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The Barriers to Occupational Mobility:
An Aggregate Analysis
Guido Matias Cortes∗
University of Manchester
Giovanni Gallipoli†
University of British Columbia
February 7, 2014
Abstract
This paper analyzes the barriers to occupational mobility using a theoretical framework
that parallels that of the gravity models commonly estimated in the trade literature. The
model provides an equation linking flows of workers across occupation pairs to a set
of source and destination occupation characteristics, and to the transition costs faced
by workers. The equation is estimated using data from the matched monthly Current
Population Survey (CPS) from 1994 to 2012. The main proxies for the transition cost
investigated in the paper are related to the task content of occupations, specifically task
distance (the degree of dissimilarity in the mix of task requirements across the occupation
pair) and a set of indicator variables for transitions that involve changes across major task
groups. Task-related variables are found to play a substantial role in increasing the cost
of switching between occupations. In a counterfactual scenario where workers are able
to switch occupations without bearing any task-related costs, occupational mobility rates
for the majority of the occupations in our sample would increase by between 7 and 30
percentage points.
∗Department of Economics, University of Manchester, Arthur Lewis Building, Oxford Road, Manchester,M13 9PL, UK. E-mail: [email protected]. Financial support from CLSRN is gratefully acknowl-edged. We thank Keith Head, Nicole Fortin, David Green, Thomas Lemieux, Vadim Marmer and John Riesfor insightful comments and suggestions. Carlos Sanchez provided valuable research assistance.†Department of Economics, University of British Columbia, 997-1873 East Mall, Vancouver, BC V6T 1Z1,
Canada. E-mail: [email protected]
1 Introduction
Several contributions to the human capital literature have analyzed the costs associated with
different types of employment transitions. Topel (1991) provides evidence that a typical male
worker in the United States with 10 years of job tenure would lose 25% of his wage if his job
were to end exogenously. Other papers have analyzed the extent to which human capital is
partially transferable across jobs. In particular, Neal (1995) and Parent (2000) argue that an
important component of human capital is industry-specific and is therefore only lost when a
worker switches to a different industry. Meanwhile, Kambourov and Manovskii (2009b) and
Sullivan (2010) find strong evidence that a major component of human capital is occupation-
specific.
The goal of this paper is to obtain an estimate of the costs of occupational mobility which
takes into account the task content of occupations. As argued by Lazear (2003), Poletaev and
Robinson (2008) and Gathmann and Schonberg (2010), different occupational transitions,
which empirically are based on whether the occupation code assigned to a worker changes,
may be very different in terms of the extent of task switching that they entail. In some cases a
worker may be completely changing careers, while in others it may involve only a minor change
in the set of tasks performed by the worker. Human capital built in an occupation should be
partially transferable to other occupations where the set of tasks performed is similar.
The approach taken by the paper in order to estimate these transition costs is somewhat
unconventional relative to previous literature. We adapt a framework which is widely used
in the trade literature in the form of ‘gravity models’. In that literature, the interest is in
estimating barriers to trade using data on flows of goods across countries, and proxies for trade
costs that include geographical distance and whether the countries share a common border
or a common language, among others. We show how the framework may be reinterpreted
in order to consider the barriers to occupational mobility using data on the flows of workers
across occupations, and proxies for mobility costs, mainly based on task data. Within the
context of the model, the barriers to occupational mobility involve losses of human capital
that are incurred when a worker needs to adapt the set of tasks that he is familiar with, or
learn a new set of tasks altogether, upon switching occupations.
The theoretical framework provides a different approach to the analysis of the barriers to
occupational mobility, and leads to the use of occupation-level rather than individual-level
data. Previous models of occupational choice, such as Gibbons, Katz, Lemieux, and Parent
(2005) or Groes, Kircher, and Manovskii (2010), have focused on the roles of comparative
advantage across skill groups and learning in driving selection into occupations. Kambourov
and Manovskii (2009a), meanwhile, have a model where occupational mobility is driven by
persistent shocks to occupations that impact the productivity of all workers in an occupation.
In the model in this paper, the driving force behind occupational mobility is a set of non-
1
persistent individual-specific productivity draws.
The framework in this paper involves a static, partial equilibrium model with perfect
information. There is a continuum of homogeneous workers, who only differ in terms of the
occupation that they start the period in (which is exogenously pre-determined). Workers make
productivity draws from a set of extreme value distributions for each potential occupation.
The extreme value assumption may be justified by thinking of workers as receiving a large set
of offers from different employers within each occupation, and only considering the highest
offer in each occupation. The distribution of ‘highest offers’ (maxima) across employers within
each occupation would converge to an extreme value distribution.
Once workers observe their draws, they decide which occupation to work in during the
period. There are costs to switching occupations, which depend on the particular occupation
that the worker starts in, and the particular occupation that he considers switching to. This
switching cost is not individual specific, but rather depends only on the identity of the worker’s
current and potential occupation. Based on his productivity draws, and taking into account
the costs of mobility, the worker chooses the occupation where he will receive the highest wage.
The workers’ optimal switching decisions and the properties of the extreme value distribution
lead to a ‘gravity-type’ equation, which predicts how the flow of workers across any given
occupation pair is related to a set of occupation-specific characteristics, and to the cost of
switching.
In order to estimate this gravity equation empirically, and to obtain an estimate of the
barriers to occupational mobility, we choose a set of variables that are related to the costliness
of an occupational switch. Following previous literature, we characterize occupations through
a vector of skill or task characteristics (e.g. Autor, Levy, and Murnane (2003), Ingram
and Neumann (2006), Gathmann and Schonberg (2010), Poletaev and Robinson (2008)).
Using data from the Dictionary of Occupational Titles (DOT), we construct a measure of
distance between occupation pairs, which captures the degree of dissimilarity in the mix
of tasks performed in the two occupations. If more specific human capital is lost when a
worker experiences a more dramatic change in the set of tasks he performs, the barriers to
occupational mobility should be increasing in task distance. We also allow for a fixed cost of
switching across occupations that belong to different major task groups (non-routine cognitive,
routine cognitive, routine manual or non-routine manual), as there may be costs associated
with these switches in excess of what is captured by the distance measure. Finally, we also
allow for non-task related occupation-specific barriers to entry, which may vary over time.
Using these proxies for occupational mobility costs, we estimate the gravity equation
using data on worker flows across 2-digit occupations from the matched monthly Current
Population Survey (CPS) from 1994 to 2012. This is a period during which the CPS employed
dependent coding techniques, which have been shown to reduce the amount of coding error in
occupational transitions. We find that task distance is an important determinant of the cost
2
of switching occupations, suggesting an important role for task-specific human capital. An
increase of one standard deviation in distance increases the cost of switching occupations by 14
to 24%. It the switch involves a transition to a different major task group, the cost is increased
by a further 8 to 63 percentage points. For some commonly observed occupational transitions,
our estimates imply that the productivity of switchers would be substantially higher if there
were no task-related costs to switching. Through a set of counterfactual experiments, we find
that for the vast majority of occupations in our sample, task-related factors account for at
least 8% and up to 50% of the gap between observed occupational mobility rates and the
mobility rates that would prevail if workers were able to switch occupations at no cost.
The rest of the paper is organized as follows. Section 2 describes how the Eaton and Kor-
tum (2002) gravity model may be adapted to think about flows of workers across occupations
and the barriers to occupational mobility. Section 3 describes the empirical strategy and the
proxies considered for the barriers to switching occupations, as well as the data sources. Sec-
tion 4 presents the findings of the paper, while Section 5 concludes and suggests possibilities
for future work.
2 Model
The model is an adaptation of the Eaton and Kortum (2002) model, modified to think about
flows of workers across occupations and the barriers to occupational mobility. The framework
involves a static partial equilibrium model with perfect information. All the equations in this
section hold at any time period t, so for notational simplicity time subscripts are omitted. We
introduce time subscripts explicitly when describing the empirical implementation in Section
3.
2.1 Setup
There is a (finite) set of occupations given by j ∈ {1, 2, ..., N}, with a large number of
employers in each occupation. Each occupation j produces a different final good which has a
price given by pj . There is a continuum of homogeneous workers of measure 1, indexed by i.
They only differ in terms of the occupation that they start the period in (which is exogenously
pre-determined). A worker’s occupation at the beginning of the period is indexed by k.
Workers maximize their current wages by choosing their optimal occupation. That is,
at the beginning of the period, they consider the wages that they would receive in every
possible occupation and select into the occupation where their potential wage is highest for
that period.1
1Extending the model in order to have forward looking agents who maximize a present discounted value ofcurrent and expected future wages remains as future work.
3
2.2 Wages and Productivity Draws
Workers’ wages are equal to the value of their marginal product. Productivity is perfectly
observable and labor is the only input in production.
The potential wage in occupation j for worker i who begins the period in occupation k is
given by:
wj(i|k) = pjf [X(i)]
(zj(i)
dkj
)(1)
pj is the price of the output produced in occupation j. X(i) are a set of individual
characteristics that augment productivity in all occupations. They may include variables
such as education or overall work experience, which reflect general human capital. zj(i) is an
occupation-specific productivity draw for the individual. The process by which individuals
draw productivity will be described in detail below. dkj represents the cost of switching
between the worker’s initial occupation k and the potential occupation j. Assume dkk = 1
(staying in the same occupation is costless) and dkj > 1 for all j 6= k. The idea is that workers
lose a fraction of their productivity if the occupation j that they choose in period t is different
from the occupation k that they started the period in. The cost is assumed to last only for
one period. Intuitively, if an individual is a newcomer to occupation j (j 6= k), then he must
spend a fraction of his time training or learning to do his job. Therefore, in the period when
he is a newcomer, his marginal productivity is f [X(i)] (zj(i)/dkj) < f [X(i)] zj(i).
For each occupation j, individuals draw zj(i) from a Frechet (or Type II extreme-value)
distribution. One can think of individuals as receiving offers from several different potential
employers in each occupation. The only offer the individuals will consider will be the highest
offer in each occupation. Thus, the set of ‘relevant’ offers for each occupation are the collection
of maxima across firms for each individual. The distribution of the maxima of a set of draws
can converge to one of only three distributions, one of which is Frechet (the distribution
assumed here).2
The Frechet distribution is given by:
zj ∼ Fj(z) = e−Tjz−θ
(2)
The occupation-specific parameter Tj governs the location of the distribution. Productiv-
ity draws will be on average higher in occupations with a larger Tj . The parameter θ (which is
assumed to be common across all occupations) is related to the dispersion of the distribution,
with a larger θ implying less variability.
Individuals sample all occupations at the beginning of the period (including the occupation
they start in), by making a productivity draw for each one. They then compare potential
2See Eaton and Kortum (2002), footnote 14, and references therein.
4
wages in all occupations. Based on their productivity draws, and the transition costs dkj ,
they choose optimally whether to switch occupations, as well as which particular occupation
to switch to. There are no search frictions, and productivity draws are considered guaranteed
job offers from an employer in an occupation, so the individual faces no uncertainty when
choosing which occupation to switch to.
All individuals make draws from the same set of distributions Fj(z), regardless of their
current occupation or their individual characteristics. Therefore, for each occupation, all
individuals have the same ex-ante expected productivity draw.
Note that taking logs of Equation (1), we have:
lnwj(i|k) = ln pj + ln f [X(i)]− ln dkj + ln zj(i) (3)
This is similar to the wage equations commonly specified in the literature, with ln pj
representing an occupation wage premium and ln f [X(i)] the return to a set of observable
characteristics. Here the equation also includes the switching cost ln dkj , and has an error
term that is extreme-value distributed.3
2.3 Flows of Workers Across Occupations
This section analyzes the implications of the model in terms of flows of workers across oc-
cupations. For individual i (who starts in occupation k), the probability that his wage in
occupation j is above some level w is given by:
Pr [wj(i|k) > w] = 1− Fj(
wdkjpjf [X(i)]
)(4)
= 1− e−Tjd−θkj (pjf [X(i)])θw−θ (5)
The probability that individual i draws a wage below w in every occupation other than j
is:
Pr [ws(i|k) ≤ w,∀s 6= j] =∏s 6=j
Fs
(wdks
psf [X(i)]
)=∏s 6=j
e−Tsd−θks (psf [X(i)])θw−θ
(6)
Individual i will optimally choose to switch to occupation j, given his current occupation
k, if j offers him the highest potential wage among all possible occupations. The probability
3Note however that this is an equation for potential rather than observed wages and cannot be directlyestimated.
5
that this happens is denoted by πkj(i) and is given by:
πkj(i) ≡ Pr[wj(i|k) ≥ max
s{ws(i|k)}
]=
∫ ∞0
Pr [ws(i|k) ≤ w,∀s 6= j] · dPr [wj(i|k) ≤ w]
=Tjd−θkj p
θj∑N
s=1 Tsd−θks p
θs
(7)
Intuitively, j will be the best choice for individual i whenever j offers him a wage w while
all other occupations offer him a wage below w. Integrating this over all possible values of w
gives us the probability that i switches from k to j, πkj(i). Note that this allows the possibility
that j = k, i.e. the optimal choice may involve staying in the current occupation. Note also
that this probability is not individual-specific, so we can omit the i index.
Taking the ratio of πkj and πkk, based on Equation (7), and using the fact that dkk = 1,
we have:πkjπkk
=Tjd−θkj p
θj
Tkpθk
(8)
Or in logs:
lnπkjπkk
= lnTj + θ ln pj − lnTk − θ ln pk − θ ln dkj (9)
Because there is a continuum of individuals in each occupation, and because all individ-
uals in occupation k have the same probability of switching to occupation j and all make
independent draws from the productivity distribution, πkj will be equal to the fraction of
k-workers who switch to j, that is:
πkj =swkjNk
(10)
where swkj is the total number of switchers from k to j and Nk is the size of occupation k
(at the start of the period).
Therefore, Equation (9) can be rewritten in terms of worker flows, leading to a gravity-type
equation:
ln
(swkjswkk
)t
= lnTj,t + θ ln pj,t − lnTk,t − θ ln pk,t − θ ln dkj,t (11)
This is the key equation of the model and it holds in every period. Time subscripts have
been added to explicitly allow for time-variation in the different components that affect the
flows of workers between occupations, which are a set of occupation-specific characteristics
(Tj,t, Tk,t, pj,t, pk,t), and the cost of switching (dkj,t).
6
3 Data and Empirical Implementation
Our goal is to estimate Equation (11) empirically, in order to understand the costs of switching
between occupations (dkj,t), and the factors that affect this variable. The main determinant
that we explore is the ‘task distance’ between occupations k and j. As suggested by Gathmann
and Schonberg (2010), Poletaev and Robinson (2008) and Robinson (2011), if human capital
is task-specific, it should be partially transferable across occupations pairs in which a similar
mix of tasks is performed. The cost of switching occupations should therefore be increasing
in the degree of dissimilarity, or ‘distance’, in the task content of the two occupations.4
To test for evidence on the impacts of task distance on switching costs, we follow previous
literature in characterizing occupations through a vector of skill or task characteristics (e.g.
Autor et al. (2003), Ingram and Neumann (2006), Poletaev and Robinson (2008), Peri and
Sparber (2009)) and construct a measure of distance between occupation pairs as in Gathmann
and Schonberg (2010). The distance measure reflects the degree of dissimilarity in the mix
of tasks performed in the two occupations, and can be considered as an ‘intensive margin’
description of the occupational transition.
The skill characterization of occupations uses data from the Revised 4th Edition of the
Dictionary of Occupational Titles (ICPSR, 1991). The DOT provides precise measures of
the different abilities that are required in different occupations, as well as the different work
activities performed by job incumbents. The dimensions along which the DOT dataset char-
acterizes occupations include complexity of work, General Education Development (GED),
specific vocational preparation requirements, aptitudes, temperaments and physical demands,
among others (ICPSR, 1981). The choice of the relevant dimensions with which to character-
ize occupations in order to construct a distance measure is somewhat arbitrary. We choose the
three GED variables and the eleven aptitudes from the 1991 DOT as the relevant dimensions.
Table 1 provides examples of the DOT task vectors for four particular occupations.5
The distance measure we consider is the log of an Euclidean distance. Let xak be the
importance level of dimension a (one of the dimensions described above) in occupation k, and
xaj the analogous measure for occupation j. The Euclidean distance is measured as:
eucl distkj =
√√√√ A∑a=1
(xak − xaj
)2(12)
where A is the total number of dimensions being considered. We use a log-distance measure,
4Task distance here parallels the traditional use of geographic distance in gravity models in the tradeliterature.
5Each DOT dimension is normalized to have mean zero and standard deviation one across the universe ofstandardized 3-digit occupations from Autor and Dorn (2013). More details are provided in Appendix A.
7
defined as:
distkj = ln(1 + eucl distkj) (13)
In addition to the task distance between occupations, we consider the possibility that
there are barriers to switching between major task groups. Following the literature (e.g.
Acemoglu and Autor (2011)), we group occupations into four broad task groups: non-routine
cognitive, routine cognitive, routine manual, and non-routine manual. Appendix Table A.1
provides details on the occupations included in each of these broad groups. We allow for
a cost of switching between task groups, which differs across groups. We define a set of
dummies switch nrckj , switch rckj , switch rmkj and switch nrmkj which are equal to one
if occupations k and j are in different broad task groups, and destination occupation j is a
non-routine cognitive, routine cognitive, routine manual, or non-routine manual occupation,
respectively. These dummies will reflect costs related to switching between task groups that
are not captured fully by the distance measure.
We also allow for an overall destination effect mj,t, which reflects general barriers to entry
to occupation j that are not related to the task content of j or to the characteristics of the
source occupation k. This barrier is allowed to vary over time. Finally, we allow for an
error term εkj,t which captures barriers to occupational mobility between occupations k and
j arising from all other factors, and which is also allowed to vary over time. This leads to the
following specification for ln dkj,t:
ln dkj,t =β1distkj + β2switch nrckj + β3switch rckj
+ β4switch rmkj + β5switch nrmkj +mj,t + εkj,t (14)
Using this specification for dkj,t and defining Sk,t ≡ lnTk,t+θ ln pk,t and Dj,t ≡ Sj,t−θmj,t,
the gravity equation (11) becomes:
ln
(swkjswkk
)t
=Dj,t − Sk,t − θβ1distkj − θβ2switch nrckj − θβ3switch rckj
− θβ4switch rmkj − θβ5switch nrmkj − θεkj,t (15)
Empirically, the left-hand-side of the equation can be measured using data on worker
flows across occupations, while Sk,t and Dj,t can be captured through time-varying source and
destination occupation fixed effects, respectively. εkj,t is assumed to be a normally distributed
random variable which is orthogonal to all other regressors.
We measure flows of workers across occupations using matched monthly data from the
Current Population Survey (CPS). The CPS is a survey of approximately 50,000 households
conducted by the Bureau of the Census for the Bureau of Labor Statistics. It is the main
8
source of labor market statistics in the United States. We make use of the fact that the
CPS is a rotating sample: households included in the CPS survey are sampled for four con-
secutive months, then leave the sample for eight months, and then return for another four
months. Given this sampling structure, up to 75% of households are potentially matched
across consecutive months. In practice, the fraction of households that can be matched is
lower, primarily due to attrition. The CPS is an address-based survey, so households that
move to a new address are not followed. Also, in certain months the CPS made changes to
household identifiers, making it impossible to match households across these modifications.6
Details about the algorithm used to match individuals across months can be found in Nekarda
(2009).
The main advantage of the CPS relative to other longitudinal datasets such as the Panel
Study of Income Dynamics (PSID) is its large sample size and the fact that it is explicitly
designed to be representative of the entire US population at each point in time. Another
advantage of the CPS is that, in January 1994, dependent coding techniques were introduced.
In order to reduce the interview burden and the possibility of misclassification, information
collected in the previous month’s interview is imported into the current interview. Instead of
having individuals verbally describe their current occupations, and having these descriptions
coded independently, interviewees were asked whether they still had the same job as in the
previous month and, if so, they were automatically assigned the same occupation code as
in the previous month.7 This method of dependent coding has been shown to substantially
reduce the amount of spurious transitions across occupations (see Kambourov and Manovskii
(2013) and Moscarini and Thomsson (2007)).
To take advantage of the dependent coding techniques, we use data starting in 1994 for
our analysis. The most recent period available in our dataset is December 2012. The sample
is restricted to adults aged 18 to 65 who are not in farming occupations or in the military.
Appendix A provides details on the procedure followed to merge the CPS and the DOT data.
Note that the changes introduced over time in the occupation coding system used by the CPS
(in 2003 and 2011) are not of concern for the purposes of this paper as the inclusion of time-
varying occupation fixed effects implies that identification is obtained solely from variation
across occupation pairs in worker flows at a given point in time.
We perform our analysis at the 2-digit occupation code level.8 More detailed occupa-
tional groupings (i.e. 3-digit codes) provide a level of aggregation that is too fine to observe
significant flows of workers across particular occupation pairs. Meanwhile, a higher level of
aggregation (1-digit level) creates groups that are too coarsely grouped together.
Using 2-digit occupation codes for matched individuals who are observed across consec-
6This affects the period between June and September of 1995.7See http://www.census.gov/cps/methodology/collecting.html.8The full universe of occupations is listed in Appendix Table A.1.
9
utive months, we construct monthly flows of workers across occupation pairs. The flow of
switchers between occupation k and occupation j in period t (swkj,t) is defined as the num-
ber of respondents (weighted using CPS sample weights) who are observed in occupation k
in month t and in occupation j in month t + 1. To reduce noise, these monthly flows are
aggregated at an annual level.
4 Results
4.1 Gravity Equation Estimation
This section presents the results from estimating Equation (15) using the CPS data on worker
flows and the proxies for mobility costs described above. One important issue that we need
to address is the fact that there are certain occupation pairs for which there are zero flows in
particular years. This occurs for approximately 12% of our occupation pair-year observations.9
We deal with the issue of zero-flows in several ways. Column (1) of Table 2 shows the
results from the estimation of Equation (15) when observations with zero flows are dropped
from the sample. In Column (2), we replace the zeros with the smallest observed value in
the sample for the left-hand-side variable in Equation (15), and estimate the regression using
OLS. Finally, in Column (3) the same replacement of zeros is done as in Column (2) but
a Tobit-style regression is estimated as in Eaton and Kortum (2001).10 All specifications
include source and destination occupation fixed effects interacted with year dummies.
The Table shows that the effect of task distance on worker flows is negative and significant,
suggesting that task distance is an important component of the cost of occupational mobility.
The estimate in Column (3) implies that, all else equal, a 1 standard deviation change in
distance (which is slightly less than 1 in the sample) leads to a 0.69% fall in the ratio of
switchers to stayers. Meanwhile, the negative and significant coefficient estimates on the
task switching dummies imply that switching into a different broad task group is costly,
particularly so when switching towards routine manual occupations. Note that, as can be
seen from Equation (15), the estimated coefficients presented in the Table are of −θβ. This
means that the findings discussed so far, such as the fact that higher distances are associated
with lower flows of workers, could be driven either by high-distance switches being very costly
(i.e. a high β) or by productivity shocks having a low level of dispersion (i.e. a high θ). We
disentangle these two components in the next subsection.
The estimated source and destination occupation fixed effects are also of interest. From
Equation (15), note that we can use the empirically estimated source and destination occu-
pation fixed effects in each year for any occupation j to back out Sj,t and −θmj,t. Recall that
9Note that the issue of zeros in gravity equations has been discussed in the trade literature; see Head andMayer (2013) for an overview.
10See Head and Mayer (2013) for a discussion of the advantages of using this method.
10
Sj,t ≡ lnTj,t + θ ln pj,t, which is a measure of the relative “attractiveness” of occupation j in
year t. A high Sj,t may be observed either because average productivity in that occupation
is high (a high Tj,t) or because the prices of the good produced in that occupation are high
(a high pj,t), both of which imply higher wages on average for workers in the occupation.
Note from Equation (15) that flows into an occupation with a high S will be relatively high,
while flows out of the same occupation will be relatively low. We normalize Tj,t and pj,t to
be equal to 1 in all years in occupation code 2, “Executives, administrators and managers”,
so S2,t = 0 ∀t, and this is our excluded category in all years. The estimates of −θmj,t reflect
occupation-specific barriers to entry, and are also relative to the same excluded category.
Figure 1 plots the estimates of Sj (on the x-axis) and −θmj (on the y-axis) for each
occupation j in the year 2012. The numbers next to each marker represent the 2-digit occu-
pation code as defined in Appendix Table A.1. The figure shows that “attractive” occupations
(those with a high Tj) tend to feature high entry barriers (a high −θmj in absolute value).
The ranking across occupations tends to remain stable over time.
4.2 Estimation of θ
In order to disentangle the role of the dispersion of the productivity shocks from that of the
switching costs in accounting for the results discussed above, we need an estimate of θ. To
estimate this parameter, we take advantage of the properties of the extreme value distribution
that is assumed in the model, which lead to a simple relationship between the distribution of
wages predicted by the model and the parameter of interest θ.
The extreme value distribution in Equation (2) has mean T1/θj Γ (1− 1/θ), where Γ is
the Gamma function. Its log has a Gumbel distribution, with standard deviation equal to
π/(θ√
6).11
Note that the (ex-post) wage for an individual starting in occupation k is also drawn from
an extreme value distribution. The probability that an individual ends up with a wage below
or equal to w is equal to the probability that his potential wage in all possible occupations is
below or equal to w. That is:
Pr(w(i|k) ≤ w) = Pr [wj(i|k) ≤ w ∀j]
=
N∏j=1
Fj
(wdkj
pjf [X(i)]
)= e−(
∑Nj=1 Tjd
−θkj (pjf [X(i)])θ)w−θ
(16)
11The Gumbel distribution has a CDF given by: F (x) = exp(−e−(x−µ)/β), with standard deviation (πβ)/√
6.In the case of the log of the productivity draws from the extreme value distribution in Equation (2), we havethat: Pr(ln zj(i) ≤ z) = Pr(zj(i) ≤ ez) = Fj(e
z) = exp(−Tje−θz), which is a Gumbel distribution withstandard deviation π/(θ
√6).
11
This is an extreme value distribution with mean[∑N
j=1 Tjd−θkj (pjf [X(i)])θ
](1/θ)Γ (1− 1/θ).
Its log has standard deviation π/(θ√
6).12
Therefore, the standard deviation of ex-post log wages for a set of individuals starting in
occupation k with common demographic characteristics (common X(i)), is a simple function
of θ. The standard deviation for the entire set of individuals starting in k (unconditional
on demographics) will be at least as large as the (common) standard deviation within each
sub-group. In other words, the standard deviation of ex-post log wages for the entire set
of individuals starting in occupation k will be bounded below by π/(θ√
6), so we have that:
σk ≥ π/(θ√
6), and therefore θ ≥ π/(σk√
6).
We can obtain a lower-bound estimate of θ from the data by calculating θ = π/(σk√
6),
where σk is the standard deviation of log wages for the set of individuals starting the period
in occupation k.13 For each month in the sample, the data will therefore give us an estimate
of θ based on the distribution of wages conditional on the occupation k from the previous
month.
In order to get a more precise estimate of θ, we also estimate the standard deviation
within groups of young workers. In particular, we focus on workers aged 25 to 30. As they
are at the start of their working life, it is reasonable to expect low heterogeneity in terms of
the characteristics that determine their wages. We therefore get estimates of θ based on the
standard deviation of wages for people aged 25 to 30, by initial occupation and separately for
males and females.
Figure A.1 in the Appendix shows histograms of the estimated values of θ and θ, using
occupations with at least 100 valid reports for θ, and bins with at least 15 observations for θ.
Table 3 shows the corresponding summary statistics. The median estimate of θ (based on the
demographic-specific dispersions) is 3.23, which implies that the standard deviation of the log
of the productivity draws in each occupation is equal to 0.40. In the next subsection we use
this estimate of θ to calculate implied mobility costs and perform counterfactual experiments.
4.3 Implied Mobility Costs
In Table 4, we use the median estimate of θ (based on the demographic-specific dispersions)
to calculate the estimated effects of the different variables on the iceberg cost. The first three
columns of Table 4 show, for each of the specifications in Table 2, the estimated marginal
effects β of each of the variables on the log of the transition cost (ln dkj). The next three
12Note from the previous footnote that the standard deviation of the log of productivity does not depend
on Tj . In the case of the distribution of log wages, Tj would be replaced by(∑N
j=1 Tjd−θkj (pjf [X(i)])θ
). The
standard deviation remains independent of this multiplicative constant.13Wage data is available in the CPS for workers in the Outgoing Rotation Groups (fourth and eighth month
in the sample). We follow the procedure in Lemieux (2006) to generate hourly wages and to trim extremevalues of wages and adjust top-coded earnings.
12
columns compute the implied percentage effect on dkj from a 1 standard deviation change
in distance, and from a change from 0 to 1 for each of the task switching dummy variables.
The results show that the impact of task distance on the cost of switching is substantial. The
implied coefficients from the Tobit-type specification suggest that a one standard deviation
increase in distance increases the cost of switching occupations by nearly 24%. This cost is
increased if the switch involves a transition into a different task group. These additional costs
range from 8% for transitions into routine cognitive occupations, to 63% for transitions into
routine manual jobs.
Next we calculate the estimated transition cost for specific occupation pairs. We calculate
this in two different ways. First, we calculate the cost that is directly attributable to the task
variables (task distance and task switching indicators). We call this dkj , and from Equation
(14), its log is given by:
ln dkj = β1distkj + β2switch nrckj + β3switch rckj + β4switch rmkj + β5switch nrmkj
We also calculate the full estimated transition cost widehatdkj,t which is given by:
ln dkj,t = β1distkj+ β2switch nrckj+ β3switch rckj+ β4switch rmkj+ β5switch nrmkj+mj,t
Table 5 shows the estimates of dkj and dkj,t for the year 2012 for commonly observed
occupational switches. The estimates use the implied β’s for the Tobit-type specification, as
shown in the third column of Table 4.14 Consider workers switching between retail occupa-
tions and other administrative support occupations. The estimation results imply that if the
cost (wage penalty) of switching arising from the task variables were eliminated, switchers’
productivity would be around 24% higher (because dkj = 1.24) than it actually is. Overall,
workers switching between these two occupations are estimated to have their productivity
cut by a factor of 3 (dkj,t = 3.07) when making the switch. Estimated switching costs are
therefore quite substantial, even across occupations that see relatively high volumes of flows.
An alternative way in which the magnitude of the estimated transition costs can be mea-
sured is by calculating counterfactual occupational mobility rates if the transition costs were
reduced. Column (1) of Table 6 shows the observed mobility rates towards other occupations
from a number of 2-digit occupations in the year 2012. The top half of the table includes
occupations with the lowest observed occupational mobility rates (between 2% and 4% of
workers are observed to switch out at a monthly frequency), while the bottom half of the
table includes the occupations with the highest mobility rates (over 5.5%). Column (2) shows
the counterfactual mobility rates if the switching costs associated with the task variables (task
distance and task switching indicators) were eliminated. The mobility rates in Column (2)
14The estimated dkj,t includes the constant from the Tobit regression (divided by the estimate of θ), as thiswould be part of mj,t.
13
are much higher, ranging between 6% and 43%. This confirms that task switches impose a
substantial barrier to occupational mobility. In fact, for 90% of the occupation-year cells in
our sample, the increase in mobility rates in the counterfactual scenario with no task-related
costs ranges between 7 and 30 percentage points, relative to the mobility rates observed in
the data. Next, in Column (3) we calculate counterfactual mobility rates if there were no
transition costs at all (i.e. no task-related costs as well as no occupation-specific barriers
mj,t). In this case mobility rates would be extremely high, as workers would find themselves
continuously re-optimizing their occupational choice at no cost based on their productivity
draws. Finally, Column (4) computes the fraction of the reduction in occupational mobility
between Column (3) and Column (1) that can be attributed to task-related costs. For the
occupations displayed in the table, this fraction ranges from 5% to 40%. Overall, for 90%
of the occupation-year observations in our dataset, task-related costs account for at least 8%
and up to 50% of the fall in occupational mobility relative to the case where switching is
completely costless.
5 Conclusion
This paper provides a new approach to the analysis of the costs of occupational mobility.
A version of the gravity model commonly used in the trade literature is adapted in order to
analyze flows of workers across occupation pairs, and the barriers that they face. In the model,
workers make productivity draws from a set of extreme value distributions for each potential
occupation, and choose optimally which occupation to work in, based on their productivity
draw and the costs of transition from their current occupation.
The empirical implementation focuses on the role of task distance (degree of dissimilarity
in the mix of task requirements) on the cost of switching occupations. This variable is found to
play an important role in explaining the barriers to occupational mobility, with a one standard
deviation of task distance increasing the cost of switching occupations by at least 14%, all
else equal. Meanwhile, switching across major task groups also significantly increases mobility
costs, in ways not captured by the distance measure. Finally, task-related costs account for
a substantial fraction of the gap between the observed occupational mobility rates and the
counterfactual occupational mobility rates that would prevail in a world where workers were
able to switch occupations with no cost.
The paper may be extended in several ways. First, the model abstracts from the role of
occupational tenure in the accumulation of (occupation-specific) human capital. Appendix
B describes how tenure can be added to the theoretical framework. Second, although the
dependent coding techniques used in the CPS reduce the incidence of coding error, it may
still be the case that some of the workers measured as switching between similar (low distance)
occupations are spuriously recorded as such. Further analyzing the impact of coding would be
14
a valuable extension of this paper. Finally, a more substantial extension of the model would
entail considering a dynamic setting where workers maximize a present discounted value of
lifetime utility, rather than current wage only. The model could also be made more realistic by
allowing for persistent shocks to productivity, such that a worker who is highly productive in
a particular occupation remains so for several periods, rather than making a new independent
productivity draw in each period.
15
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18
Figure 1: Estimates of Sj and −θmj for the year 2012
Note: Each dot represents a 2-digit occupation, labeled with its corresponding occupation code. SeeAppendix Table A.1 for the definitions of each code.
19
Table 1: Examples of DOT-91 scores
Math, Computer Retail Private ConstructionOccupation & Natural & Other Household Trades
Scientists Salespersons Cleaners & Servers
GED-Reasoning 1.82 -0.13 -1.21 -0.42GED-Math 2.26 0.11 -1.12 -0.54GED-Language 1.80 0.07 -1.09 -0.75Intelligence 2.58 -0.30 -0.78 -0.49Verbal 2.46 -0.16 -0.78 -0.64Numerical 2.77 -0.02 -0.80 -0.49Spatial 1.26 -0.41 -0.73 0.00Form Perception 1.18 -0.50 -0.61 0.05Clerical Perception 1.20 0.00 -0.88 -0.72Motor Coordination -0.32 -0.61 -0.85 0.49Finger Dexterity 0.13 -0.29 -0.58 0.10Manual Dexterity -0.30 -0.79 -0.27 0.68Eye-Hand-Foot Coord 0.03 -0.21 -0.20 1.28Color Discrimination 0.64 0.06 0.15 0.00
Table 2: Estimated coefficients on ‘gravity-type’ equation, 1994-2012No Zeros Zeros Replaced Tobit
(1) (2) (3)
logd91 -.460 -.663 -.704(.010)∗∗∗ (.017)∗∗∗ (.018)∗∗∗
switch-to-nrc -.339 -.778 -.879(.027)∗∗∗ (.046)∗∗∗ (.050)∗∗∗
switch-to-rc -.447 -.321 -.273(.033)∗∗∗ (.056)∗∗∗ (.061)∗∗∗
switch-to-rm -1.270 -1.546 -1.588(.031)∗∗∗ (.054)∗∗∗ (.058)∗∗∗
switch-to-nrm -.772 -.864 -.863(.048)∗∗∗ (.085)∗∗∗ (.091)∗∗∗
Const. -4.070 -2.801 -2.563(.195)∗∗∗ (.345)∗∗∗ (.372)∗∗∗
Obs. 22592 25308 25308R2 .577 .522
Note: The Table presents the results from the estimation of Equation (15). The dependent variable isln(swkj/swkk)t. All specifications include source and destination occupation-year dummies.
20
Table 3: Summary statistics of estimates of θ and θ using occupation-months with at least100/15 reports
Sample: Full RestrictedEstimate of: θ θ
10th Percentile 2.2024 2.4623Median 2.8880 3.2306Mean 2.8442 3.323290th Percentile 3.4212 4.2903
Note: The table is based on the distribution of the estimated values of θ and θ. The estimation ofθ uses the full sample in each month, by initial occupation, excluding occupation-months with lessthan 100 observations. The estimation of θ uses a restricted sample of gender-specific demographicbins for those aged 25 to 30, by month and by initial occupation, excluding occupation-demographicbin-months with less than 15 observations.
Table 4: Estimated effects on occupational transition costs for each of the specifications inTable 2
VariableImplied β Percentage effect on dkj
No Zeros Zeros Replaced Tobit No Zeros Zeros Replaced Tobit
logd91 0.142 0.205 0.218 14.270 22.159 23.691switch-to-nrc 0.105 0.241 0.272 11.075 27.241 31.251switch-to-rc 0.138 0.099 0.085 14.854 10.444 8.824switch-to-rm 0.393 0.479 0.491 48.168 61.388 63.474switch-to-nrm 0.239 0.267 0.267 27.002 30.646 30.609
Note: Percentage effect on dkj refers to the effect of a 1 standard deviation increase in distance inthe corresponding sample (all switches or non-zero only), and of a change from 0 to 1 for the othervariables.
21
Table 5: Estimated barriers to occupational transition for some commonly observed transi-tions, 2012
Source Occupation Destination Occupation dkj dkj,tManagement related occupations Executives, administrators and managers 1.079 2.266Executives, administrators and managers Management related occupations 1.079 3.158Retail and other salespersons Other administrative support occupations 1.236 3.071Other administrative support occupations Retail and other salespersons 1.236 3.889Executives, administrators and managers Sales, finance and business 1.356 5.322Construction trades Helpers, construction and production occ 1.567 9.063Retail and other salespersons Sales, finance and business 1.358 5.331Helpers, construction and production occ Construction trades 1.567 6.054Sales, finance and business Executives, administrators and managers 1.635 3.433Retail and other salespersons Food service occupations 1.841 7.476
22
Tab
le6:
Ob
serv
edan
dco
unte
rfac
tual
occ
up
atio
nal
mob
ilit
yra
tes
for
sele
cted
occ
up
atio
ns,
2012
Occ
up
ati
on
Mob
ilit
yT
asks
Ob
serv
edN
ota
skb
arri
ers
No
bar
rier
sF
ract
ion
(1)
(2)
(3)
(4)
Law
yers
and
jud
ges
0.02
30.
064
0.88
40.
047
Hea
lth
asse
ssm
ent
an
dtr
eati
ng
occ
up
atio
ns
0.02
80.
203
0.96
90.
186
Hea
lth
dia
gn
osi
ng
occ
up
atio
ns
0.02
90.
208
0.97
00.
190
Tea
cher
s,ex
cep
tco
lleg
ean
du
niv
ersi
ty0.
029
0.20
60.
970
0.18
8P
rote
ctiv
ese
rvic
eocc
up
ati
on
s0.
033
0.18
10.
964
0.15
8T
each
ers,
coll
ege
and
un
iver
sity
0.03
60.
111
0.93
70.
083
Tra
nsp
orta
tion
and
mate
rial
mov
ing
0.03
90.
243
0.97
70.
217
Lib
rari
an
s,so
cial
scie
nti
sts,
reli
gio
us
wor
ker
s0.
041
0.22
50.
973
0.19
8O
ther
per
son
alse
rvic
eocc
up
atio
ns
0.04
10.
293
0.98
10.
268
Food
serv
ice
occ
up
atio
ns
0.04
20.
250
0.97
70.
222
Ret
ail
an
dot
her
sale
sper
son
s0.
056
0.37
50.
987
0.34
2C
onst
ruct
ion
trad
es0.
057
0.21
40.
972
0.17
1F
ab
rica
tors
,ass
emb
lers
an
dh
and
wor
kin
gocc
up
atio
ns
0.05
90.
136
0.95
00.
086
Oth
erad
min
istr
ati
vesu
pp
ort
occ
up
atio
ns,
incl
ud
ing
cler
ical
0.06
00.
432
0.99
00.
400
Mac
hin
eop
erat
ors
and
ten
der
s,n
otp
reci
sion
0.06
00.
229
0.97
40.
185
En
gin
eeri
ng
and
scie
nce
tech
nic
ian
s0.
062
0.20
00.
968
0.15
2O
ffice
sup
ervis
ors
an
dco
mp
ute
rop
erat
ors
0.07
00.
280
0.98
00.
230
Info
rmati
on
and
reco
rds
pro
cess
ing,
exce
pt
fin
anci
al0.
070
0.35
50.
986
0.31
1F
reig
ht,
stock
an
dm
ate
rial
han
dle
rs0.
084
0.41
40.
989
0.36
5H
elp
ers,
con
stru
ctio
nan
dp
rod
uct
ion
occ
up
atio
ns
0.09
80.
187
0.96
60.
102
23
Appendix A Matching DOT with CPS
The National Crosswalk Service Center provides a crosswalk between the occupation codes in
the 1991 Dictionary of Occupational Titles (DOT) and the 1990 Census Occupation Codes
(COC).15 1990-COC codes are first converted to the standardizes 3-digit occupation codes
from Autor and Dorn (2013), which are adapted from Meyer and Osborne (2005). Next,
because the DOT classification is much more detailed than the standardized occupation codes,
unweighted means are calculated for each DOT dimension at the standardized occupation code
level. Each dimension of the DOT is then rescaled to have mean zero and standard deviation
one across the universe of standardized occupation codes. Finally, to generate scores at the
2-digit level, an unweighted average is taken across all 3-digit occupations that are within the
same 2-digit category.
Appendix B Extension: Occupational Tenure
This section extends the model to allow for occupation-specific human capital.16 Let an
individual’s tenure in occupation j be denoted tenj(i), and assume that occupational tenure
increases productivity at a rate of γ for each additional year of tenure. This leads to the
following modified version of Equation (1):
wj(i) = pjf [X(i)] (1 + tenj(i))γ
(zj(i)
dkj
)(A.1)
The extra productivity from tenure is due to the accumulation of occupation-specific
human capital. It is entirely non-transferable and lost when switching out of occupation j.17
With this modified wage specification, the probability that occupation j offers individual
i the highest wage, which is the probability that individual i will optimally choose to switch
to occupation j, given his current occupation k (denoted by πkj(i)) is given by:
πkj(i) ≡ Pr[wj(i) ≥ max
s{ws(i)}
]=
∫ ∞0
Pr [ws(i) ≤ w,∀s 6= j] · dPr [wj(i) ≤ w]
=Tjd−θkj [pj (1 + tenj(i))
γ ]θ∑Ns=1 Tsd
−θks [ps (1 + tens(i))
γ ]θ
(A.2)
15The crosswalk is the National Occupational Information Coordination Committee (NOICC) Master Cross-walk, Version 4.3, downloadable from ftp://ftp.xwalkcenter.org/download/xwalks/, file xwalkv43.exe.
16For evidence on the importance of occupation-specific human capital, see Kambourov and Manovskii(2009b).
17Occupation-specific human capital is assumed to be transferable across employers within the same occu-pation but is completely lost when switching occupations.
24
Note that tenj(i) = 0 ∀j 6= k. Therefore, ∀j 6= k:
πkj(i) =Tjd−θkj p
θj∑
s 6=k Tsd−θks p
θs + Tkp
θk (1 + tenk(i))
γθ(A.3)
Meanwhile, individual i’s probability of staying in occupation k, πkk is given by:
πkk(i) =Tkp
θk (1 + tenk(i))
γθ∑s 6=k Tsd
−θks p
θs + Tkp
θk (1 + tenk(i))
γθ(A.4)
Dividing (A.3) by (A.4), and taking logs of the ratio, we have:
lnπkj(i)
πkk(i)= lnTj + θ ln pj − lnTk − θ ln pk − θ ln dkj − γθ ln(1 + tenk(i)) (A.5)
Averaging this across individuals in occupation k leads to the gravity-type equation:
1
Nk
Nk∑i=1
lnπkj(i)
πkk(i)= lnTj + θ ln pj − lnTk − θ ln pk
− θ ln dkj − γθ1
Nk
Nk∑i=1
ln(1 + tenk(i))
(A.6)
where Nk is the number of individuals in occupation k.
Note that the right-hand-side of the equation is the same as in the main body of the paper,
with the addition of a weighted average of log-tenure in the source occupation. Given that
the only individual-specific component on the right-hand-side of the equation is occupational
tenure, all individuals with tenure level x have the same transition probabilities. With access
to a dataset with a large number of individuals at a number of different tenure levels, the
left-hand-side of the equation could be empirically measured as a weighted average:
∑x
Nxk
Nklnswxkjswxkk
(A.7)
where Nxk is the number of individuals in occupation k with tenure level x (at the start of
the period), swxkj represents the number of switchers from occupation k to occupation j with
tenure x, and the sum is over the different levels of x.
However, it can also be shown that:
1
Nk
Nk∑i=1
lnπkj(i)
πkk(i)= ln
(∑Nki=1 πkj(i)∑Nki=1 πkk(i)
)+ ck (A.8)
where ck is a constant specific to occupation k. Moreover, with a large number of individ-
uals in each occupation we hae that:
25
ln
(∑Nki=1 πkj(i)∑Nki=1 πkk(i)
)= ln
(swkjswkk
)(A.9)
Given (A.8) and (A.9) can rewrite the gravity equation (A.6) as:
lnswkjswkk
= lnTj + θ ln pj − lnTk − θ ln pk + ck
− θ ln dkj − γθ1
Nk
Nk∑i=1
ln(1 + tenk(i))(A.10)
This can be estimated exactly as in the main text using source and destination occupation
fixed effects (interacted with time dummies) and a set of proxies for mobility costs. However,
the interpretation of the estimated source occupation fixed effects would change, as they
would reflect not only Tk and pk, but also the adjustment factor ck as well as the effects of
occupational tenure.
26
27
Figure A.1: Histogram of estimated values of θ
Note:The histogram for the entire sample includes estimated values of θ for each occupation with at least100 reports. The histogram for the restricted sample includes estimated values of θ for each gender byinitial occupation, restricted to workers aged 25-30, and to groups with at least 15 earnings reports.
28
29
Table A.1: 2-digit occupation groupings for the Autor and Dorn (2013) coding system, orga-nized by task categories
3-digit2-digit Category 2-digit Code Autor and Dorn (2013)
Codes
Non-Routine Cognitive:Executives, administrators and managers 02 004-022Management related occupations 03 023-037Engineers and architects 04 043-059Mathematical, computer and natural scientists 05 064-083Health diagnosing occupations 07 084-089Health assessment and treating occupations 08 095-106Teachers, college and university 09 154Teachers, except college and university 10 155-163Librarians, social scientists, religious workers 11 164-177Lawyers and judges 12 178Writers, artists, entertainers, athletes 13 183-199Health technologists and technicians 14 203-208Engineering and science technicians 15 214-225Technicians, except health engineering, and science 16 226-235Protective service occupations 27 415-427
Routine Cognitive:Sales supervisors and sales reps, finance and business 17 243-256Retail and other salespersons 18 258-283Office supervisors and computer operators 19 303-308Secretaries, stenographers, and typists 20 313-315Information and records processing, except financial 21 316-336Financial records processing occupations 22 337-344Office machine operators and mail distributing 24 346-357Other administrative support occupations, including clerical 25 359-389
Routine Manual:Mechanics and repairers 35 503-549Construction trades 36 558-599Other precision production occupations 37 614-699Machine operators and tenders, not precision 38 703-779Fabricators, assemblers and hand working occupations 39 783-789Production inspectors and graders 40 799Transportation and material moving 41 803-859Helpers, construction and production occupations 43 865-873Freight, stock and material handlers 44 875-889
Non-Routine Manual:Private household cleaners and servers 26 405-408Food service occupations 28 433-444Health service occupations 29 445-447Cleaning and building service occupations, except household 30 448-455Other personal service occupations 31 457-472
30