Welfare Eﬀects of Polarization:
Occupational Mobility over the Life-cycle ∗Shinnosuke Kikuchi†
Sagiri Kitao‡
July 27, 2020

Abstract
What are the welfare eﬀects of polarization: wage and employment losses of
middle-class workers relative to low- and high-skill groups? We build a model ofoverlapping generations who choose consumption, savings, labor supply, and occupations over their life-cycles, and accumulate human capital. We simulate a wage
shift observed since the early 1980s and investigate individuals’ responses. Polarization improves welfare of young individuals that are high-skilled, while it hurts
low-skilled individuals across all ages and especially younger ones. The gain of thehigh-skilled is larger for generations entering in later periods, who can fully exploit
the rising skill premium.
Keywords: Occupational choice and mobility, routine-biased technological shock,overlapping generations model, polarization, welfare eﬀects.
JEL Classiﬁcation: E24, J21, J24, J62∗
We thank Matthias Doepke, Heejeong Kim, Satoshi Tanaka, Gianluca Violante, Minchul Yum, and participants ofseminars at the University of Tokyo, RIETI, and GRIPS-UT Macroeconomics and Policy Workshop for useful comments.
†‡

Massachusetts Institute of Technology, Email: shinnkikuchi@gmail.com.
University of Tokyo, Email: sagiri.kitao@gmail.com.

1

Introduction

The polarization in the labor market observed during the past several decades generated apeculiar pattern of employment and wage growth. Middle-class workers lagged behind lowand high-skilled workers, resulting in U-shaped growth in both employment shares andwages across skill distribution. A compositional shift in the demand of tasks was shown tobe critical in explaining the phenomena by empirical studies such as Autor et al. (2003).
Introduction of industrial robots in the manufacturing sector and technological innovations
replaced many routine tasks that had been performed by middle-skilled workers. The
consequence of this structural change was an erosion of demand for routine workers, as
documented by Autor and Dorn (2009), Acemoglu and Autor (2011), Barany and Siegel(2018) and Acemoglu and Restrepo (2018), among others.1
Autor and Dorn (2013) build a model of the goods and services sectors and three
types of tasks to show how computerization and replacement of routine tasks lead topolarization in employment and wages. Barany and Siegel (2018) study eﬀects of unbalanced technology shocks and show how a rise in productivity in the manufacturingsector results in an increase in demand for workers in low- and high-skilled services sector
that are complements, while driving down demand for and relative wage of manufacturing workers. Acemoglu and Restrepo (2018) build a task model with directed technicalchange and endogenous capital, and show that technological change can decrease real
wage for some workers, which cannot be accounted for by canonical factor-augmenting
technological changes.
Empirical studies clearly identify a group of occupations that are “winners” and“losers” ex post in terms of wages and employment. This fact, however, does not indicate
how polarization aﬀects the fate of individuals. A worker engaged in a losing occupation
may switch to a winning occupation to exploit diﬀerential wage growth. Young workers
in a winning occupation may enjoy higher wages for decades throughout their career but
others in the same occupation may enjoy the premium for just a few years until retirement.
Mobility cost to particular occupations may diﬀer according to the skills or education of
an individual and a switching barrier may be too high for some individuals to overcome.
Switching occupations may imply a loss of accumulated human capital for an experienced
worker and the need to re-accumulate it for a new occupation. Such a switch may be
worthwhile for a young worker but it may not be appealing for an older worker. A movethat involves a temporary wage decline may be costly for an individual with little saving
but consumption may not be aﬀected for someone else who has enough saving or an accessto public insurance. All of these are important factors in accounting for welfare eﬀects of1

Acemoglu and Autor (2011) review canonical models with two skill groups and factor-augmenting
technology, present a task-based approach that endogenizes substitution of machines for certain tasks toaccount for recent phenomena in the labor market, including job polarization, and provide a comprehensive survey of the literature.

2

polarization.
While there are a large number of empirical and theoretical studies on routine-biased
technological changes and polarization, not many studies focus on how these shifts aﬀect
behavior and welfare of heterogeneous individuals. In particular, there is a limited numberof papers that investigate a life-cycle dimension, although age appears to be one of thecritical factors in evaluating the welfare consequences of polarization.
Heathcote et al. (2010) build a life-cycle model to study welfare and macro eﬀects ofskill-biased technological change on individuals’ decisions of education, intra-family labor
supply, consumption and savings. Sachs and Kotlikoﬀ (2012) and Benzell et al. (2018)
build a two-period life-cycle model with two goods to theoretically investigate roles ofa technological shock. They argue that technological innovation beneﬁts owners of thetechnology, and that automation can lead to immiserating growth because young savers
with limited skills will own fewer assets. They propose that a proper intergenerationaltransfer be administered in order to restore productive investment and avoid a decline ofcapital in the long-run. These papers, however, do not explicitly consider occupational
decisions of individuals in response to technological changes and how decisions evolve
over a life-cycle. In this paper, we argue that these considerations are crucial in analyzing
welfare consequences of polarization.
Closest to our paper in terms model features are Dvorkin and Monge-Naranjo (2019)
and Cociuba and MacGee (2018).2 Dvorkin and Monge-Naranjo (2019) build an extended
Roy model of a dynamic occupational choice and human capital accumulation. They quantify eﬀects of automation and task-biased technological change on growth and earnings
inequality in the U.S. economy since 1980. In their quantitative analysis, they also embeda simple demographic structure, assuming entry of new workers and a stochastic exit ina perpetual youth model. Cociuba and MacGee (2018) construct a search model withthree sectors where individuals accumulate sector-speciﬁc human capital and own sectoral preferences and analyze how a change in the demographic structure aﬀects sectoral
reallocations and the aggregate economy. The model is populated with two generations
that age and exit stochastically.
2

For the papers with more empirical approach, see Cortes (2016), who uses panel data to follow theexperience of routine workers and documents their occupational and wage dynamics during decades ofpolarization. He focuses on how the mobility of employed individuals changes over time, accounting
for a shift of occupational distribution. See also Cortes et al. (2017), who build a neoclassical modelwith endogenous occupation and participation decision and investigate eﬀects of automation on workers’
mobility decisions.
There are also recent papers that emphasize roles of the demand side in response to changes in demographics. Acemoglu and Restrepo (2019) analyze the relationship between a demographic structure andautomation and argue that aging is associated with a more pronounced adoption of robots and automation. Abraham and Kearney (2018) study changes in employment by skill and age groups during thelast two decades and emphasize roles played by changes in demand factors including the penetration ofrobots and trade.

3

Our model diﬀers from and complements these papers in several dimensions. We build
a full-blown overlapping generations model of individuals that choose occupations while
they go through stages of their careers and life-cycles and accumulate physical and humancapital. They eventually decumulate physical capital as they approach retirement age andchoose to exit the labor force. The model accounts for the patterns of occupational choice
as part of a set of life-cycle decisions. Working-age individuals are hardly homogeneous,and heterogeneity matters in accounting for welfare eﬀects of polarization. We show thatquantitative eﬀects diﬀer not only across skills of individuals but also across stages of
their life-cycles when the structural change in occupational wages proceeds.
We use the Current Population Survey (CPS) to calibrate paths of occupation-speciﬁcwages since the early 1980s. We estimate functions that govern human capital accumulation using wage data of individuals that diﬀer in age, education, occupation, cohort, andtime. The Panel Study of Income Dynamics (PSID) is used to derive an idiosyncraticcomponent of wage growth that is consistent with the estimated occupation-speciﬁc wages
and life-cycle proﬁles of human capital. Our model is calibrated with these life-cycle data
and also accounts for the pattern of retirement across diﬀerent types of workers. The
model generates reasonable proﬁles of assets, consumption and overall earnings acrossages and allows individuals to make occupational decisions under tradeoﬀs faced at different life-cycle stages and under diﬀerent economic conditions.
We parameterize the economy to approximate the labor market in the early 1980s andthen simulate the polarization in this initial economy, a change in the wage structure acrossoccupations that occurred during the following decades. We show that the polarization
on average has had positive welfare eﬀects on high-skilled individuals in the economy. For
example, the high-skilled aged 25 will gain 1.2% in consumption equivalence while thelow-skilled of the same age will lose by about 2%. The gain of the high-skilled is larger for
generations that enter the economy in later periods although it remains in a narrow range
and stays at less than 2% in consumption equivalence. The welfare loss for the low-skilled
rises more quickly over time. Upward mobility to occupations with rising wages is limitedwith high mobility cost and many will choose to accept lower wages. As a generation,
future generations fare worse. Note that this is not because the gain of the polarization
accrues to the old while sacriﬁcing welfare of the young, but because the welfare loss of
the low-skilled rises more rapidly. The high-skilled future generations continue to gain.
Diﬀerent experiences across skill types through evolution of their occupations contributes
to a rising skill premium and more inequality in earnings and wealth.
The paper is organized as follows. Section 2 presents data used in the analysis andreviews the labor market trends and polarization in employment and wage across occupation categories during the past several decades. We also review cross-sectional trendsof employment shares and wages across age groups and investigate employment mobility
and wage growth of individuals. Section 3 presents our life-cycle model and section 4
4discusses parametrization. Section 5 presents numerical results and section 6 concludes.

2

Data and Trends in the Labor Market

2.1

Data

This section documents the polarization in the labor market in the US over the past
several decades. The data source of our analysis is mainly the Current Population Survey(CPS) for occupational distribution and wage proﬁles, and is supplemented by the Panel
Study of Income Dynamics (PSID) for wage growth.
2.1.1

CPS Data

Selection of Individuals:
The main data source for our analysis is the CPS from1983 to 2018, and we use employment and wage data of male heads of household aged atand above 25. We use the labor market data since the early 1980s to capture the long-run
polarization trend that continued during the last several decades.3
Employment Status and Occupational Distributions: Individuals are either employed or not employed, and the employed are divided into three groups according to theiroccupations. To construct occupation categories, we use the 3-digit occupation codes of
the Census and categorize them into three groups: Abstract, Routine, and Manual, following Acemoglu and Autor (2011).4 Occupations are classiﬁed as follows.
• Abstract: managers, management-related, professional specialty, technicians andrelated support• Routine: construction trades, extractive, machine operators, assemblers, inspectors, mechanics and repairers, precision production, transportation and material
moving occupations, sales, administrative support• Manual: housekeeping, cleaning, protective service, food preparation and service,building, grounds cleaning, maintenance, personal appearance, recreation and hospitality, child care workers, personal care, service, health care support
For non-employment, we exclude those who report unemployed as their employment status. As we will discuss below, the frequency of our model is annual and the model is not
built to account for in-and-out labor market mobility of a high frequency and, in particular, frictional unemployment of a short duration, which represents most unemployment
3

We let our sample data start in 1983 because of a known discrepancy in CPS occupational categories
between the time before and after 1983, as documented in Kambourov and Manovskii (2013).
4
We use the 1990 Standard Occupational Classiﬁcation (SOC) codes of the CPS.

5

incidences in normal times.5 Such unemployment would not necessarily involve major
depreciation of human capital, mobility to another occupation as a result, or a permanent
exit from the labor force.
We identify from data and distinguish between short-term unemployed (less than orequal to 3 months) and long-term unemployed (more than 3 months), and include theformer as employed based on the occupation that the individual reported he was engaged
in during his previous job.6
Hourly Wage:
Hourly wage is computed as the sum of wage and business incomeof an individual divided by work hours. Following Baum-Snow and Neal (2009), in thecomputation of wages, we drop samples that report weekly hours of less than 5 hours andwhose computed hourly wage is less than $1.5. Also, we drop those whose hourly wage isgreater than $99.8 in 1999 dollars.
2.1.2

PSID data

The data source to estimate idiosyncratic income shock is the PSID from 1983 to 1997.
We limit samples to male household heads aged 30 to 59 and employed in either threeoccupation categories of abstract, routine, and manual to be consistent with CPS data.
We exclude the oversample of low-income households (SEO samples) and the immigrantsamples.7 We document the detailed procedure of the estimation in section 4.8

2.2

Polarization in the Labor Market

This section reviews and documents polarization in the labor market in the US over the
past several decades. The data source is CPS data.
Macro Dynamics of Employment and Wage:
Figure 1a shows the distributionof workers aged 30-59 across the three occupation groups from 1983 to 2018. A share
5

Among our unemployed male-head CPS samples (since 1968, those aged between 25 and 64), theaverage elapsed duration of unemployment was 16 weeks and the median 11 weeks.
6
We also drop samples that are unemployed for less than or equal to 3 months but fail to report theirprevious occupations. We note that there is no major change in the occupational distribution when we
adjust the cutoﬀ from 3 months to 6 months or 12 months.
7
Consistent with our treatment of the CPS data, when computing wages, we drop samples that report
weekly hours of less than 5 hours and whose computed hourly wage is less than $1.5 or greater than $99.8
in 1999 dollars, following Baum-Snow and Neal (2009).
8
We use the PSID data only for calibration of idiosyncratic income shock. We could have used PSID
data for occupational mobility. However, CPS data and PSID data are not entirely compatible, andoccupational distributions are diﬀerent as documented in Kambourov and Manovskii (2013). Thus, wechoose to use a variable in the CPS, occly, which reports the person’s primary occupation during theprevious calendar year. See section 4 for more details.

6

of the routine occupations, which employed approximately 60% of the workforce in theearly 1980s, has fallen steadily to 45% in 2018. Employment shares of both abstract andmanual occupations absorbed the decline and rose nearly monotonically during the last
decades. Figure 2 plots shares of abstract and manual occupations relative to that ofroutine occupations of the same year, which more clearly indicates a rapid and almost
monotone decline of routine occupations relative to the other two.
Figure 1b shows the share of non-employment out of all individuals in our sample
aged 30-59 in each year. This fourth group includes those not in labor force and full-timestudents. The non-employment rate of working-age individuals was less than 7% in theearly 1980s and increased steadily to reach 13% by the early 2010s.

(a) By Occupation Category(b) Non-employment Rate

Figure 1: Employment Share and Non-Employment Rate (Age 30-59)
Note: The left ﬁgure shows the share of employment by occupation category. The right ﬁgure shows thefraction of non-employment out of all individuals. For both ﬁgures, we restrict samples male heads ofhousehold aged 30-59.

7

(a) Abstract(b) Manual

Figure 2: Relative Employment Share (Routine=1, Age 30-59)
Note: The left ﬁgure shows the fraction of workers in abstract occupations relative to routine occupations.
The right ﬁgure shows the fraction of workers in manual occupations relative to routine occupations. For
both ﬁgures, we restrict samples to male heads of household aged 30-59.

In tune with employment shares, wages evolved diﬀerently across the three occupation
categories. The left panel of Figure 3 shows hourly real wage in the three occupations overtime. Routine wages declined from the 1980s to the mid-1990s and they have stagnatedsince 2000. Manual wages have always lain below routine wages, but the diﬀerence between
the two has declined since the 1980s.
The right panel of Figure 3 shows the dynamics of abstract and manual wages relative
to routine wages in each year. While relative wages of manual occupations grow andapproach 1 from below, abstract wages have quickly diverged from 1 since the early 1980s,
indicating a decline in the relative wage of routine workers against both occupations.

8

1.8

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3
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1985 1990 1995 2000 2005 2010 2015

1985

1990

1995

Year

2000

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2010

2015

Year

(a) Hourly Wage (in log)(b) Relative Wage (routine=1)

Figure 3: Wages by Occupation Category
Note: The left ﬁgure shows the average hourly wage (in log) of workers by occupation category. The rightﬁgure shows the same data in relative term, in which the average hourly wage for routine occupations
is normalized to one. For both ﬁgures, we restrict samples to male heads of household aged 30-59. In
addition, we drop samples that report weekly hours of less than 5 hours and whose computed hourly
wage is either less than $1.5 or more than $99.8 in 1999 dollars.

Employment and wage data across three occupation categories indicate that the polarization and decline of routine occupations is not a phenomena that occurred during aparticular decade or a trend that started recently but it has continued for a much longer
period and continuously over the last several decades.9
Polarization and Life-cycle:
Figure 4 shows an age dimension of the polarization
during the past decades, indicating how individuals of diﬀerent ages have been spread
across diﬀerent occupations and how the distribution evolved since the 1980s.10 We groupindividuals of a given age in each year into the four bins of employment types, including
employment in the three occupation categories and a state of non-employment, and plot
the shares by age on a horizontal axis for each decade from the 1980s to the 2010s.11
9This is consistent with the argument of recent papers including Barany and Siegel (2018), who argue
that the polarization started in as early as the 1950s using the US Census and American Community
Survey (ACS) data, and Cortes (2016), who analyzes the PSID data since the 1970s.
10
We compute shares for a ﬁve-year age group in each decade as it helps remove noisy spikes thatwould make it hard to read the proﬁles due to a very small sample size in some combinations of age andoccupation.
11
For example, 0.5 in Figure 4b at age 40 in 2000-2009 indicates that 50% of individuals at age 4044 in 2000s were employed on a routine occupation, while 8% were not in labor force as shown for acorresponding sample in 4d.

9

0.4

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(a) Abstract(b) Routine
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Age

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0
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Age

(c) Manual(d) Non-Employment

Figure 4: Employment Status by Age
Note: The four ﬁgures show the lifetime path of the share of each employment status category (Abstract,
Routine, Manual, Non-Employment) within each age group (25-29, ..., 60-64) for four sample periods(1983-1989, 1990-1999, 2000-2009, 2010-2018). For all the ﬁgures, we restrict samples to male heads ofhousehold aged 25-64.

Shapes of the proﬁles are uniquely diﬀerent across occupation categories. A crosssectional life-cycle proﬁle of the abstract occupations, as shown in Figure 4a, is mildly
hump-shaped in all decades. The share is slightly lower among individuals in their 20s
and reaches a peak of 35-38% thereafter. The proﬁles show a decline well before theretirement age, reaching 18-25% by the early 60s.
The rising trend of the employment share of abstract occupations as seen in Figure 2a
is less visible in life-cycle proﬁles and the increase is not monotone across age groups.
During the past few decades, the peak of the share has shifted to a younger age andthe share is the highest among those in their 30s in the 2010s, and proﬁles show a steep
10decline thereafter as the age increases, indicating the eﬀects of changes across cohorts as
we will discuss below.
A decline in the employment share of routine occupations is more clearly visible acrossall age groups, as shown in Figure 4b. From the 1980s to the 2010s, the shares fell by
more than 10 percentage points for individuals ranging from their 20s to 40s. The decline
is more pronounced among those in the early stage of their lives. For example, the sector
declined by about 19 percentage points among those aged 25-29.
Manual shares remain low during this period. Since the 1980s, however, the proﬁlestarted to become more negatively sloped in age while the level increased, implying an
increase in the inﬂow of workers in their 20s into manual occupations as they entered to
the labor market.
In addition to the three occupation categories for the employed, we include a fourthstate of non-employment in the analysis. As shown in Figure 4d, individuals start toleave the labor force in their 50s, when they have more than a decade before reaching thenormal retirement age and starting to collect social security beneﬁts. At the same time, alarge fraction of individuals remain in the labor force even in their early 60s and, in fact,
in their late 60s and later as well, though the latter is not indicated in the ﬁgure.
The share of non-employment has increased since the 1980s across all age groups.
Non-employment is an important state to include when we analyze labor market mobilityof individuals over their life-cycle and across occupations.
Figure 5 shows life-cycle proﬁles of wages in abstract, routine and manual occupations,
respectively during the past few decades. The shapes of proﬁles are somewhat similar,
rising fast during the early phases of careers in their 20s and 30s and slowing down laterin their 40s and 50s. The decline in wages in later years is more visible in the routine andmanual occupations, but the wages are ﬂatter until individuals are in their late 50s andearly 60s in the abstract sector. Abstract wages declined from the 1980s to the 1990s androse afterwards. Routine wages showed a decline from the 1980s to the 1990s and havestagnated since then, which is consistent with the shift with the aggregate wage transition
seen in Figure 3. The decline is particularly large among those in their 20s to mid-40s.
Routine occupations of these age groups experienced a signiﬁcant decline not only in theemployment share as we saw in Figure 4 but also in wages.

11

3.6

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Age

Age

(a) Abstract(b) Routine

50

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2.5
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(c) Manual

Figure 5: Wage by Age (in log)
Note: The ﬁgures show the lifetime path of the average hourly wage (in log) within each age group (2529, ..., 60-64) for four sample periods (1983-1989, 1990-1999, 2000-2009, 2010-2018) for each occupation
category (Abstract, Routine, Manual). We restrict samples to male heads of household aged 25-64. In
addition, we drop samples that report weekly hours of less than 5 hours and whose computed hourly
wage is either less than $1.5 or more than $99.8 in 1999 dollars.

Occupation by Skills:
In the quantitative model we build below, we also divide
individuals by skills, distinguishing between those with and without a college degree.
The distinction is motivated by their very diﬀerent patterns of occupations over theirlife-cycles.
Figure 6 shows a life-cycle proﬁle of occupations by skills according to CPS data inthe early 1980s (1983-1985). Low-skilled workers are predominantly engaged in routine
occupations throughout their life-cycle and the high-skilled are most likely to be engaged
in abstract jobs. 10-20% of low-skilled workers are engaged in abstract jobs from their 20s
to 60s, while about 20-30% of high-skilled workers assume routine occupations. Manual
occupations constitute a very small fraction of both types of workers, though there are
relatively more of them among low-skilled than high-skilled individuals.
Low-skilled workers tend to leave the labor force earlier than the high-skilled andparticipation rates at age 65 are less than 40% among our low-skilled samples, whereas it
is as high as 60% among the high-skilled.

12

1

1
Abstract
RoutineManualNo-work

0.8

Abstract
RoutineManualNo-work

0.8

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0
30

40

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60

70

30

40

50

Age

Age

(a) Low-skilled(b) High-skilled60

70

Figure 6: Occupation by Age and Skills (CPS Data in 1983-1985)
Note: The left ﬁgure shows the lifetime path of the share of each employment status category (Abstract,
Routine, Manual, Non-Employment) within each age group (25-29, ..., 75-79) for individuals withoutcollege degrees. The right ﬁgure shows the same but for individuals with college degrees. For bothﬁgures, we restrict samples to male heads of household in 1983-1985.

Figure 7 shows how the distribution shifted over time using cross-sectional distribution
for the selected years of 1985, 2000 and 2015.12 Although the share of workers in abstract
occupations rose monotonically at the aggregate level as we saw in Figure 1, the share has
not increased or even changed much conditional on age and skills. The seemingly puzzling
discrepancy is explained by a rise in skills of new entrants, as shown in Figure 8. The
share of high-skilled individuals, a large fraction of whom are in abstract occupations,increased from around 30% in the early 1980s to more than 40% by the late 2010s, withsome non-monotonicity during the transition.
The share of routine occupations has decreased across all ages among the low-skilled,
who constitute the majority of the occupation. Manual occupations have also increased
relative to other occupations, although changes are not monotonic among the high-skilled.
These ﬁgures emphasize the importance of taking into account heterogeneity in skills andphases of life-cycle in quantifying welfare eﬀects of polarization that occurred during thelast decades.
12

Similar ﬁgures can be generated for life-cycle proﬁles of diﬀerent cohorts, rather than in the crosssection. The main observations about the occupational trend remain the same.

13

Abstract

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(b) High-skilled

Figure 7: Occupation by Age and Skills over Time (CPS Data in 1985-2000-2015)
Note: The left panel shows the share of each employment status category (Abstract, Routine, Manual,
Non-Employment) within each age group (25-29, ..., 75-79) for the selected years of 1985, 2000, and 2015
for individuals without college degrees. The right panel shows the same but for individuals with college
degrees. For all the ﬁgures, we restrict samples to male heads of household.

0.5
0.45
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0.35
0.3
0.25

1985 1990 1995 2000 2005 2010 2015

Year

Figure 8: Fraction of High-skilled (CPS Samples Aged 25-29 in 1983-2018)
Note: The ﬁgure shows the fraction of individuals with college degrees out of all the individuals. We
restrict samples to male heads of household aged 25-29.

14

3

Model

This section describes elements of the model and individuals’ life-cycle problem.
Demographics: At age j = 1, individuals enter the market with initial assets denoted
as a1 . ϕj+1 represents the conditional survival probability that individuals aged j remain
alive until age j + 1. We assume that individuals die with certainty at the end of age
j = J and ϕJ+1 = 0 by assumption.
Endowment, Occupation and Human Capital:
Individuals are born with a skill
type, s = {L, H}, which represents their education prior to entry into the labor market.
A state variable, o, summarizes employment status and an occupation of a worker, thatis, o = {A, R, M, N }, where the last element N denotes a state of non-employment. The
employment status is an individual’s choice and evolves endogenously over the life-cycle.
Workers are employed in one of the three occupations: abstract, “A,” routine, “R,” andmanual, “M .”At time t, earnings of an individual at age j, of skill s, and in occupation o is given as
yt,j,s,o = ηs,o hj,s,o wt,o l. Here, ηs,o denotes an idiosyncratic labor productivity shock, which
may depend on skill and occupation. hj,s,o represents human capital, which endogenously
grows over an individual’s life-cycle. wo,t ∈ {wA,t , wR,t , wM,t } is occupation-speciﬁc wage
and l is an indicator for participation and equals 1 if o = {A, R, M } and 0 if o = N .
Workers accumulate occupation-speciﬁc human capital on the job. Human capital of
an individual of age j and skill s evolves according to function h′ = f h (h, j, s, o, o′ ), whereo′ denotes his occupation in the next period. Human capital grows endogenously withthe decision of participation and occupation. Initial human capital at age j = 1 is given
as h1,s,o for each skill type and occupation.
There are two types of shocks that aﬀect earnings of individuals. First, an individualof skill s and occupation o faces an exogenous separation from his current occupation withprobability λs,o . Upon receiving the separation shock, the individual will have a choiceof leaving the labor force or choosing another occupation in the following period. The
occupation-speciﬁc human capital he has accumulated will be lost.
Second, an individual of skill s draws a vector of idiosyncratic productivity shockη s = {ηs,A , ηs,R , ηs,M } from skill-speciﬁc distribution in each period.
Preferences:
Individuals derive utility from consumption and disutility from labor
participation, and a period-utility function is denoted as u(c, l). β is the subjective discount factor.
When individuals change occupations, they incur a mobility cost of csoo′ in terms of lost
utility, which depends on skill level s as well as the occupational origin o and destinationo′ .
15

Social Security and Transfers:
Individuals receive social security beneﬁts once
they reach the eligibility age jR . We assume that the payment is constant at ss. The
government also operates a means-tested transfer program which guarantees a minimum
level of consumption c and the amount of the transfer is given as max{0, c − (1+ r)a − ss}.
The total transfer payment from the government including social security beneﬁts anda means-tested transfer is denoted as tr, which depends on the set of individual states, as
explained below in the life-cycle problem of an individual.13
Life-cycle Problem:
A state vector of an individual is given by x ≡ {j, a, s, o, h},where j denotes age, a assets, s skill, o occupation, and h human capital.
We solve the problem of an individual in two steps, using two value functions, V and
W . The former, V , is determined by participation and occupation decisions, subject toshocks to productivity and changes in human capital as a consequence of his occupation
decision. The latter, W , is determined by consumption and saving decisions.
As an individual enters a new period, he learns whether he is subject to separation
shock λs,o or not. At the same time, he draws a vector of idiosyncratic productivityη s = {ηs,A , ηs,R , ηs,M } that would aﬀect his earnings in each occupation o′ .14 Based on
the information, he will choose a new occupation. The choice will aﬀect his new humancapital h′ , which his occupational decision will take into account, as shown in the following
Bellman equation.
∫
V (j, a, s, o, h) =ηs

λs,o max{W (j, a, s, o′ , h′ , ηs,o′ ) − csoo′ }′o (̸=o)+(1 − λs,o ) max{W (j, a, s, o′ , h′ , ηs,o′ ) − csoo′ } dη s′owhere h′ = f h (h, j, s, o, o′ ).
Next, given a new occupation o′ as well as productivity ηs,o′ , which is occupationo′ speciﬁc, and a new level of human capital h′ , an individual chooses consumption cand savings for the next period a′ . tr(x) denotes a transfer from the government which
includes a means-tested transfer as well as old-age social security beneﬁts and depends
on a state vector of an individual.
W (j, a, s, o′ , h′ , ηs,o′ ) = max{u(c, l) + βϕj+1 V (j + 1, a′ , s, o′ , h′ )}
′
c,a

s.t.
a′ + c = (1 + r)a + h′ ηs,o′ wo′ l + tr(x)Note l = 1 if o′ = {A, R, M } and 0 if o′ = N .
13

Note that we do not explicitly impose the government budget constraint in each period.
Note that if he is separated from his current occupation o, he is unable to stay in the same occupationin the following period and the draw of ηo is irrelevant.
14

16

4

Calibration

Preliminaries: We use the model described above to quantify eﬀects of polarization on
individual decisions and welfare. We will ﬁrst calibrate the model to an initial economy
that approximates the distribution of individuals across occupations and labor market
in the early 1980s. We will then introduce “polarization” that changes the paths ofoccupation-speciﬁc wages, as well as the distribution of new entrants across occupationand skills as we will discuss in more details below.
The model frequency is annual. We let individuals enter the economy at age 25 andlive up to a maximum age of 85 (j = 1, · · · , 61). Survival probabilities ϕj are based on
the U.S. life table of 1990. We abstract from population growth and assume that age
distribution is stationary. The interest rate is assumed constant and set to 4%.
Endowment, Productivity and Wages:
Skills are represented by education levels
which are determined prior to the entry of individuals into the labor market. We assume
that individuals start their life with zero initial assets, a1 = 0.
We let individuals of given skills draw a set of initial productivity and initial occupations from skill-speciﬁc distributions. In particular, the idiosyncratic productivity ηs,ois drawn from a stationary distribution of ηs,o shocks for each occupation. Occupationspeciﬁc wage in year t, wo,t , is computed from CPS data. We explain a detailed calibration
procedure after discussing calibration of human capital below.
Human Capital:
The level of human capital at the initial age for each skill andoccupation is given by h1,s,o , which is the average wage of individuals aged 25 of diﬀerent
skills and occupation based on the age-speciﬁc wage proﬁles we estimate using CPS data,as presented below.
After entry, the level of an individual’s human capital evolves according the law of
motion h′ = f h (h, j, s, o, o′ ), which depends on the individual’s age, current human capital,
skills and new and old occupations.
When an individual continues to work in the same occupation, his human capitalh, which depends on his age, skills and occupation. When he moves to a
grows at rate gj,s,o
new occupation, he would lose occupation-speciﬁc human capital that he has accumulated
and need to accumulate human capital in the new occupation o′ , starting from an entry
level of human capital, h1,s,o′ . Note that, however, his earnings do not necessarily fall due
to an occupational transition since they also depend on an occupation-speciﬁc wage ratethat varies over time and idiosyncratic productivity shock. The law of motion for humancapital h′ = f h (h, j, s, o, o′ ) is summarized as follows.
{h)h if o′ = oh′ = (1 + gj,s,oh′ = h1,s,o′
if o′ ̸= o17Three components related to earnings, ﬁrst, idiosyncratic shock process for ηs,o , second,
human capital dynamics, and third, occupation-speciﬁc wage paths, are calibrated with
CPS data. We use wage data wi,j,s,o,t,τ of individual i of age j, skill s, occupation o, inyear t and cohort τ and decompose the series into the three components. We describe thecalibration process in four steps.
First, we regress the wage data on age, occupation, skill, cross terms of age andoccupation, cross terms of age and skill, year dummies, cohort dummies, and cross termsof year dummies and occupation.15 As is well known, including full vectors of time-related
dummies of age, year, and cohort would generate collinearity. Following Aguiar and Hurst(2013), we attribute wage growth to age and cohort eﬀects and use year dummies tocapture cyclical components.
Second, we extract average predicted values for each age, skills and occupations tocompute age-wage proﬁles for each combination of skills and occupations. Figure 9 shows
the lifetime path of average human capital for each skill and occupation, where we normalize estimates by the average wage of low-skilled workers aged 25-29 for each occupation.16his computed as the age-derivative of these proﬁles.
The growth rate of human capital gj,s,o
1.7

2
High
Low

1.6

1.8

2.4
High
Low

2.2

1.5

2

1.6

1.4

1.8

1.4

1.3

1.6

1.2

1.4

1.1

1.2

1.2
1
25

30

35

40

45

50

55

60

1
25

30

35

40

45

50

55

60

1
25

High
Low

30

35

40

45

Age

Age

Age

(a) Abstract(b) Routine(c) Manual

50

55

60

Figure 9: Estimated Lifetime Human Capital (Low, aged 25/29=1)
Note: The ﬁgures show the lifetime path of average human capital for each skill and occupation, which
we obtain from the estimation described in the main text. We normalize the estimates by the average
human capital of low-skilled workers aged 25-29 for each occupation to one. We restrict samples to maleheads of household, and the sample period is 1983-2018.
15

We use age dummies for a ﬁve-year age group in each year as it helps remove noisy spikes due to avery small sample size in some combinations of age and occupation.
16
We assume that the path is time-invariant. As shown in Figure 5, this assumption may well bejustiﬁed for workers in abstract or routine occupation. For manual occupation, the lifetime path of
the 1980s is slightly diﬀerent from those in other periods. We assume a time-invariant path since thediﬀerences are quantitatively small, and the eﬀects of an alternative assumption would be quantitatively
small, because the share of manual occupations accounts for less than 10% of the population as shownin Figure 1.

18

Third, we calibrate occupation-speciﬁc wage rate wo,t by averaging predicted values
for each occupation in year t. Figure 10 shows the path of estimated occupation-speciﬁcwage in log from 1983 to 2018. We normalize the proﬁle by wages of routine occupations
in each year. Note that these proﬁles are diﬀerent from the simple average age-wage
proﬁles computed for all workers of each occupation in Figure 3. The latter proﬁles do
not take into account heterogeneous human capital that varies by age while the former
proﬁles do. The trend, however, that both abstract and manual occupation wages growfaster than those of routine occupations during this period remains unaﬀected.

1.4
1.2
1
0.8
0.6
1985 1990 1995 2000 2005 2010 2015

Year
Figure 10: Estimated Occupation-Speciﬁc Wage wo,t (Routine=1)
Note: The ﬁgure shows path of estimated occupation-speciﬁc wage (in log) from 1983 to 2018. We
normalize the average hourly wage for routine occupations is normalized to one. We restrict samples tomale heads of household.

Fourth and lastly, we calibrate idiosyncratic productivity shock ηs,o , estimated fromresiduals of log-wage after removing average age-speciﬁc human capital and occupationalspeciﬁc wage rates estimated in above steps. Since we need panel data for the estimationof wage growth, we use PSID data from 1983 to 2018 in this step. The standard deviationof the i.i.d. shock is 0.18 for wages of all occupations on average and we use this value tocalibrate the draws of ηs,o .17
Preferences:

We assume the period utility functionu(c, l) =c1−γ− Bs · l,1−γ17

We also estimated the standard deviation for each occupation and for each combination of occupations
and skills. The values for the former lie in the range from 0.17 to 0.24. We choose to use the average
across occupations since some groups, for example a group of high-skilled manual workers, has a verysmall number of samples and estimates are not accurate.

19

and that an individual derives utility from consumption and incurs disutility from work Bs ,if l = 1. We set the values of disutility so that the model matches average participation
rates of 35% and 60% at age 65 for low- and high-skilled individuals, respectively. γ
represents the degree of risk aversion and is set to 2.0. The subjective discount factor β
is set at 0.982, calibrated to match the ratio of average wealth (for the poorest 99%) toaverage pre-tax earnings, at 3.9.18
We calibrate the occupational switch cost csoo′ together with other parameters related
to occupational mobility and discuss them in the next paragraph.
Occupational mobility:
We use CPS data to calibrate two sets of parameters thatare closely tied to mobility across occupations: ﬁrst, probabilities of exogenous separation
λs,o and second, occupational mobility cost csoo′ .
Our model accounts for an individual’s exit from the labor force associated with atransition from a working phase to retirement. We do not, however, account for various
reasons behind non-employment among young individuals, for example, due to healthconditions and disability, or full-time study. Therefore, we assume that mobility from
employment to non-employment in our model is due to retirement and that employment
status N is an absorbing state.
We use a variable, occly, of the CPS that indicates an occupation of an individualin the previous year, and construct a transition matrix across three occupations. We use
mobility data of workers aged between 30 and 49 over the three years from 1983 to 1985 toapproximate mobility of active workers in the initial economy. The transition probability
is given in (1) and (2) below. psoo′ , the {o, o′ }-th element of the transition matrix, denotes
the probability that a worker of skill s moves from occupation o in the current period too′ in the next period.
A
A
0.967

R  0.008
0.009
M

A
0.987

R  0.036
M
0.042


Low =

High =

RM 
0.029 0.005

0.986 0.006 
0.047 0.944

0.012 0.001

0.961 0.003 
0.040 0.919

(1)

(2)

For calibration of mobility cost csoo′ across occupations, we make the following assumptions.
First, we assume that individuals do not transition from manual occupations to abstract
occupations directly and set csM A = ∞ for all s. We make this assumption given the verysmall number of workers making such a transition.19 Besides the move from M to A, we
18

Heathcote et al. (2010) use the 1992 SCF and report the average wealth to earnings ratio of 3.94.

19 L
pM A is less than 1% and although pH
M A is larger at 4.2%, the number of such moves is extremely20assume that mobility cost in all other directions is zero except for moves from M to R andfrom R to A, which involve an upward change in occupation-speciﬁc wages. We calibrate
mobility cost csRA to match an average share of abstract occupations and mobility cost
csM R to match transition probabilities psM R for each skill type s = {L, H} in the initial
economy.
We calibrate probabilities λs,o of exogenous separation so that the model matches total
separation rates from each occupation and skill as shown in the transition matrices above
for our initial economy.
Government: The consumption ﬂoor c is set to 10% of average earnings in the initial
economy.20 Annual social security beneﬁts ss are provided to individuals once they reachage 66 (j = 42). The amount is set so that beneﬁts replace 38% of average earnings
in the initial economy, based on the average gross replacement rate.21 Both the levelof the consumption ﬂoor and pension beneﬁts are ﬁxed throughout the transition. Accidental bequests are assumed to be conﬁscated by the government and used for public
expenditures that do not aﬀect individuals’ budget constraint or utility.
Other Variables in Transition:
As explained above, entrants of age j = 1 are
randomly assigned to initial occupations, based on the CPS distribution. We use data ofoccupational distribution of workers of each skill type aged between 30 and 34.22 Figure 11
shows occupational distribution between 1983 and 2018. As already seen in Figure 7,
there is no major change in the share of abstract occupations in both low- and highskilled workers and it rises only very mildly over the last decades. There is a more visible
increase in manual occupations and a decrease in routine occupations. We use a smoothedversion of the paths as the initial distribution for entrants in the transition computation.
The time path of skill distribution is based on CPS data, as we already saw in Figure 8.
This does not aﬀect the optimization problem of individuals, but is relevant when wecompute cohort-speciﬁc welfare eﬀects of polarization as it is used as a weight on eachskill type within a cohort.
small given that very few high-skilled individuals of this age group work in manual occupations in theﬁrst place.
20
The level of consumption ﬂoor is in the range of estimates in studies such as De Nardi et al. (2010)
and papers cited therein.
21
The replacement rate is from OECD Pension At A Glance (2017).
22
We use data of those aged 30-34 in 1983 to 2018, rather than those aged 25-29 or younger, for the
initial distribution. The model does not account for worker mobility in the very early phase of a career,which involves frequent occupational switches and churning, for various reasons that the features of ourmodel do not capture.

21

0.8

0.8

0.6

0.6
Abstract
RoutineManual

0.4

0.2

0

Abstract
RoutineManual

0.4

0.2

0

1985 1990 1995 2000 2005 2010 2015(a) Low-skilled

1985 1990 1995 2000 2005 2010 2015(b) High-skilled

Figure 11: Distribution of Initial Occupations
Note: The left ﬁgure shows the path of the share of employment by occupation category for workers
without college degrees. The right ﬁgure shows the same but for workers with college degree. For bothﬁgures, we restrict samples male heads of household aged 30-34.

5

Numerical Results

In this section we ﬁrst present the numerical results for the initial economy. We thendiscuss the transition dynamics after the economy experiences polarization. Finally, we
analyze welfare eﬀects from polarization and compare impact on individuals of diﬀerent
skills, ages and cohorts.

5.1

Initial Economy

Figure 12 shows occupation shares by age for low- and high-skilled individuals, respectively. The data counterpart of this ﬁgure is Figure 6 in section 2. The match is successful
partly because of the calibration strategy where we set certain parameter values to match
key moments in the data.
The initial occupations are randomly assigned so that the distribution is consistent
with the CPS data. We also restrict upward occupational mobilities, for example, frommanual to abstract and from routine to abstract occupations, by calibration of mobility
cost so that the overall transition is consistent with the data. Also, a preference parameter that represents participation cost for each skill type is set to match the average
participation rate at age 65. Other than these parameters, moves from one occupation toanother and transitions from work to retirement are endogenously chosen by individuals

22

Table 1: Parameters of the model: initial economy
Parameter Description
Demographics{ϕj }Jj=1
conditional survival probabilities
Jmaximum ageµs
skill distribution (H and L)
Preferenceβsubjective discount factorγ
Bscurvature parametercost of labor force participationcsoo′
occupational mobility costs
cooccupational entry cost
Labor productivity and human capitalhhuman capital growth rate
gj,s,oh1,s,oinitial human capitalηoidiosyncratic productivity shock(standard deviation)
λs,oseparation shock
Factor prices: wages and interest raterinterest ratewo
wage rate by occupation
Governmentc
consumption ﬂoorsssocial security for retirees

23

Values, source and target
SSA Life Table (1990)
61 (85 years old)
CPS data
0.982
average wealth-income ratio of 3.9
2.0{0.36, 0.59}
CPS participation data (age 65)
CPS mobility data (age 30-49)
CPS occupation distribution (age 25-29)
CPS life-cycle proﬁle (estimated)
CPS life-cycle proﬁle (age 25-29, estimated)
0.18
PSID wage data (residual, estimated)
CPS mobility data (age 30-49)
4%
CPS data (estimated)
10% of average earnings
average replacement rate of 38%

in the model, while they also choose optimal consumption and savings and accumulate
human capital over their life-cycles.
As in the data, routine and abstract occupations are dominant occupations for lowand high-skilled individuals, respectively, and this does not change throughout their lifecycles. Among the low-skilled, a large number of individuals, especially those engaged inroutine occupations, start to leave the labor force as early as in their 50s, well before theyreach the social security eligibility age of 66. High-skilled individuals start to leave thelabor force at a slower pace, and more than 20% of them remain in the labor force evenat age 75 in the data.
1

1

0.8

0.8

0.6

0.6

Abstract
RoutineManualNo-work

0.4

Abstract
RoutineManualNo-work

0.4

0.2

0.2

0

0
30

40

50

60

70

30

(a) Low-skilled

40

50

60

70

(b) High-skilled

Figure 12: Occupation over the Life-Cycle by Skills in the Initial Economy
Note: The left ﬁgure shows the lifetime path of the share of each employment status category (Abstract,
Routine, Manual, Non-Employment) within each age group (25-29, ..., 75-79) for individuals withoutcollege degrees, which is computed in the model. The right ﬁgure shows the same but for individuals
with college degrees.

Figure 13a shows average earnings by age and skills, normalized by average earningsof low-skilled individuals at age 25. Earnings rise steeply in their 20s and 30s as they
accumulate human capital, and start to fall gradually in the late 40s and more sharply
in the 50s and 60s, exhibiting a hump-shaped proﬁle over the life-cycle. Figure 13b
displays life-cycle proﬁles of assets. Individuals start with zero assets (by assumption)
and accumulate wealth for both precautionary and retirement reasons. The proﬁle peaksin the late 50s for the low-skilled and at around age 60 for the high-skilled and they
decumulate assets as they age, in line with the hump-shaped age-wealth proﬁles reported
in papers such as Kuhn and Rı́os-Rull (2016).

24

2

12
High
Low

High
Low

10

1.5
8
1

6
4

0.5
2
0

30

40

50

0

60

30

(a) Earnings

40

50

60

70

(b) Assets

Figure 13: Earnings and Assets by Age and Skills in the Initial Economy (Low, aged
25=1)
Note: The left ﬁgure shows the lifetime path of earnings by skills in the initial economy. The right ﬁgureshows the lifetime path of earnings by skills in the initial economy. For both ﬁgures, we normalize thevalue of low-skilled workers aged 25-29 to one.

5.2

Transition Dynamics

In this section, we discuss numerical results of the transition dynamics. The initial economy approximates the U.S. economy in the early 1980s and the transition begins in 1980,
when individuals learn the paths of occupation-speciﬁc wages.
We compute wages for the three occupations in 1983/85 (initial) and 2015/18 (ﬁnal),
as summarized in Table 2. The wages of routine occupations in the initial economy arenormalized to one. We assume that wages change smoothly over a 30-year period fromthe initial economy and converge to the values in 2015/2018. After the wages converge tothe ﬁnal level, we assume that they will stay constant.
Table 2: Occupation-Speciﬁc Wages in the Transition(1) Initial(2) Final

Abstract Routine
1.06
1.00
1.15
0.92

Manual0.60
0.62

Note: The table shows the occupation-speciﬁc wages in (1) initial economy and (2) ﬁnal steady state.
We normalize the wages of routine occupations in the initial economy to one.

In addition to the occupation-speciﬁc wages, we also change the assignment of initial
occupations among entrants according to the CPS data for the period between the early
1980s (1983/85) to the late 2010s (2015/18). Table 3 shows the change in the distribution.
25

We let them change smoothly over a 30-year period, in the same way as occupation-speciﬁcwages.23
Table 3: Initial Distribution of Occupations in the Transition
Abstract Routine
Low(1) Initial(2) Final
High(1) Initial(2) Final

Manual

Total

0.16
0.19

0.74
0.64

0.10
0.17

1.00
1.00

0.70
0.74

0.27
0.20

0.04
0.06

1.00
1.00

Note: The table shows the occupation share in (1) initial economy and (2) ﬁnal steady state. The upper
half show the one for low-skilled workers, and the bottom half show the one for high-skilled workers.

Figure 14 shows changes in the shares of occupations for each skill type. The data
counterpart of the ﬁgure is Figure 7. Although there is a major shift in the shares fromroutine to abstract and manual occupations at the aggregate level data, such changes
are not universally obvious once we express shares conditional on skill and age. For
example, in Figure 7, there is no visible increase in the shares of abstract occupations,especially among the high-skilled who constitute the majority of the occupation. Ourmodel generates a similar outcome among the high-skilled, despite a rapid increase in
abstract wages, especially relative to wages of routine occupations, which continue todecrease.
Even after they learn about a more favorable wage path in abstract occupations,individuals do not switch occupations immediately, partly because of obstacles in moving
across occupations captured by mobility costs in our model and also because of the lossof accumulated occupation-speciﬁc human capital and the need to reaccumulate humancapital in a new occupation.
As shown in the upper right panels of Figure 14a and 14b, shares of routine occupations
decline in the model for both low- and high-skilled individuals. The model also generates
a rise in the shares of manual occupations for individuals in their 20s to early 40s as
shown in the lower left panels, although we do not match well a rise in manual shares forindividuals in their 40s and 50s among low-skilled individuals as seen in the CPS data.
There are other parts of the proﬁles in the transition that our model does not explain
perfectly. For example, there is an increase in the shares of non-employment among
23

Obviously, an alternative simulation would be to feed in the exact paths of occupation-speciﬁc wages
and initial occupation distribution as in the data. We chose to simulate smoothed paths of these variables
because the focus of the paper is to quantify eﬀects of the polarization trend. Our model does not attempt
to evaluates eﬀects of cyclical ﬂuctuations that occurred at the same time as polarization.

26

both types of individuals and more noticeably among the low-skilled in the CPS data.
Also, a decline in the routine share among the low-skilled is observed across a wider
range of age groups in the data than in our model. Enriching the model with additional
elements beyond factors associated with polarization are likely needed to fully explain theoccupation trend observed in the past decades.24
Abstract

0.3
0.2

Routine

0.8
1985
2000
2015

0.6

0.2

0
40

50

60

70

Manual

0.3

40

50

60

70

0
30

No-work

1

40

50

60

70

Manual

0.1

1985
2000
2015

0.05

0

0

30

40

50

60

70

No-work

0.8

1985
2000
2015

0.5

1985
2000
2015

0.1

0
30

1985
2000
2015

0.2

0.2
1985
2000
2015

0.2

0
30

0.3

0.4
1985
2000
2015

Routine

0.4

0.6

0.4
0.1

Abstract

0.8

1985
2000
2015

0.6
0.4

0.1

0.2

0
30

40

50

60

70

30

40

50

60

70

0
30

(a) Low-skilled

40

50

60

70

30

40

50

60

70

(b) High-skilled

Figure 14: Occupation by Age and Skills in Transition
Note: The left panel shows the share of each employment status category (Abstract, Routine, Manual,
Non-Employment) within each age group (25-29, ..., 75-79) for the selected years of 1985, 2000, and 2015
for individuals without college degrees, which is computed in the model. The right panel shows the samebut for individuals with college degrees.

Figure 15 shows occupation shares for each skill type, averaged over individuals aged
between 30 and 49, based on our model outcome. They show more clearly the overall
trend of rising shares of abstract and manual occupations and a decline in routine sharesfor both skill types of workers, in line with the CPS data.
24

For example, we conjecture that changes in provision of public insurance through social security
and disability insurance systems that occurred during the past decades may help match a rise in nonparticipation, as explored, for instance, by Autor and Duggan (2003) and Kitao (2014).

27

0.205

0.75

0.2

0.74

0.195

0.1

0.095

0.73
0.09

0.19
0.72
0.185

0.085
0.71

0.18

0.17
1980

0.08

0.7

0.175

1990

2000

2010

2020

0.69
1980

(a) Low/Abstract

1990

2000

2010

2020

0.075
1980

(b) Low/Routine

0.73

1990

2000

2010

2020

(c) Low/Manual

0.275

0.025

0.27
0.725
0.265
0.72

0.26

0.02

0.255
0.715
0.25
0.71
1980

1990

2000

2010

(d) High/Abstract

2020

0.245
1980

1990

2000

2010

(e) High/Routine

2020

0.015
1980

1990

2000

2010

2020

(f) High/Manual

Figure 15: Occupation Shares in Transition (Workers aged 30/49)
Note: The panel shows the path of the share of each employment status category (Abstract, Routine,
Manual, Non-Employment) for workers aged 30-49, which is computed in the model. The upper halfshow the path for workers without college degrees, and the bottom half show the path for workers withcollege degrees.

Figure 16 shows average earnings by age and skills for the three selected years during the transition. While average earnings of high-skilled individuals rise monotonically,
driven by a rise in abstract wages, earnings decline among low-skilled individuals. The
path of skill premium, computed as a ratio of earnings of low- and high-skilled individuals, is shown in Figure 17, pointing to a rise in earnings inequality across skills driven bypolarization. Figure 18 shows the life-cycle proﬁles of assets in 1980 and 2015 and they
indicate a rise in inequality in wealth across skill types.

28

2.2
2
1.8

H 2015
H 2000H 1985
L 1985
L 2000L 2015

1.6
1.4
1.2
1
0.8
25

30

35

40

45

50

55

Figure 16: Earnings by Age and Skills in Transition

Note: The ﬁgure shows the lifetime path of average earnings by skills for the selected years of 1985, 2000,
and 2015, which is computed in the model.

0.7

0.6

2015
2000
1985

0.5

0.4

0.3
25

30

35

40

45

50

55

Figure 17: Skill Premium by Age in Transition

Note: The ﬁgure shows the lifetime path of skill premium for the selected years of 1985, 2000, and 2015,
which is computed in the model. We deﬁne skill premium by a ratio of earnings of low- and high- skilledworkers.

29

14
H 2015
H 1980
L 1980L 2015

12
10
8
6
4
2
0
30

40

50

60

70

Figure 18: Assets by Age and Skills in Transition

Note: The ﬁgure shows the lifetime path of assets by skills for the selected years of 1980 and 2015, whichis computed in the model.

5.3

Welfare Analysis

We now turn our attention to welfare analysis of polarization. We quantify welfare eﬀects
by computing a consumption equivalent variation, denoted as CEV . More precisely, we
ask each individual whether he would prefer to live in the status quo economy where there
is no polarization, or in an economy that goes through polarization. We quantify welfare
eﬀects by asking how much compensation, in terms of a percentage change in consumption
levels across all possible states for the rest of his remaining life, he needs to receive inorder for him to be indiﬀerent between the status quo economy and the economy withpolarization.25
Figure 19a shows CEV for individuals of diﬀerent skills and ages in the initial economy
and Figure 19b displays welfare eﬀects for future generations, where each generation isindexed by the year of entry at age 25.
High-skilled and young individuals are the winners of polarization. The welfare gain of
the high-skilled aged 25 in the initial economy is 1.2% in consumption equivalence, 0.8%
for those aged 40 and 0.4% for age 50. The low-skilled experience a welfare loss and thelarger the magnitude, the younger they are in the initial economy, and the welfare loss isnearly 2% in consumption equivalence for entrants in 1980.
As shown in Figure 19b, the gain of the high-skilled is larger for later generations as
25

In other words, the welfare eﬀect is computed as a proportional growth rate in consumption tokeep the value of the value function unchanged from the status quo economy. Note that individuals
in our model incur disutility from participation and from mobility across occupations. These costs areheld unchanged at the levels under each of the two transition scenarios and only consumption levels areadjusted proportionally to quantify welfare eﬀects.

30

they would be able to fully enjoy higher abstract wages during their career. Symmetrically,
the welfare loss of the low-skilled is larger for later cohorts and those entering the labormarket in 2010 would lose up to as much as 6% in consumption equivalence relative toan economy without polarization.
The low-skilled suﬀer from the path of routine wages that falls by 8% in the end, as well
as from a change in the initial occupational distribution. As shown in Table 3, the shareof routine occupations among low-skilled entrants falls by 10 percentage points from 74%
to 64%, and large part of the decline is absorbed by an increase of manual occupations,whose share rises by 7 percentage points. Most of the welfare loss, however, is due tothe shift in occupation-speciﬁc wages. To disentangle the two eﬀects, we also computewelfare eﬀects in an alternative economy, in which only occupation-speciﬁc wages change
and initial occupation distribution is ﬁxed at the level of the initial economy. Results areshown in Figure 20.26 Welfare gains of the high-skilled are slightly higher and the welfare
losses of the low-skilled are smaller than in the baseline polarization scenarios.
2

2
High
Low

0

1

-2
High
Low

0
-4
-1

-2

-6

30

40

50

60

-8
1980 1985 1990 1995 2000 2005 201070(a) By Age in 1980(b) By Entry Year

Figure 19: Welfare Eﬀects of Polarization (in CEV , %)Note: The left ﬁgure shows the welfare eﬀects (CEV) of polarization in percentage point by skills and ages
in 1980 (initial economy). The right ﬁgure shows the welfare eﬀects (CEV) of polarization in percentage
point by skills and years when individuals enter the labor market at age 25.
26

Note that there is no change in welfare for those already in the labor force in 1980 and welfare eﬀects
are the same as in baseline scenario.

31

4
2
0
-2
-4
-6
-8
1980

High (Baseline)
Low (Baseline)
High (Experiment)
Low (Experiment)

1985

1990

1995

2000

2005

2010

Figure 20: Welfare Eﬀects of Polarization (in CEV , %): By Entry Year: Changes in
Occupation-Speciﬁc Wages Only
Note: The ﬁgure shows the welfare eﬀects (CEV) of polarization in percentage point by skills andyears when individuals enter the labor market at age 25 under the baseline case (dashed lines) and thealternative case, in which only occupation-speciﬁc wages change and initial occupation distribution is
ﬁxed at the level of the initial economy.

Figure 21 shows the average welfare eﬀect by cohort, computed as a populationweighted average of welfare eﬀects across individuals of diﬀerent skills. By just looking
at these ﬁgures, one might conjecture that polarization brings welfare loss to the young
and hurts also future generations. The ﬁgures, however, mask important heterogeneity inwelfare eﬀects across skills.
0.2

-0.5

0

-1

-0.2

-1.5

-0.4

-2

-0.6

-2.5

-0.8

-3

-1

30

40

50

60

-3.5
1980 1985 1990 1995 2000 2005 201070(a) By Age in 1980(b) By Entry Year

Figure 21: Welfare Eﬀects of Polarization: By Cohort (in CEV , %)Note: The left ﬁgure shows the welfare eﬀects (CEV) of polarization in percentage point by age in 1980
(initial economy). The right ﬁgure shows the welfare eﬀects (CEV) of polarization in percentage pointby years when individuals enter the labor market at age 25.

32

Welfare Eﬀects under Alternative Wage Scenarios:
We run two additional experiments to understand the roles of a decline in routine wages and a rise in abstract
wages. Figure 22 shows welfare eﬀects of polarization in which routine wage is ﬁxed at
the level of the initial economy throughout the transition. The large welfare loss of lowskilled individuals of all ages in the initial economy is wiped away as shown in Figure 22a.
Future generations are also better oﬀ as shown in Figure 22b, although the welfare effects remain negative due to a shift in the initial distribution to manual occupations thatremains under this experiment.
3

4High (Baseline)
Low (Baseline)
High (Experiment)
Low (Experiment)

2

2
0

1
-2
0
-4
-1

-6

-2
30

40

50

60

-8
1980

70

(a) By Age in 1980

High (Baseline)
Low (Baseline)
High (Experiment)
Low (Experiment)

1985

1990

1995

2000

2005

2010

(b) By Entry Year

Figure 22: Welfare Eﬀects of Polarization: Without a Decline in Routine Wages (in CEV ,%)Note: The left ﬁgure shows the welfare eﬀects (CEV) of polarization in percentage point by skills andages in 1980 (initial economy) under the baseline case (dashed lines) and the alternative case, in whichroutine wage is ﬁxed at the level of the initial economy. The right ﬁgure shows the welfare eﬀects (CEV)of polarization in percentage point by skills and years when individuals enter the labor market at age 25.
under the baseline case (dashed lines) and the alternative case, in which routine wage is ﬁxed at the levelof the initial economy.

If abstract wages do not increase, welfare gains of high-skilled individuals disappear as
shown in Figure 23. The welfare loss of the low-skilled will be larger but the quantitativeeﬀects, compared to a decline in the welfare of the high-skilled, are much smaller.

33

1.5

2

1
0
0.5
0

-2

-0.5
-4

-1
-1.5

High (Baseline)
Low (Baseline)
High (Experiment)
Low (Experiment)

-2

-6

-2.5
30

40

50

60

-8
1980

70

(a) By Age in 1980

High (Baseline)
Low (Baseline)
High (Experiment)
Low (Experiment)

1985

1990

1995

2000

2005

2010

(b) By Entry Year

Figure 23: Welfare Eﬀects of Polarization: Without a Rise in Abstract Wages (in CEV ,%)Note: The left ﬁgure shows the welfare eﬀects (CEV) of polarization in percentage point by skills andages in 1980 (initial economy) under the baseline case (dashed lines) and the alternative case, in which
abstract wage is ﬁxed at the level of the initial economy. The right ﬁgure shows the welfare eﬀects (CEV)of polarization in percentage point by skills and years when individuals enter the labor market at age 25.
under the baseline case (dashed lines) and the alternative case, in which abstract wage is ﬁxed at thelevel of the initial economy.

6

Conclusion

This paper builds a full-blown life-cycle model populated by individuals of diﬀerent occupations, skills, human capital, idiosyncratic labor productivity, and assets. It is used
to account for occupational distribution and mobility over the life-cycle of heterogeneous
individuals and to quantify welfare eﬀects of polarization that occurred during the past
decades on diﬀerent groups of individuals. We show that high-skilled individuals gainfrom polarization while the low-skilled lose from it. Everyone in the economy faces thesame changes in occupation-speciﬁc wages and is able to move across occupations in theory. Our results, however, indicate that mobility is limited due to upward mobility costs
as well as opportunity costs associated with occupation-speciﬁc human capital that individuals at diﬀerent ages have already accumulated. The welfare gain is larger among
younger high-skilled individuals since they can enjoy a continued rise in abstract wages
throughout their careers. Similarly, the welfare loss of the low-skilled is larger among theyounger and later generations.
The model can be extended in various dimensions to answer related questions. One
natural question may be whether the trend of welfare eﬀects across generations, which
the model identiﬁes, will be extrapolated for the future. It is an open question whether
34the high-skilled will continue to gain and polarization will continue, increasing inequality
in income and wealth. We leave the question for future research.

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