by the fourth term, which we callthe replacement component of the composition effect.
In sum, our decomposition yields exit and entry components for the composition effect for those
who move along (i) the part-time and self-employment margin, (ii) the unemployment margin, and(iii) the participation margin. It yields a wage growth effect as well as a replacement component forthe composition effect for those (iv) persons who remained in the same job, and (v) persons whochanged jobs (NISJ).
14

Daly, Hobijn, and Wiles

One final detail is worth noting. Since we do not observe the actual distribution and density
functions needed to construct the right-hand side of equation (9), we estimate them. The estimation
procedure we use is consistent with the one used to construct Median Usual Weekly Earnings, as
published by the BLS. The BLS rounds the weekly earnings values reported by individuals to thenearest multiple of 50.20 It then linearly interpolates the distribution function over the interval inwhich the percentile boundary lies, implicitly assuming that the earnings of those who report in theinterval that gets rounded to a particular multiple of 50 are uniformly distributed over that interval.
To be consistent with this methodology we estimate the distribution and density functions, , , ,and , in (9) the same way. That is, we group all earnings observations on the nearest multiple offifty and assume that earnings are uniformly distributed over the intervals that get rounded to eachof these points.
This introduces one problem for our percentile decomposition framework.

This way of

estimating the distribution functions implies that they are not continuously differentiable and, as aresult, the mean value theorem that we applied to derive (9) is not applicable. However, we can still
use the percentile decomposition. We replace (
(

| )

(

| )

(

| )

| ) and (, and (| )| ) by
(

| )

(

| )

.

(10)

In that case (9) still holds and we can thus decompose changes in earnings percentiles.21 Thismethod is applicable to any percentile of the earnings distribution. Since we focus in particular on
the median in the rest of our analysis, we drop the subscript

when we present the results.

4. Results
In the remainder of the paper we present the results of our decomposition of the log changes in
the median weekly earnings from the CPS from 1980 through 2011. The results are organized asfollows. We begin by reviewing the time series movements of each of the components that go into
20

According to the BLS: “The estimation procedure places each reported or calculated weekly earnings value into $50-wide
intervals which are centered around multiples of $50. The actual value is estimated through the linear interpolation of the intervalin which the quantile boundary lies.” (BLS, 2011)21

This estimation method works if. If
then we use the value of the density implied by the assumption thatearnings are uniformly distributed over the intervals that are rounded to the same multiple of 50. The case whereforand in which this does not work because of the kinked distribution function does not occur in our data.

15

Dissecting Aggregate Real Wage Fluctuations

our analysis. We then describe the key results. First, we consider in detail the composition effect of
unemployment, since this is the margin most commonly focused on in macroeconomic models that
aim to match the limited variation and cyclicality of aggregate real wages (Gertler and Trigari,2009, for example). We then show how other groups contribute to the composition effect. Having
shown when and by how much the composition effect influences aggregate wages we turn toexplaining the wage growth effect, paying particular attention to the role of job switchers. We
conclude our results section with an adding up of all the effects and discuss both the averagecontributions of the composition and wage growth effects and how their respective contributions
change over the business cycle.
Share and shift components of the decomposition
To begin, recall from the derivation above that what matters for our decomposition of the log
change in median earnings are the shares of each subgroup and the (changes) in their earnings
distributions. These are the two things displayed in Figures 5 and 6 along with references to theelements of the decomposition in equation (9). Figure 5 shows the time series plots of the shares ofthe full-time employed made up by each subgroup in the sample, namely same job (SJ), not in thesame job (NISJ), part-time/self-employed (PT), unemployed (U), and not in the labor force (NILF).
Panel (a) of the figure shows the share of those classified as “same job” and NISJ as a fractionof the full-time employed. 22 Taking into account that the data are normalized at the end of the year
and that the figure plots the 4-quarter moving average, panel (a) suggests that NISJ transitions areprocyclical—they go up when the labor market is strong and then decline during labor market
downturns. In Appendix A we describe our imputation results of the composition of NISJ over thebusiness cycle. These results suggest that about two-thirds of those classified as NISJ are job-to-job
switchers and that they account for this procyclicality of the NISJ share over the business cycle,
shown in panel (a) of Figure 5. This is consistent with the view that when the labor market is strong
workers quit more frequently and leave for higher paid jobs (Akerlof, Rose, and Yellen 1988) andwhen the labor market is weak, layoffs increase and a higher number of persons lose their full-timejob, go through unemployment, and end up in a different full-time job a year later.23
22

The sudden shift in 1983 is a data anomaly due to the change in occupation codes in the CPS. In particular after 1983 these codes
were more detailed, allowing us to be more precise about our “same job” versus “not-in-the-same-job” imputation.
23
This contrasts somewhat with Hall (2005) who argues that the behavior of quits and layoffs offset such that overall separations arebarely cyclical. Our findings suggest that these opposing forces do not cancel out to the same extent for the sample of those16

Daly, Hobijn, and Wiles

The remaining panels of the figure (panels b-d) plot the time series of entry into and exits out offull-time employment by our three other labor market groups: unemployed, part-time/self
employed, and not in the labor force. The first thing to notice is that consistent with Table 2, exitersand enterers account for a small share of the total full-time employed. On average, flows into andout of unemployment are smaller than those along the part-time and self-employment margin as
well as the labor force margin. However, as expected, flows into unemployment (exits from fulltime employment into unemployment, panel b) are much more cyclical than those to part-time andself employment or out of the labor force (panels c and d). One notable deviation from this general
pattern occurred in 2007, when flows from full-time to part-time employment spiked, leading toabout 6 percent of the labor force being part-time employed for economic reasons during 2009 and2010. The last time that this rate was so high was in October 1982. What seems to be different
about the run-up of the rate of part-time employment in the 2007 recession compared to that in 1982
is that it consisted more of persons whose full-time status changed to part-time, rather than theunemployed and labor force entrants being unable to find full-time employment.24 Exits from fulltime employment to NILF vary little with the business cycle and are mostly determined bydemographic factors and retirement norms. Entry into full-time employment from NILF is, notsurprisingly, slightly more procyclical.
In Figure 6 we plot the shifts in the earnings distributions for each of our subgroups. Since weare interested in log changes in median earnings these plots show the shares of our five worker
groups moving around the overall median. Specifically, Panel (a) of the figure plots the fraction of
full-time employed, classified as either “same job” or NISJ, that moves from below median weekly
earnings to above it. In terms of our notation, it is calculated as
( (

| )

(

| ))

( ( | )

( | ))

*

+.

(11)

As can be seen from the panel, during strong labor markets a larger share of job-switchers than jobstayers break through the median. In downturns and recoveries, this pattern is reversed and a larger
fraction of those in the same job break through the median. These findings are consistent with thetransitioning from full-time to full-time employment; for these movements the cyclicality of quits seems to dominate. The result isthat NISJ transitions in our full-time employed sample are procyclical.
24

This finding is consistent with changes in UI rules in several states that allowed individuals to claim benefits when reducing hours
of work as well as when losing jobs.

17Dissecting Aggregate Real Wage Fluctuations

previous discussion that highlighted the importance of quits in NISJ during expansions versus
layoffs in contractions.
Panels (b-d) of Figure 6 show where in the earnings distribution exit and entry for different
subgroups occurs. In terms of our notation, these are calculated as( ( | )(| )) and ( ( | )(| )) for

*

+

(12)

for exiters from and entrants into full employment respectively. The first thing to note from each ofthese panels is that the vast majority of those who enter full-time employment from any of thesestates earn less than MWE. This can also be seen in Table 3, rows 3-5. Surprisingly, entry into andexit from unemployment takes place at a higher part of the income distribution than do movementsfrom and to part-time and self-employment and not-in-the-labor-force. This is evident in from thefact that a lower fraction of entries into and exits from full-time employment come from below
median earnings for unemployment than for the other two groups.
Turning to the dynamics of the earnings of these flows, panel (b) shows that there isconsiderable cyclicality in the composition of those exiting (entering) full-time employment into(from) unemployment.

During recessions, the fraction of workers moving from full-time

employment to unemployment (exits), from below MWE, falls.

This is consistent with

Mueller (2010) who finds that during recessions the incidence of unemployment among highincome earners increases. This pattern is reversed in expansions, when the share of workers exiting
full-time employment to unemployment with earnings below MWE rises. A similar pattern isobserved for entries into full-time employment from unemployment but with a lag; the fraction
making this transition from below MWE falls during recessions and rises during expansions. Thislargely reflects that those high-income earners who end up unemployed during a recession generally
also find relatively higher paid full-time jobs when they exit unemployment.
Relative to the unemployment subgroup, there is very little cyclicality in the position in theearnings distribution of those who flow into NILF or part-time and self-employment originate. The
main pattern in both series is that the gaps between the entries to and exits (from) full-time
employment narrow over time, suggesting that in the decomposition most of the cyclical variationin the contributions from the part-time and self-employment and NILF margins will come throughtheir shares rather than shifts in the earnings distributions.

18

Daly, Hobijn, and Wiles

Decomposition of median weekly earnings growth by subgroup
To see how the individual patterns displayed in Figures 5 and 6 combine to produce changes inaggregate real earnings growth in the U.S., we turn to our decomposition. Specifically, we use
equation (9) to decompose the log-change of median weekly earnings into the wage growth effectand the composition effect. The results are displayed in Figure 7. Panel (a) plots the composition
effect which is the replacement components for the “same job” and NISJ subgroups and the net
contribution of the entry and exit components for the other subgroups. Panel (b) plots the wage
growth effect for those in the same job and NISJ.
Given the number of moving parts underlying the decomposition we begin with a detailed
description of how the components displayed in Figures 5 and 6 produce the net composition effectfor the unemployment margin shown in panel (a) of Figure 7 and for the NISJ wage growth effectshown in panel (b) of the same figure. These also are the two margins of adjustment commonly
thought to explain the bulk of the patterns in aggregate real wage growth.
Composition effectIn equation (9), up to the scaling factor,⁄ , the net composition effect of the unemployment

margin is given by( )*( (| ))( ( | ))+( )*( (| ))( ( | ))+.

(13)( ) is the share of full-time employed at the beginning of the year who are unemployed atHere,the end of the year and ( ) is the share of full-time employed at the end of the year who were
unemployed at the start. Both of these shares are plotted in panel (b) of Figure 5.

(| ) and( | ) reflect the share of those moving from full-time employment to unemployment who madeless than the median wage, measured either at the end and the beginning of the year respectively.
( | ) measures the same share, but for those entering full-time employment from unemployment.
Recall from panel (b) of Figure 6 that unemployed workers pay a displacement penalty such that
(

| )

( )

(

| ) and( | )( | ). In terms of equation (13), this implies that when( )—exit to and entry from unemployment are roughly equal—the composition effect of

unemployment pulls down median wage growth since the distribution of earnings for thosetransitioning from full-time employment to unemployment is higher than for those transitioning
from unemployment to full-time employment. Looking at the line for the unemployment margin in
19

Dissecting Aggregate Real Wage Fluctuations

Figure 7 (panel a), this is exactly what happens on average; the unemployment margin reduces
aggregate wage growth. In general then, the composition effect of the unemployed is negative.
Two things cause this, on average, negative effect to fluctuate over the business cycle. The firstis when( ) moves relative to ( ) For example, as can be seen from panel (b) of Figure 5, in

economic downturns( ) goes up and ( ) goes down so that unemployment increases. These

cyclical fluctuations make the composition effect of unemployment less negative during recession
than during expansions, causing it to move countercyclically.
The second is when the difference between( | ) and( | ) rises or falls. This happens

when the magnitude of the displacement penalty changes. As can be can be seen from the difference
between the dashed and solid lines in panel (b) of Figure 6, in economic downturns thedisplacement penalty rises as the incidence of unemployment moves up the earnings distribution
and reemployed workers take a bigger wage cut. This partially counteracts the countercyclicality of
the composition effect of unemployment induced by the movements of ( ) and ( )Turning to the other subgroups displayed in panel (a) of Figure 7, all of them contribute to thecountercyclicality of the composition effect. Though small, even the replacement components turnout to move countercyclically. In terms of contributions to the composition effect, the part-time andself employment margin contributes more to the composition effect for median weekly earnings
growth and cyclicality than the unemployment margin. The magnitude of the part-time and self
employment effect relative to other margins owes to the fact that a larger fraction of flows into andout of part-time and self-employment occur below MWE (Figure 6, panel (c)). In contrast to theunemployment margin, the part-time and self-employment effect does not have offsetting
components. In business cycle downturns, the share of exits from full-time to part-time rises andthere is little change in the earnings difference between entrants to and exits from full-time
employment from (to) part-time employment. In line with the shares presented in panel (c) of
Figure 5, the importance of the part-time and self-employed for the composition effect increased
significantly during the 2007 recession.
Wage growth effect
The wage growth effects are displayed in Panel (b) of Figure 7; the figure shows the wage
growth effect for both the same job and NISJ subgroups. We describe the calculation for the NISJ
group, but an analogous strategy applies to the SJ group.
20Daly, Hobijn, and Wiles

The wage growth effect for NISJ is obtained by combining the information in panel (a) of
Figures 5 and 6 in the context of equation (9), ignoring the scaling coefficient, to obtain()* ( |

)

( |

)+

(

)* (

|

)

(

|

In particular, the terms in (14) are the share of full-time employed who are NISJ,
(

)+.

(14)

( (

)

)), from Figure 5 and the movements in the earnings distribution of NISJ at the median from

Figure 6,

* ( |

)

( |

)+

* (

|

)

(

|

)+.

The net effect of

combining these terms is given by the NISJ line in Panel (b) of Figure 7.
The results reveal that those who change jobs over the year contribute more to the wage growtheffect than those who remain in the same job. This owes to the fact that the NISJ share of full-time
employed is larger while on average the earnings changes of NISJ and same job are similar. Whenlabor markets are tight, the NISJ effect is amplified by an increase in the share and an increase in
the fraction moving from below to above the MWE. In labor market downturns the wage growtheffect of NISJ and same job groups converge as both the share of NISJ falls and their earnings gains
relative to the same job group subside. In general, during labor market expansions the strong
performance in terms of wages of those who are in the “same job” and NISJ (displayed in Figure 6)
is accentuated by an increase in their share as shown in Figure 5. The result is that the wage growtheffect shows large procyclical fluctuations, driven primarily by job-changers, most of whom switch
job-to-job.
Putting all the effects together
Our decomposition allows us to express the time series of 12-month log change of real MWE,(), as the sum of the seven components shown in Figure 7. We index these components by, where, such that we can write(

For each of the individual components,

)

∑

.

(15)

, we discussed the magnitude and cyclicality of theirfluctuations. The fact that the individual components add up to the aggregate time series that westudy allows us to assess how important they are, on average, over our sample period 1980-2011,
for the variance and cyclicality of real MWE growth.

21

Dissecting Aggregate Real Wage Fluctuations

To measure the contribution of each of the components to the variance of real wage growth, weapply a simple variance decomposition. The additive relationship in equation (15) allows us towrite the variance of aggregate real wage growth as the sum of the covariances between each of theindividual components,(, and the aggregate,). Column I of Table 4 lists the share of eachof the components in the variance of real wage growth. Rows 2 through 6 of the table show thateach of the composition effects only account for a small share of the variance of real wage
fluctuations. In total, the composition effect accounts for 8.8 percent of the variance of real MWE
growth (row 7, column I). The other 91.2 percent is due to the wage growth effect. In fact, wagechanges of those who are NISJ alone account for more than half of the fluctuations in real wage
growth over the past three decades (row 9, column I).
As for the cyclicality of real wage growth, we measure it by the coefficient, , from a regressionof real wage growth on the level of the unemployment rate,. Both real wage growth as well as

the unemployment rate are measured in percentage points in this regression.

The particularregression equation is(
The coefficient

)

.

(16)

is reported in row 1 of column II of Table 3 and equals -0.112 and is not

significant. This indicates that over the past 30 years real wage growth has only been mildlyprocyclical. Real wage growth has tended to be high when the unemployment rate was low andvice versa. However, this relationship has not been particularly strong, leading to the statisticalinsignificance of the coefficient.
By construction, the cyclicality coefficient,cyclicality coefficients,for, is the sum of seven component-specific, obtained using regressions of the form.

(17)

These component-specific coefficients are listed in rows 2 through 10 of column II of Table 4. As
can be seen from the table, on the one hand, each of the composition effects, except that for
unemployment, is significantly countercyclical. On the other, each of the wage growth effects issignificantly procyclical. Though the wage growth effect is more important than the composition
effect for the cyclicality of real wage growth, half of its movements over the business cycle areundone by the composition of entries into and exits out of full-time employment. This is what22

Daly, Hobijn, and Wiles

makes the aggregate cyclicality coefficient negative, just like that associated with the wage growtheffect, but statistically insignifant.
Table 4 quantifies the average importance of the composition and wage growth effects for thevariance and cyclicality of real MWE growth over the past 30 years. It hides, however, that therelative importance of these effects varies over the business cycle and differs across recessions andexpansions. This variation can be seen in Figure 8 which plots the time series of the contributionsof the wage growth and composition effects to real wage growth.
The first thing that stands out from the figure is that the wage growth effect was especially
important during the strong labor markets of the mid 1980‟s and the second half of the 1990‟s. It‟s
impact on real wages was much more subdued during the 2000‟s. Moreover, the second thing that
Figure 8 reveals is that during the first three of the four recessions in our sample, the offsetting
countercyclicality of the composition effect was not particularly large. However, during the 2007
recession the composition effect turned from negative to positive, something previously unseen in
the data.

This large increase in the composition effect means that real wage growth in 2008 and2009 was greatly affected by changes in the composition of the workforce.

In terms of theimportance of the composition effect for growth in median usual weekly earnings the 2007
recession is an outlier compared to the three recessions before.

5. Conclusion
Using data from the Current Population Survey from 1980 through 2011 we examined what drives
the variation and cyclicality in the growth rate of real wages over time. To do this we employed anovel decomposition technique that allows us to divide changes in percentiles of aggregate usual
weekly earnings growth into the part associated with the wage growth of persons employed at the
beginning and end of the period (the wage growth effect) and the part associated with changes in thecomposition of earners (the composition effect).
Our results show that the relative importance of these two effects varies widely over thebusiness cycle. When the labor market is tight, job-changers get high wage changes, making themaccount for about half of the variation in median weekly earnings growth over our sample. Their
wage growth as well as that of job stayers is procylical. During labor market downturns this23

Dissecting Aggregate Real Wage Fluctuations

procylicality is partly offset by the change in the composition of the workforce. As a result,aggregate wages exhibit only limited cyclicality. Surprisingly, the composition effect works
primarily through the part-time employment margin.

Remarkably, the unemployment margin

neither accounts for much of the variation nor much of the cyclicality of median weekly earnings.
Our conclusion that job switchers are more important for understanding real wage growth thanflows in and out of unemployment has an important implication for studies that try to reconcile real
wage cyclicality in macroeconomic models with search frictions. Such studies often, for simplicity,
assume that the separation rate from employment is exogenously given. However, our results
suggest that such an assumption would mean discarding the cyclical fluctuations in the compositionof these separations that drive the bulk of U.S. wage growth.25 This suggests that, in order tounderstand the magnitude of variations in real wage growth, one has to explain the reasons why
people switch jobs, especially job-to-job switches, and how this affects their wages.

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Rigidity: Evidence from the Employment Cost Index,” Advances in Macroeconomics, 3 article
2, 1-28.
Lucas, Robert E.B. (1977), “Hedonic Wage Equations and Psychic Wages in the Returns to
Schooling,” American Economic Review. 64 (4), 549-558
Madrian, Brigitte. C., and Lars John Lefgren (1999), “A Note on Longitudinally Matching Current
Population Survey (CPS) Respondents,” NBER Working Paper Series #t0247.
Mankiw, N. Gregory, (1989), “Real Business Cycles: A New Keynesian Perspective,” Journal of
Economic Perspectives, 3 (3), 79-90.
Martins, Pedro, Gary Solon, and Jonathan Thomas (2010), “Measuring What Employers Really Do
about Entry Wages over the Business Cycle,” NBER Working Paper Series #15757.
Moscarini, G., & Thomsson, K. (2008). Occupational and Job Mobility in the US. Scandinavian
Journal of Economics , 109 (4), 807-836.
Mueller, Andreas (2010), “Separations, Sorting and Cyclical Unemployment,” mimeo, IIES
Stockholm University.
Nagypál, Éva (2008), “Worker reallocation over the business cycle: The importance of job-to-job
transitions,” mimeo, Northwestern University.
Nekarda, Christopher J. (2009), “A Longitudinal Analysis of the Current Population Survey:
Assessing the Cyclical Bias of Geographic Mobility,” mimeo, Federal Reserve Board ofGovernors.
Perry, George L. (1972), “Real Spendable Weekly Earnings,” Brookings Papers on Economic
Activity, No. 3, 779-787.
26

Daly, Hobijn, and Wiles

Pissarides, Christopher A. (2009), “The Unemployment Volatility Puzzle: Is Wage Stickiness theAnswer?” Econometrica, 77, 1339-1369.
Rotemberg, Julio J and Woodford, Michael, (1992). "Oligopolistic Pricing and the Effects ofAggregate Demand on Economic Activity," Journal of Political Economy, University of
Chicago Press, 100 (6), 1153-1207.
Shimer, Robert (2005), “The Cyclical Behavior of Equilibrium Unemployment and Vacancies,”
American Economic Review, 95, 25-49.
Shimer, Robert (2007), “Reassessing the Ins and Outs of Unemployment,” NBER Working Paper#13421.
Solon, Gary, Robert Barsky, and Jonathan A. Parker (1994), “Measuring the Cyclicality of Real
Wages: How Important is Composition Bias,” Quarterly Journal of Economics , 109 (1), 1-25.
Swanson, Eric T. (2007), “Real Wage Cyclicality in the Panel Study of Income Dynamics,” Scottish
Journal of Political Economy, 54, 617-647.

27

Dissecting Aggregate Real Wage Fluctuations

A. Data and Variable Details
Matching individuals across CPS interviews in different months
We use the matching criteria employed by Madrian and Lefgren (1999) for matching the outgoingrotations and Moscarini and Thomsson (2008) for matching month-to-month transitions. Our
matching procedures are similar to Fallick and Fleischman (2004) and Card and Hyslop (1997). 26
Specifically, individuals in our sample must match on age (+3 or -1 between subsequentinterviews), race, household ID, and line number.27 Our procedure produces match rates that are
identical are quite similar to previous researchers.
One thing to note is that our match procedure could introduce some bias into our results due togeographic mobility. Our results are conditional on staying within the same household, and people
within the unemployment, NILF, and NISJ margin are more likely to move.

However,

Nekarda (2009) shows that the effect of geographic mobility on aggregate CPS measures such as
the job finding rate and the separation rate is small. Nekarda (2009) also incorporates a match
similar to ours, which allows for households to non-report or misreport in months between valid
matches.
Constructing the same-job variable
Various researchers have used strategies to identify when individuals switch jobs in the CPS. Cardand Hyslop (1997) compare 2-digit industry and occupation codes between IM4 and IM828. In
1994, new variables were introduced to the CPS to help identify month-to-month changes in
employment. Fallick and Fleishmann (2004) and Nagypál (2008) use one of these variables—
whether an individual still works for the same employer as last month, providing the employer‟sname. Both of these studies look at month-to-month transitions. This is also touched on in
Moscarini and Thomsson (2008)‟s study of occupational mobility. Our “Same Job” definition can
26

Fallick and Fleischman (2004) require age to be decreased by no more than one year or increased by no more than two years. Cardand Hyslop (1997) use age plus or minus one year.
27
Within 1994 and 1995, HHID‟s are only consistent within state, so we add a state constraint within those years. For 2003-2004 wedon‟t use the HRSAMPLE and HRSERSUF variables, since they seem to be randomized, and HHID coupled with the demographic
variables successfully matches individuals.
28
From their appendix: “The industry and occupation are matched using detailed (2-digit) industry and occupation codes for all years
except 1982-83, 1983-84, and 1988-89. Matching for the 1983-84 sample is based on 3-digit 1980 census codes; for the 1982-83
sample, industry is matched using the detailed (2-digit) codes which are comparable across years, while occupation was matchedusing an algorithm devised to convert 1970 census 3-digit5 occupation codes to their 1980 census counterparts; and for the 198889 sample, occupation was matched using the detailed codes, and an algorithm was devised to match the detailed industry codes.”28

Daly, Hobijn, and Wiles

be considered a combination of the month-month SJ calculation of Fallick and Fleischman (2004),
Nagypál (2008) and the year-to-year SJ calculation of Card and Hyslop (1997). We want to use allavailable information on a matched individual, but we are also constrained by missing data between
IM4 and IM5.
Our procedure then is as follows. After 1994, we define a job stayer as an individual observed
as employed in IMs 4, 5, 6, 7, and 8, with the same detailed industry and occupation in each of thesemonths, and who reports being with the same employer and reports the same job description and job
duties, or who has missing values for these dependent-coding variables in MIS 6, 7, and 8. Nagypál(2008) and Fallick and Fleischman (2004) only use the “same employer” variable, so includingthese three variables enables a wider definition of job re-negotiation. Prior to 1994, we do not havethe dependent coding variables, and industry and occupation data is reported anew each month.
Thus, to get a “same job” measure, we match industry and occupation between IMs 4 and 8, and at
least 2 out of the 3 months in IMs 5, 6, and 7, keeping the constraint of employment throughout IMs
4-8. This gives us a reasonably consistent same job rate across the 1994 boundary, and a slightly
more restrictive test than Card and Hyslop (1997), who only constrained industry, occupation, andlabor status in IM 4 and IM 8. Our “Same Job” rates are consistent with other estimates in theliterature.
Not-in-the-same-job (NISJ) versus job-to-job (J2J) transitions
Following Fallick and Fleischman (2004) and Nagypál (2008) we consider a job-to-job transition as
one in which a CPS respondent reports to be employed in a particular job in one month and anotherjob in the next month. Unfortunately, this definition does not account for the possibility of such aworker having moved through a short spell of unemployment or part-time or self employment
during the month in between the two responses.

Since identifying the fraction of the NISJ

individuals who moved directly from one full-time job to another, i.e. job-to-job (J2J) transitions isimportant for our study, we impute the fraction of NISJ transitions that are J2J.
Our imputation method relies heavily on the gross worker flows measurement methodologies
used in Shimer (2005) and Fujita and Ramey (2009). Given the CPS survey structure (see Table 1)
individuals we classify as NISJ consist of four groups: (i) Those who have missing data for IM5,
IM6, or IM7 (ii) employed in IM4 and employed in another job in MIS8 but either unemployed, notin the labor force, or part-time or self employed in IM5, IM6, or IM7, (ii) not in (i) and (ii) and29

Dissecting Aggregate Real Wage Fluctuations

employed in IM4 in the same job in IM5 and in a different job at IM8, (iii) not in (i) and (ii) andemployed in IM4 and in a different job in IM5.
Those in (ii) are not part of J2J transitions. These are individuals who have not been employed
for the whole 12-month period between the two levels of earnings they report. For our imputation,
we ignore temporary layoffs and assume that everyone who reports to have the same job as 8months earlier has remained in that job over the intervening period. Hence, we classify those in (iii)as part of J2J transitions.
The imputation is made complicated by those in (iv) and (i). We discuss the imputation for thosein (iv) first. Some of the individuals in that group who changed jobs between IM4 and IM5 actuallywent through unemployment, dropped out of the labor force, or were part-time of self employed.
However, these episodes are not observed because they occurred during the eight months when theindividuals were not part of the CPS sample. Hence, we have to impute what share of those in group(iii) did not experience any episodes of unemployment, part-time employment, or self employment
and did not drop out of the labor force.
We impute this share by assuming that labor market status transitions follow a first-orderMarkov process.29 We denote the different labor market statuses as: (i)same job as at the beginning of the period, (ii)of the period, (iii)

unemployed, (iv)full-time employed in the

full-time employed in a different job as at the end

not in the labor force, and (v)part-time or self

employed. The arrow → denotes the transition during the 9 months between IM4 and IM5.
The first-order Markov assumption allows us to write transition probabilities over multiple
months in terms of monthly transition probabilities. We define these monthly transition probabilities
in month as( ), whereHere
end up in

*

+.

(18)

( ) is the fraction of persons with labor market status at the beginning of the period thatat the end of the period.

As we discussed above, we assume that persons who are in the same job in IM5 as in IM4 havebeen continuously employed in that job. This implies that
29

This assumption means that, due to data-limitations, we do not account for duration dependence of unemployment outflow rates, or
tenure duration dependence of worker separation rates. Consequently, our imputations should only be interpreted as indicative of
cyclical fluctuations of the composition of the NISJ group in our sample rather than a precise estimate.

30

Daly, Hobijn, and Wiles

( )

*

, for

+.

(19)

Note that( ) is the probability of remaining full-time employed in the same job during themonth and( ) is the probability of a job-to-job transition.30

We construct the Markov transition matrix that is associated with these probabilities based onmonthly matched CPS data, similar to Shimer (2007), Fujita and Ramey (2009), and Elsby, Hobijn,
and Şahin (2010).
The share we are imputing is the ratio of two probabilities. The numerator is the probability thatan individual reports to have changed jobs in IM5 relative to nine months before in IM4 and has notflown through ,, or. This probability can be written as

[ →

]

∏

{

( )

( )}

∏

( ).

(20)

The denominator is much harder to impute. It is the probability that an individual reports to havechanged jobs in IM5 relative to eight nine months before in IM4 irrespective of what she or he didin the meanwhile. It is,-(∏

Here, the Markov transition matrix( ) is given by

[ →

]

( )),

-.

(21)

( )
( )
( )
[

.

( )
( )
( )

( )

( )/
( )
( )
( )

( )

( )

( )

( )
( )
( )

( )
( )
( )

( ).
( )
( )]

(22)

Thus, only a fraction
[ →

]⁄

[ →

]

(23)

of those in the third group of individuals classified as NISJ will be imputed as having gone directlyfrom job to job rather than flowing through unemployment, part-time or self employment, or
temporarily leaving the labor force.

30

This job-to-job transition is slightly different from that reported in Fallick and Fleischman (2004) and Nagypál (2008) because it isconditional on full-time employment.

31

Dissecting Aggregate Real Wage Fluctuations

As for those in group (i) we can do the same as for those in (iv). The share of this group that we
attribute to NISJ is given by
[ →

]⁄

[ →

].

(24)

The numerator and denominator for this group are calculated in a very similar way as for group (iv).
In particular
[ →

]

∏

( )

{

( )}

∏

( ),

(25)

and
[ →

]

,

-(∏

( )),

-.

(26)

That is, if one or more observations in IM5, IM6, and IM7 are missing for an individual we treat allthese observations as missing and impute the share of such individuals that are J2J through theassumed first-order Markov transition process.
The first-order Markov assumption in our imputation method assumes that a person flowing
through unemployment is just as likely to become unemployed later in the year as someone that did
not. In actuality, this person is more likely to become unemployed (again) but the CPS data do notallow us to correct for this.

Not correcting for this leads to an overestimate of the number of

persons flowing through unemployment (and non-participation and part-time and self-employment
for the same reason). Hence, it is best to interpret our imputed fraction of NISJ flows that are J2J asa lowerbound estimate.
Figure A.1 shows the results of our imputation. The figure indicates that, on average, a bit lessthan two-thirds of NISJ flows are J2J. Just like quits as a share of separations in the Job Openings
and Labor Turnover Survey, J2J flows are procyclical, increasing during the strong labor market atthe end of the 1990‟s, with a bit of a lull during the dip in 1998, and again increasing from 2006
through 2007. Their share sharply dropped during the 2007 recession. 31 This is consistent with
Akerlof, Rose, and Yellen (1988) who argue that job-to-job quits in pursuit of higher wages and job
satisfaction drive a large part of U.S. labor market dynamics.
31

It is important to note that, because we count changes of the job description of a worker who stays with the same employer as achange in jobs, we find more job-to-job switches than studies, like Fallick and Fleishmann (2004) and Nagypál (2008), which
consider job-to-job switches conditional on changing employers. Moreover, we only consider switches from one full-time job toanother.

32

Daly, Hobijn, and Wiles

B. Mathematical details
Derivation of equation (2)Equation (2) can be derived by realizing that
(

)

(

)

. (

)

(

)/

. (

)

(

)/

. (

)

(

)/

. (

)

(

)/ (27)

. (

)

(

)/

. (

)

(

)/

. (

)

(

)/

. (

)

(

)/

Moving the first two terms in this expression from the right-hand side to the left-hand side yields
equation (2).
Derivation of equation (6)The version of (2) for more than one subgroup, , reads∫ ( )[ (| )(∫ ( ) (| )∫ ( ) (

∫ ( )[ (

| )]

| )

(

∫ ( ) (

| )

| )]
(28)

| )

∫ ( ) (

| )The right-hand side of this expression can be rewritten as∫ ( ) (| )∫ ( ) (| )∫ ( ) (

∫ ( )[ (

| )

(

| )]

∫( ( )( )) (| )∫ ( )[ (

| )

(

| )]

∫( ( )( )) (| )Combining terms, we obtain equation (6).
Derivation of equation (9)Equation (9) follows from

33

| )

∫ ( ) (

| )(29)

Dissecting Aggregate Real Wage Fluctuations

(

)

{∫
{∫

( ){ (
[{ (

| )
| )

{∫

( ){ (

{∫

[{ (

{∫

( ){ (

(
}

| )

| )

}
| )

| )}
{ (

| )

(

| )}

{ (

| )

(

( ){ (

∫

| )}

| )

(

}]* ( )( )+}}]* ( )

( )+

}

| )}

}

}

}
(30)

{∫
{∫

[{ (

| )

}

( ){ (

| )

{ (
(

| )}

∫

( ){ (}}{∫( ){ (

| )

(

| )

{∫

( ){ (

| )

(

| )

{∫

[{ (

| )

}

}]* ( )

| )

{ (

| )

}

( )+

}

| )

(

| )}

}

}
}]* ( )( )+}This is the equation we are supposed to derive.
Comparison of our percentile decomposition with DiNardo, Fortin, and Lemieux (1996)
The percentile decomposition that we introduced in this paper is not the first one that can be used.
Our decomposition is almost directly derived from a standard shift-share decomposition in means
but then translated into shifts in earnings distribution functions and changes in the composition,
shares, of the full-time employed.
An alternative is the decomposition by DiNardo, Fortin, and Lemieux (DFL, 1996). DFL do not
specifically explain how their methodology can be used to decompose changes in percentiles. Thisis actually explained is a more general framework in Fortin, Lemieux, and Firpo (2011).
Where our decomposition measures changes in the distribution function evaluated at thepercentile at the beginning and at the end of the period, i.e. lines A and B in figure 4, and then uses

34

Daly, Hobijn, and Wiles

the mean value theorem to translate changes in the distribution function into changes in thepercentile, the DLF decomposition involves the calculation of counterfactual percentiles.
This difference between these two methods is illustrated in figure A.2. The top panel, (a), of the
figure illustrates our percentile decomposition in an extended version of figure 4. In addition to the
distribution functions at the beginning at the end of the period, Panel (a) of figure A.2 also contains( ) ( | ), is the one that would have

two counterfactual distribution functions. The first,

prevailed if all subgroups had their own conditional earnings distribution from the beginning of theperiod and the only thing that happened was a shift in the composition of the full-time employedfrom ( ) to ( ). The second, ( ) ( | ), is the one that would have prevailed if all subgroups
had their own conditional earnings distribution from the end of the period and the only thing that( ) tohappened was a shift in the composition of the full-time employed from( ). Ourdecomposition evaluates what is the fraction of earners whose earnings crossed the percentile
evaluated either at the beginning of the period,, or at the end of the period,.

In terms of figure 4, the former fraction is given by A. Figure A.2 shows that this fraction can be
decomposed as
(
{ (

)

∫( ( )∫( ) (( )) (

)

(

)

| )

}

{∫

| )

( ) (

∫ ( ). (

| )

| )

(

(

| )/

)}

(31)

Thus, Ashare is the change in the value of the earnings distribution function at the percentile at the
beginning of the period that is attributable to the change in the shares of the subgroups that make up
full-time wage and salary earners. While, Ashift is the change in the earnings distribution function
due to the earnings distribution functions of each of the underlying subgroups changing.
Similarly, the fraction of earners whose earnings crossed the percentile at the end of the period,
given by B, can also be decomposed into shift and a share part.
Our decomposition then aggregates the shift and share parts of A and B uses the mean value
theorem to translate those into relative contributions to the changes in the percentile. We thenreshuffle the shift and share terms to obtain a decomposition in parts that are better interpreted as
the composition and the wage growth effects.

35Dissecting Aggregate Real Wage Fluctuations

The DFL decomposition requires the construction of counterfactual percentiles. Define thesecounterfactual percentiles, ̃ and ̃()(

Thus, ̃ would have been the

)

as
∫

( ) (̃ | )∫( ) (̃ | )

.

(32)

-th earnings percentile if the each of the subgroups had theirearnings distribution from the beginning of the period and the share of full-time employment at theend of the period. Conversely, ̃would have been the -th earnings percentile if the each of thesubgroups had their earnings distribution from the end of the period and the share of full-time
employment at the beginning of the period.
These counterfactual percentiles are drawn in panel (b) of figure A.2. The DFL decomposition
then basically implies that one can decompose the change in the percent fromtointo a shift

and a share part in two ways.
The first is
(

)

(

̃ )

(̃

)

.

(33)

Here, Ashare is the part of the change in the percentile that is due to shares of each of the subgroupschanging assuming their respective earnings distributions remain the same as at the beginning of theperiod. The part Ashift is the remainder of the change in the percentile due to the changes in theearnings functions. The second, Bshare and Bshift, switch the order in which the changes in the sharesand shifts are being evaluated.

36

Daly, Hobijn, and Wiles

Table 1. CPS survey design
CPS survey design
1.
2.

CPS survey months (SM)Interview months (IM)

1
1

2
2

3
3

4
4

1

2

3

4
4

5

6

7

8

9

10 11 12 13 14 15 16
5 6 7 8CPS data collected
3.
4.

Labor force status
Earnings

5

37

6

7

8
8

Dissecting Aggregate Real Wage Fluctuations

Table 2. Labor Market Status Subgroups used in the Decomposition
I
Subgroups

II

III

Labor Market Status Beginning and End of Year

Name
SM4 (IM4)
Full-time employed at beginning and end of year
Full-time employed
1. Same Job (SJ)
Full-time employed
2. Not in Same Job (NISJ)
Total
Entry to/Exit from full-time employed
Part-time or self-employed
3. Part-time/self-employed (PT)Full-time employed
Unemployed
4. Unemployed
Full-time employed
Not in the labor force
5. Not-in-labor-force (NILF)
Full-time employed

38

IV

V

Share of All Wage Earners

SM16 (IM8)SM4 (IM4)

SM16 (IM8)

Still employed in the same job
Employed in different job

40.8
48.4
89.2

40.9
48.2
89.1

Full-time employed
Part-time or self-employed
Full-time employed
Unemployed
Full-time employed
Not in the labor force

5.1
3.9
2.6
2.7
3.2
4.3

Daly, Hobijn, and Wiles

Table 3. Summary statistics by subgroup of full-time wage and salary earners
I

II

Share of subgroup below the median
Beginning of period

End of period

1.

Same Job

45.4

43.9

2.

Not in the Same Job

50.1

48.4

From full-time employment:

To full-time employment:

3.

Part Time / Self Employed

76.4

80.7

4.

Unemployed

64.0

72.8

5.

Not in the Labor Force

65.6

80.5

Note: All shares reported are average shares over our 1980-2011 and are reported in percentages.

39Dissecting Aggregate Real Wage Fluctuations

Table 4. Decomposition of variance and cyclicality of real MWE growth: 1980-2011.

Measure
1.

Total

I

II

Variance

Cyclicality

100.0-0.112(-1.52)

A. Composition Effect
Replacement component

2.

Same job

0.6

0.012
(4.47)

3.

Not in the same job

0.2

0.003
(2.83)

Exit and entry components

4.

Part-time or self employed

4.1

0.063
(3.32)

5.

Unemployed6.

Not in the labor force

3.6-0.004(-0.28)0.2

0.036(2.62)

7.

Total

8.8

0.110

B. Wage Growth Effect8.

Same job9.

Not in the same job

41.0-0.080(-2.26)50.2-0.142(-3.05)

10

Total

91.2

-0.222

Note: Rows 2 through 10 in column I are reported in percent of the total variance reported in row 1 in squared percentage points.
Totals do not add up to 100 due to rounding. Column II reports regression coefficients, , of cyclicality regression, ln(w)=+u+,for total real MWE growth measured in percentage points and its subcomponents. t-values are in parentheses.

40Daly, Hobijn, and Wiles

Figure 1. Real wage growth and changes in the unemployment rate
Quarterly observations; 4-quarter growth in real MWE; level of unemployment rate

Percent

Percent

512

10

MWE growth(left axis)

3

8

0

6

4

Unemployment rate(right axis)

-3

2

-5
1980

0
1985

1990

1995

2000

2005

2010

Source: Bureau of Labor Statistics and Bureau of Economic Analysis

Figure 2. Four aggregate measures of real wage growth4-quarter log change; 4-quarter moving average; PCEPI deflated

Percent

6
Correlation with MWE:
AHE: .66
ECI: .79
CPH: .62

5

CPH

4
3
MWE

2
ECI

1
0

AHE

-1
-2
-3
1980

1985

1990

1995

Source: Bureau of Economic Analysis, Bureau of Labor Statistics

41

2000

2005

2010

Dissecting Aggregate Real Wage Fluctuations

Figure 3. MWE growth for published and matched CPS samples.
Percent

54-quarter log change; 4-quarter moving average; PCEPI deflated
Scrambled
Household Identifiers

Scrambled
Household Identifiers

MWE
Matched

4
3

2
1
0
-1
-2
-3
1980

1985

1990

1995

Source: Bureau of Labor Statistics, CPS, and authors' calculations

42

2000

2005

2010

Daly, Hobijn, and Wiles

Figure 4. Graphical representation of equation (2).

Pr[Ww]

1

F(w’ p)

B

I

G(W)

p

p=F(wp )=G(w’ p)
F(W)
A

II

wp

w’p

G(wp)
0

43

Dissecting Aggregate Real Wage Fluctuations
Figure 5. Subgroups as shares of the full-time employed.
(a) Share of full-time employed in Same Job and NISJ subgroups

Percent

55

Scrambled
Household Identifiers(b) Share of full-time employed exiting to and entering from unemployment

Percent

7

Scrambled
Household Identifiers

Scrambled
Household Identifiers

Scrambled
Household Identifiers

6
50

5

Not in the same job½(j(NISJ)+g(NISJ))

45

4
Exit out of FT employment, j(U)403Same Job½(j(SJ)+g(SJ))

2
35

Entry into FT employment, g(U)

1
30
1980

1985

1990

1995

2000

2005

0
1980

2010

Percent (c) Share of full-time employed exiting to and entering from part-time and self employment

7

Scrambled
Household Identifiers

1985

1990

1995

2000

2005

2010

Source: Current Population Survey and authors' calculations

Source: Current Population Survey and authors' calculations(d) Share of full-time employed exiting to and entering from not-in-the-labor-force

Percent

7

Scrambled
Household Identifiers

6

Scrambled
Household Identifiers

Scrambled
Household Identifiers

6
Entry into FT employment, g(PT)

5

5

4

4

Exit out of FT employment, j(NILF)

Exit out of FT employment, j(PT)
3

3

2

2

1

1

Entry into FT employment, g(NILF)

0
1980

1985

1990

1995

2000

2005

0
1980

2010

1985

1990

1995

2000

2005

2010

Source: Current Population Survey and authors' calculations

Source: Current Population Survey and authors' calculations

Note: All panels contain 4-quarter moving averages. Panel (a) contains the average of the shares at the beginning and end of the year. Other panels show shares indexed at end of year.

44Daly, Hobijn, and Wiles
Figure 6. Shifts in earnings distribution function at median for different subgroups.
(a) Fraction of full-time employed that moves from below to above the median

Percent

4

Scrambled
Household Identifiers

90

3

75

2

70

1.5

65

1

60

0
1980

1990

1995

2000

2005

Scrambled
Household Identifiers

1990

1995

2000

2005

2010

(d) Fraction of flows into and out of NILF below MWE

Percent

90

Scrambled
Household Identifiers

Entries into FT employment,½{G(w|PT)+G(w'|PT)}

85

1985

Source: Current Population Survey and authors' calculations(c) Fraction of flows into and out of part-time and self employment below MWE

90Exits out of FT employment,½{F(w|U)+F(w'|U)}

50
1980

2010

Source: Current Population Survey and authors' calculations

Percent

Entries into FT employment,½{G(w|U)+G(w'|U)}55

Same Job½{F(w|SJ)-G(w|SJ)}+½{F(w'|SJ)-G(w'|SJ)}
1985

Scrambled
Household Identifiers

80

2.5

0.5

Scrambled
Household Identifiers85

Not in the same job,½{F(w|NISJ)-G(w|NISJ)}+½{F(w'|NISJ)-G(w'|NISJ)}

3.5(b) Fraction of flows into and out of unemployment below MWE

Percent

Scrambled
Household Identifiers

Scrambled
Household Identifiers

Scrambled
Household Identifiers

Entries into FT employment½{G(w|NILF)+G(w'|NILF)}

85
80

80

75

75
Exits out of FT employment,½{F(w|PT)+F(w'|PT)}

70

70

65

65

60

60

55

55

50
1980

1985

1990

1995

2000

2005

Exits out of FT employment½{F(w|NILF)+F(w'|NILF)}

50
1980

2010

Source: Current Population Survey and authors' calculations

1985

1990

1995

Source: Current Population Survey and authors' calculations

Note: All panels contain 4-quarter moving averages

45

2000

2005

2010

Dissecting Aggregate Real Wage Fluctuations

Figure 7. Decomposition of composition effect and wage growth effect by subgroup.
(a) Composition effect

Percent

0.4

Scrambled
Household Identifiers

Scrambled
Household Identifiers

0.2
0
-0.2
-0.4

-0.6
-0.8
-1

Same Job
NISJ

-1.2

Part time / self employment
Unemployed

-1.4

NILF

-1.6
1980

1985

1990

1995

2000

2005

2010

Source: Current Population Survey and authors' calculations(b) Wage growth effect

Percent

4

Scrambled
Household Identifiers

Scrambled
Household Identifiers

NISJ

3.5
3
2.5

2
1.5
1
0.5

Same Job

0
1980

1985

1990

1995

2000

Source: Current Population Survey and authors' calculations

Note: All panels contain 4-quarter moving averages

46

2005

2010

Daly, Hobijn, and Wiles

Figure 8. Contributions of changes in shares and shifts in earnings distributions to log change of MWE.
Contributions to 4-quarter log change; 4-quarter moving average

Percent

7

Scrambled
Household Identifiers

Scrambled
Household Identifiers

6

Wage growth effect

5
4
3
2
1
Total

0
-1
-2

Composition effect

-3
-4
1980

1985

1990

1995

Source: Current Population Survey and authors' calculations

47

2000

2005

2010

Dissecting Aggregate Real Wage Fluctuations

Figure A.1. Share of not-in-the-same-job imputed as job-to-job transitions.
Percent

68

66

64

62

60

58

56
1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011
Source: Current Population Survey and authors' calculations

Note: 12-month moving averages

48

Daly, Hobijn, and Wiles

Figure A.2. Comparison of decomposition in this paper with that in DiNardo, Fortin, and Lemieux (1996).
(a) percentile decomposition

Pr[Ww]

1

F(w’ p)

g(
s)
F(
W
|s)

Bshiftpp=F(wp)=G(w’ p)

j(
s)
G(
W
|s)

F(W) A

share

G(W)

BshareAshift

G(wp)
0

wp

w’p

(b) DiNardo, Fortin, and Lemieux (1996)

Pr[Ww]

Bshift1

F(w’ p)Bshare
|s)
W
(
s)G

j(

G(W)

p

p=F(wp)=G(w’ p)
F(W)
|s)
W
(
s)F

G(wp)
0

g(

AshiftAshare
wp

~
w
p
49

~
w’
p

w’p