Immigrant Wage Assimilation in the United States:
The Role of Occupational Upgrading
Rebecca Lessem∗and Carl Sanders†
November 23, 2014
Abstract
We quantify the import of a prominent explanation for the wage assimilation of immigrants to the US, which we term occupational upgrading:
due to a lack of opportunities, new immigrants take jobs below their true
skill levels, but with more time in the US they find better matches for their
skills. To do this, we create a simple model that links immigrant skills to
wages, job offers, and occupational upgrading. We estimate the model on
representative labor market and migration data from US immigrants. Our
results show that only high-skilled immigrants would be better matched by
policies to reduce frictions.
JEL Codes: J31, J15, J62
∗
Tepper School of Business, Carnegie Mellon University. rlessem@andrew.cmu.edu
Department of Economics, Washington University in St. Louis. carlsanders@wustl.edu
Thanks to seminar participants at CMU, Kansas State University, Montana State University, NYU,
Washington University in St. Louis, LSE, UCL, and the Society for Economics Dynamics, the Society of Labor Economics, and the North American Summer Meeting of the Econometric Society
for helpful comments. Financial support from the National Center for Border Security and Immigration at the University of Arizona is gratefully acknowledged.
†
1
1 Introduction
Immigrants to the United States earn lower wages than natives who have the
same levels of education and work experience. But with time in the US, this
gap between immigrants’ wages and their comparable natives’ wages decreases,
from 35% below natives at entry to 10% below after 15 years in the labor force.1
This empirical phenomenon is called “wage assimilation” and is one component
of an active debate among politicians and pundits discussing proposed changes
to US immigration policy. Policymakers would like to improve the process of
assimilating immigrants into the existing social and economic structure of the
US.2 While there is a good deal of evidence documenting empirical wage assimilation patterns, the primary problem that policymakers face is that both they
and economists do not know the importance of the potential reasons why immigrants experience wage assimilation.
In this paper, we quantify the role of a primary explanation given in the literature for immigrant wage assimilation in the US, which we term “occupational upgrading.” Occupational upgrading is the idea that immigrants may be restricted
from finding the best job for their skills when they enter the US. Consider an accountant immigrating from India: she may have the same education and skills as
native accountants, but lack state-level licenses, personal connections, or knowledge of US accounting firms. Given these frictions, she may begin her time in the
US as a secretary. With time in the US, she can get the licenses she needs, meet
people in her field, and learn about the best way to find a job as an accountant.
In the long run, she can overcome the frictions she faces and can find the best
job for her skills. Her wages will catch up to her “comparable” natives; that is,
natives who had her level of education but also had opportunities to get licenses,
connections, and field-specific knowledge before she even entered the US.
We determine the importance of occupational upgrading for wage assimi1
Numbers taken from our data.
E.g. the debate between Ross Douthat (http://douthat.blogs.nytimes.com/2013/06/12/thegreat-assimilation-debate), David Frum
(http://www.thedailybeast.com/articles/2013/04/24/the-immigrants-haven-t-changed-thedestination-has.html), and David Brooks (http://www.nytimes.com/2013/05/07/opinion/brooksbeyond-the-fence.html).
2
2
lation by combining data from the New Immigrant Survey (NIS) with a novel
econometric model. The NIS is a representative3 sample of recently-legalized
immigrants to the US which includes detailed migration and employment histories as well as a number of demographics not typically available in Census-based
data sets. Our econometric model jointly estimates the wages and occupational
choices of immigrants over their careers in the US. By combining model estimates with data on native US workers, we then quantify the role of occupational
upgrading for the closing of the native-immigrant wage gap as immigrants gain
experience in the US.
If occupational upgrading we the primary driver of wage assimilation, policies that helped immigrants find better jobs (without associated skills training)
could reduce misallocation of immigrants to jobs and help close the native-immigrant
wage gap. There is reason to believe these policies might help: occupational upgrading has been found to be a significant component of wage assimilation in
non-US contexts. Most notably, Eckstein and Weiss (2004) and Weiss et al. (2003)
studied the role of occupational upgrading in immigrant wage assimilation in a
sample of Russian migrants into Israel after the collapse of the Soviet Union. Our
results show that their numbers should not be directly applied in the US: the migrants in their sample were highly-educated engineers in Russia, so the sample
had almost no variation in educational levels, home country occupations, and
legal/illegal immigration status. We find that the importance of occupational
upgrading for an immigrant depends dramatically on their skill levels, so the experiences of the engineers in their sample are not generalizable.
The data available in the NIS is well suited for quantifying occupational upgrading and wage assimilation in the US. The NIS sample reports retrospective
labor market outcomes of immigrants in the US and information on both legal
and illegal experience in the US. Additionally, it has extensive details on immigrants’ pre-immigration characteristics, in particular education, English skills,
visa status, and home country occupation. For outcomes in the US, the NIS con3
The NIS is representative of immigrants who received a Green Card between May-November
2003, not the overall immigrant population. See Section 2 for information on the sampling
scheme.
3
tains information on immigrants’ first occupation in the US and their occupation
in the US at the time of the survey in 2003. We first document that the cognitive tasks of occupations are an important driver of immigrant wages even conditional on immigrant characteristics. Next, we document the existence of occupational upgrading: simple regressions show that immigrants move to higher
cognitive task occupations with time in the US.
The basic patterns in the data show that immigrants upgrade their occupations over time in the US, but are only suggestive that occupational upgrading
may be a significant component of immigrant wage assimilation. The regressions cannot be used directly to quantify its importance because of endogenous
missing data in our sample. The NIS data asks information on first and current
jobs in the US, but no information on any jobs in between those two. This means
the missing data on jobs is non-random: immigrants who upgrade occupations
more often have more missing job observations.
To deal with this missing data issue, we create a novel latent variable model
of occupational upgrading and immigrant skills and estimate it on the NIS. In
the model, workers’ wages are a function of their latent skills, their labor market
experience, and their current occupation. Their occupational choices then come
from a latent variable structure: every period, they may remain at their previous
job, receive a shock into the unemployment pool, or get an outside offer from
another job, which they only accept if the new job is better than their current
one. Instead of simply estimating latent skill levels as residuals in the wage and
occupation equations, we estimate a mapping from the detailed individual demographics available in the NIS to immigrant skills. We show that the model is
non-parametrically identified even with incomplete worker histories in our data,
estimate it by Simulated Maximum Likelihood, and show that it provides an excellent fit on observed immigrant occupational transitions.
With the parameter estimates, we perform decompositions to determine the
importance of occupational upgrading for immigrant wage assimilation. Our
primary decomposition estimates how the wage assimilation process would change
if immigrants were immediately placed in the estimated job they would end up
with after 25 years in the US. That is, if the model predicts a worker starting as
4
a secretary has the skills to end up as an accountant, how would starting her as
an accountant at entry to the US affect her wage gap with comparable natives?
While this is obviously impossible as a policy solution, we interpret the results
from the thought experiment as an upper bound for the effectiveness of programs that aim to reduce job frictions.
The results show that while occupational upgrading plays a significant role
in wage assimilation, its importance varies dramatically depending on the immigrants’ skill levels. If immigrants were moved immediately to the occupation
they would end up with in the long run in the US, the average native-immigrant
wage gap at entry would decrease by 20%, a non-trivial amount which still leaves
room for other factors. The effects of this decomposition depend strongly on the
pre-immigration characteristics of the immigrants: higher-skilled immigrants
also tend to be those who get the most benefit from immediately moving to their
long-run job. For example, for immigrants with high English skills, moving them
to their optimal occupation decreases the wage gap at entry by 54% and reduces
the average wage gap over the first 15 years to -1% (they earn more than natives).
On the other hand, moving immigrants with low English skills to their long-run
occupation at entry only reduces the initial wage gap by 10% and the gap over
the first 15 years to 26% (from 24% before). We show more generally that the estimated reduction in the wage gap from moving an immigrant to her long-term
job is increasing in the immigrant’s entry wage.
Our results have implications for both US immigration policy and future research into wage assimilation. We find that eliminating the need for occupational upgrading would increase the speed of wage assimilation, but it would
have a significant impact only for high-skilled immigrants who already have the
best time in the US labor market. Rather than policies that look to help immigrants find the right jobs, a policy that specifically focused on increasing the skills
of low-skilled immigrants may have better distributional consequences. For future research, our results show that the higher-skilled the immigrant, the higher
estimated role of occupational upgrading in assimilation. Given that many data
sets used in the immigration literature (including ours) have some selectivity of
the sample, this result emphasizes that effects of potential policies cannot be un-
5
critically applied to immigrants of different skill levels.
The previous literature on wage assimilation in the US has almost universally been focused on documenting its existence and extent. Chiswick (1978),
Borjas (1985), and LaLonde and Topel (1992) document assimilation using crosssectional data from the US Census, and Duleep and Dowhan (2002) and Lubotsky
(2007) use longitudinal data from Social Security Administration records. These
results of these studies differ in the specifics depending on the data set and timeframe, but they all document the general phenomenon of wage assimilation4 .
They do not, however, go beyond documenting the existence and extent of wage
assimilation.
While we also document the existence of wage assimilation in our sample,
our primary contribution to is to be the first to analyze the role of occupational
upgrading in immigrant assimilation into the US labor market. There is a small
group of papers attempting to quantify the importance of occupational upgrading for wage assimilation, but they typically focus on non-US labor markets. As
mentioned above, Eckstein and Weiss (2004) and Weiss et al. (2003) look at the
role of firm and occupational transitions for wage growth of a non-representative
sample of highly-skilled Russian immigrants to Israel, while de Matos (2011) shows
reduced form evidence on immigrants moving to more productive firms over
time in linked employer-employee data from Portugal. Imai et al. (2011) use
Canadian data to show that home country occupation predicts immigrant wage
growth, but does not explicitly consider occupational upgrading within Canada
or quantify the effects of home country occupation on the observed wage gap
between immigrants and natives.
2 Data: Immigrant Histories and Occupational Characteristics
The New Immigrant Survey (NIS) has an unusual sampling scheme, and the
structure of the sample matters for our estimation strategy and interpretation of
4
There is some argument over whether recent cohorts are still seeing wage growth in the US;
see Borjas and Friedberg (2009).
6
the results. In this section, we discuss the sampling scheme and construction of
our data; see Section 3 for summary statistics and a discussion of sample selection issues.
The NIS drew a random sample from a group of individuals who had applied
for permanent residency in the US and were granted Legal Permanent Resident
(LPR) status between May and November 2003, becoming what is colloquially
known as “Green Card” holders. The Green Card recipients were interviewed inperson over that 6-month period at the location where the LPR documentation
was sent. The immigrants were asked a wide variety of demographic and labor
market questions, as well as a detailed retrospective migration history.
The demographics we use are year of birth, year of entry in the US, education,
home country (which we combine with a measure of home country per capita
GDP), US entry visa status, gender, home country occupation, and English skills.
The data also includes years of experience both as a legal and illegal immigrant
in the US. All of this information is self-reported, so the measures are necessarily
crude for some demographics: for example, English skills is a self-reported “low,”
“medium,” and “high” skill scale. We restrict our sample to LPR recipients who
were currently living in the US at the time of the interview.
The labor market questions include occupation, industry, wage, firm characteristics, and firm tenure. These questions were asked about the current job, but
also retrospectively about 1) the immigrant’s first job after age 16 in their home
country; 2) their final job in their home country; and 3) their first job in the US.
Of these three additional questions we do not use responses to #1 unless it was
also their final job in the home country, since the job at age 16 is not typically
informative of later outcomes. Using these responses, we construct a panel of
wages and occupations for immigrants in the US. The structure of this panel is
that for both the first job in the US and the immigrant’s current job, we have the
wage at the job, the main occupation of the job, and job tenure in years. This
data structure has quite a bit of missing labor market information in the US: any
information on jobs between the first and current is missing. Additionally, this
missing data is non-random, since a worker who moves jobs often will have more
missing job characteristics than an immigrant who never moves.
7
To quantify the occupational upgrading of immigrants, we use the “task-based”
approach of classifying occupations; for a summary of this topic see Sanders
and Taber (2012). The NIS data includes the 3-digit 2000 Census Occupational
Codes for each job. Without aggregation, there are far too many occupational
cells relative to observations to perform inference. We could classify jobs into
different bins, such as “skilled” and “unskilled”, but this results in a loss of variation between jobs that are put into the same grouping. To avoid these problems,
we characterize occupations by a continuous measure of the cognitive, manual,
and interpersonal tasks performed. We follow the literature and use the O*NET
database of occupational tasks to score each occupation. O*NET was created by
the US Bureau of Labor Statistics and is a representative survey that asks workers about the tasks they perform in their occupation. Using these responses we
create a low-dimensional index of different tasks performed in each occupation
using the procedure discussed in Appendix A.
Although we form measures of the cognitive, manual, and interpersonal task
scores for each occupation from the O*NET data, in the remainder of paper we
focus on cognitive tasks. In preliminary wage regressions, we found strong returns to cognitive tasks and only small effects of the other tasks, which we take as
evidence that cognitive tasks best represent the occupational ladder that workers
climb to increase their wages. This result holds true even though immigrants are
significantly more likely to be working in more manually-intensive occupations
than equivalent natives and even in more manually-intensive occupations than
their home country occupations. Despite this, we see almost no wage returns
to moving up the manual task job ladder, suggesting that these jobs are more
stopgaps than parts of the immigrant’s occupational upgrading path.
3 Descriptive Statistics
3.1 Summary Statistics
Table I shows general summary statistics for the sample. The average age
in the sample is close to 40, and the sample is about 55% male. The average
immigrant has about 4.5 years of work experience in the US as a legal immigrant.
8
Even though the survey is a sample of legalized immigrants, many (19%) had
worked as illegal immigrants for some period of time. Conditional on having any
illegal experience, the average amount of illegal experience in the data is around
13 years.5 About one-quarter of the sample moved to the US on a visa sponsored
by an employer. This is an important control as people in this group likely had a
job offer before moving to the US, so we expect them to be higher skill workers
and to suffer less of a drop in the skill level of their job after moving to the US.
Most of the remainder of the sample moved on family reunification visas. Over
60% of the sample has had some schooling beyond high school, and around a
third of the sample reports high English skills.
While this sample is representative of LPR recipients, clearly it is not a representative sample of all US immigrants: it does not contain information on immigrants who never apply for LPR status or those who apply and are not granted
a Green Card. We expect the sample selection issue to bias our results towards
measuring more wage assimilation than a truly representative sample of all immigrants for two reasons. First, LPR recipients are likely to simply be higher
skilled relative to non-LPR immigrants. Second, even if they had the same skills
as non-LPR recipients, immigrants who are unsuccessful in the US are presumably under-represented in the pool of LPR applicants and recipients. Lubotsky
(2007) emphasizes that return migration can bias wage assimilation estimates
upwards. On the other hand, given an observed level of wage assimilation of this
selected group, it is not obvious which direction selection bias would work in
terms of quantifying the role of occupational upgrading in that assimilation.
To gain some information on the extent which our sample differs from the
overall population of immigrants in the US, we calculated basic summary statistics on the sample of immigrants in the 2003 Current Population Survey. Individuals who were born abroad have an average age of 39, 36% have attended college,
and 49% are male. The average age and gender composition of the NIS sample
are similar to the overall immigrant population, but the NIS sample has a significantly higher percentage with some college education (60% vs. 36%).
5
Illegal experience is self-reported, so there is no way to know to what extent it is being understated.
9
3.2 Occupational Upgrading
In this section we describe how immigrants in our sample moved up the occupational ladder with time in the US and how this relates to their skills as proxied by pre-immigration characteristics. The cognitive task measures of jobs are
standardized to be between 0 and 1, with 0 being the lowest-cognitive task occupation in the US and 1 being the highest. Figure I shows the distribution of
cognitive tasks for the home job, initial job in US, and current job in the US.
While there is only the slightest amount of occupational upgrading within the
US in this picture, the three distributions are not independent and there is a significant variance of pre-immigration characteristics, including mixing across different arrival cohorts. The conditional means of occupational choices are much
more informative about occupational transitions over time.
The first column of Table II shows the results from a regression of the immigrant’s initial job at entry to the US onto their pre-immigration characteristics. This column can be interpreted as showing the importance of the preimmigration characteristics for the skills needed to get high-level cognitive task
jobs at US entry. There is a great deal of variation in the predicted initial cognitive tasks by demographics. Taking a (non-existent) “worst” immigrant who
was in the lowest cognitive task occupation in his home country with no English
skills, no education post-high school, etc., the regression predicts he would begin
in the occupation located in the 23rd percentile of cognitive task occupations in
the US. Repeating the same exercise for the “best” possible immigrant, he would
end up in the 75th percentile of the US cognitive task distribution. Of particular note is the interaction between home occupation and home country GDP: as
might be expected, coming from countries with higher per capita GDP means
that cognitive tasks in that country are a stronger proxy for skills.
The regression of the cognitive task level of the current job onto demographics and the initial US job (shown in the second column of Table II) are unsurprising. Cognitive tasks increase with both legal and illegal work experience, but as
expected the effects of legal work experience are larger. This regression also suggests that the cognitive task growth rates of higher skilled immigrants are faster
10
than lower skilled immigrants, since even conditioning on initial job and time in
the US many of the demographics still have significant effects.
To look more carefully at the relationship between skills and occupational
upgrading, Table III shows the determinants of task growth between the first and
current job in the US. At first glance, conditional on everything else, time in the
US leads to higher task growth. However, the coefficient on initial US cognitive
tasks is large and negative. The interpretation of this in terms of an occupational
upgrading framework is actually straightforward: if a worker gets a job with cognitive tasks above his true skill level, we should expect to see low or even negative
growth in cognitive tasks over time. A simple example using these numbers can
illustrate this: consider the “best” immigrant discussed above, who has the highest possible skills as proxied by the demographics. If this immigrant enters the
US at the cognitive task job predicted by the initial job regression, the 75th percentile cognitive task job, the task growth regression predicts upgrading of from
the 75th to the 83rd percentile cognitive task job over 10 years of legal experience.
But say this worker got very unlucky and instead only could find a job at the 25th
percentile of the cognitive task distribution. This regression now predicts this
worker would move from the 25th percentile cognitive job to the 52nd percentile
job, a significantly higher growth rate.
The descriptive statistics are informative to the overall degree of occupational
upgrading in the sample, but there are issues with attempting to directly use the
regressions to measure the rates of occupational upgrading. For one, we actually
have more data on the jobs than used here: we have not used the durations of
the jobs to provide any information. Additionally, the endogenous missing data
problem of not observing intermediate jobs is not fixed by simply conditioning
on the last observed job. To use the duration information and deal with the missing data problem, in the next section we develop a simple econometric model
which uses flexible functional forms from the intuition behind occupational upgrading.
11
4 Model
Our econometric model is a multiple-equation latent variable model relating
wages and occupations with immigrant skills. First, in the wage equation, we
assume that log wages for worker i in occupation j in time t are given by
¡
¢
w i j t = w h i t , π j t + εi j t ,
(1)
where w is a function to be estimated, h i t is their current stock of productive
human capital, π j t is the productivity of occupation j that the worker chose at
time t , and εi j t is white noise independent of everything else.
Second, in the occupation equation we model the productivity of the immigrant’s occupation of choice at time t as
¡
¢
π j t = π s i , π j (t −1) , νi j t
(2)
where π is a function we specify later, s i is the worker’s skill at finding jobs (potentially distinct from her human capital h), π j (t −1) is the previous period’s occupational productivity, and νi j t is an i.i.d. shock the worker observes but we do
not.
There are some decompositions of wage assimilation that do not require estimation of the function π in equation (2). For example, how would the wage
gap between natives and immigrants change if immigrants never changed occupations after US labor market entry? Clearly simply estimating equation (1) (as
long as sufficiently good measures of human capital were used) and plugging in
πi t = π j 0 for all t would work. This is just assuming π (·) = π j 0 : immigrants are always at their initial job. On the other hand, a decomposition of wage growth that
depends on keeping the π process fixed but changing where the worker begins
requires estimation of the occupational upgrading function π.
Our primary interest is in one such decomposition: we will assume that workers begin their occupation in their “optimal” occupation they would have reached
in the long run. In this case, we need to know the occupational upgrading process. For the thought experiment, we need to know each person’s long run occu12
pation, but we do not have this in the data for all individuals. To get an estimate
of a worker’s long run job as a function of their characteristics, we need to estimate the occupational upgrading function to determine what happens to that
workers after a long time in the US.
Our estimation strategy will estimate the wage equation, equation (1), using
standard regression techniques, but we cannot do that for the occupational upgrading function π in equation (2). Our panel data structure for occupations has
a typical case that looks like
Year 1: τc = 0.33, Year 2: τc = 0.33, Year 3: Missing, Year 4: Missing, Year 5: τc = 0.5
where τc gives the worker’s cognitive task level at their job. If we estimated the
occupational upgrading process as a linear model, we would never have workers remaining in the same job for more than one period. Additionally, as in the
example we will be missing the previous productivity π j (t −1) for some year (in
the example, Year 5). The number of missing years is higher for immigrants who
move more since we do not observe even the second job. A simple example will
illustrate why this is a problem. Consider two workers, A and B, who both begin
in the job τc = 0. In period 2, we see worker A still in job τc = 0 but are missing data for worker B. In period 3, we see both workers at τc = 1. If the missing
data was random, using worker B for inference is no problem. But since missing
data on B means we know she moved jobs between periods 1 and 2, the correct
inference about job offer rates for the two workers would be different.
¡
¢
This missing data problem motivates us to choose a functional form for π s i , π j (t −1) , νi j t
that uses a latent variable structure to deal with both these censored observations and the missing data for middle jobs. We model π as
¡ ¢
Fired ∼ Bernoulli s iF
(3)
¡ ¢
Offer ∼ Bernoulli s iO
(4)
13
¡ ¢
πOffer
∼ K s iπ , supp (K ) = [0, 1]
jt
πj t =



π j (t −1)





−1
(5)
if Fired = 0, Offer = 0
if Fired = 1, Offer = 0


πOffer
if Fired = 1, Offer = 1

jt


n
o


max πOffer , π j (t −1)
if Fired = 0, Offer = 1
jt
.
(6)
This can be motivated by a simple search model: at the beginning of a period,
a worker may get fired with probability s iF and then may receive a job offer with
probability s iO , as seen in equations (3) and (4). If she receives an offer (Offer = 1),
she draws the productivity of the offer between 0 and 1 from some distribution K
conditional on her skills s iπ (equation 5). Lastly, there are four separate cases seen
in equation (6), the occupational choice equation. In the first case, the worker
neither got fired nor received a new job offer, so she remains at her previous job.
In the second case, she got fired and did not receive a new offer, so she must be
unemployed, which is indicated by the (arbitrary) notation π = −1. In the third
case, she was both fired and received a new job offer right away and so takes that
offer, and her new firm is πOffer . In the fourth and final case, she did not get fired
but did receive a new offer, so she chooses the more productive of the two jobs.
This model can be derived from an optimizing model of worker behavior
where their reservation value is 0 and there are no dynamic effects of the current productivity level of the job. However, it is not essential for our results that
these be considered deep structural parameters. Most importantly for our purposes, this model does an excellent job fitting the immigrant occupational career
paths when we use cognitive tasks as proxies for the occupational productivities
and pre-immigration demographics as proxies for immigrant skills.
An example path generated by the model is shown in Figure II (a). Modelgenerated paths can match observed sample paths in terms of workers spending
multiple periods in the same job, as well as both upwards and downwards occupational transitions and movements into and out of unemployment. Of course,
given the data structure we would not be able to observe this example immi-
14
grant’s full career: the observed data we would see given this path is shown in
Figure II (b).
While each individual will have these “jumpy” occupational paths, the average changes in occupation over time in the US for any given skill level and initial
occupation are monotonic. Figure III shows smoothed versions of sample paths
averaged over many workers and many simulations of each worker. Different
lines correspond to different initial draws of job in the US (with a distribution
given by the pdf on the left side of the figure). In the example, the “long run”
occupation for the immigrant’s skills is 0.52. Immigrants who receive low initial
job offers start off significantly lower on the occupational ladder than those who
receive high offers, but over time in the US there is convergence in occupations.
5 Estimation
Given the model setup, estimation can be done in two steps. First, we estimate the wage parameters with a semi-parametric regression of wages onto
skills and occupational productivity. Since we do not directly observe either of
those variables, we assume pre-immigration characteristics and cognitive tasks
are good proxies for these factors. In the second step we derive the likelihood
function for the observed occupation choices. The likelihood is complicated by
the fact that we do not observe entire worker histories but just the first and current jobs in the US and their durations. Simulated Maximum Likelihood allows
us to get an estimator even with this missing data in a computationally straightforward way. In this section here we discuss the parametrization of the wage
equation and the occupational transition process, while in the Appendices we
derive the likelihood show our estimator is identified.
5.1 Parametrization
From the model section, the log wage equation is
¡
¢
w i j t = w h i t , π j t + εi j t .
(7)
Since we see neither human capital levels nor occupational productivity, we as15
sume that w can be written as a polynomial expansion of pre-immigration characteristics, US labor market experience, and occupational cognitive tasks,
¡
¢
w h i t , π j t ≡ PolynomialExpansion (X i t , τct )
(8)
where X i t are individual characteristics and τct are the cognitive tasks performed
in occupation j chosen in time t . The vector of X i t , which includes home occupation, legal and illegal experience, English skills, etc., is shown in Table IV.
For the occupational upgrading process, we assume that occupational productivity offers πOffer are drawn from the Kumaraswamy distribution, a computationally simpler variant of the Beta Distribution. This allows for a variety of
shapes for the offer distribution while still being bounded between 0 and 1. The
Kumaraswamy distribution has 2 parameters, a and b, but we restrict a = 2 for
simplicity, which gives the one-parameter pdf
¢b ¡s π ¢−1
¡ ¢ ¡
i
.
k (π) = 2 · b s iπ · π 1 − π2
(9)
where we allow b to depend on the immigrant’s unobserved skill. Given this
parametrization, as b increases, the average occupational productivity offer the
worker receives falls.
We then make additional assumptions about the existence of a mapping from
demographics to skills. We here assume that both the skill that determines the
probability of getting a job offer and the skill that determines the occupational
offer distribution have single-index form in demographics:
¡
¢
s iO = Φ γ0 + X iOt γ
(10)
¡
¢
s iπ = Φ ψ0 + X iπt ψ
(11)
for some γ and ψ, where the X O and X π can be different sets of covariates and Φ
is the Standard Normal cdf to ensure the s are between 0 and 1. To reduce the dimensionality, we also assume that the firing probability s iF = κ, a constant shared
by all workers. In earlier versions of the estimation we allowed for more generality, such as allowing s iF to vary across individuals, but none of the estimates
16
on these parameters were statistically significant and the qualitative results were
identical.
Lastly, we allow for a few more generalizations of the offer process. All the
parameters may be different for the initial job offer in the US in order to allow
for the possibility that skills which help an immigrant’s initial placement in the
US may not be determinative of her success after she arrives. Additionally, we let
the entire offer distribution be different if the worker is working illegally in the
US versus legally in a given period since there is reason to believe the illegal labor market rewards significantly different skills than the legal market, or perhaps
does not reward skills at all.
Given our parametrization, writing the likelihood of any given offer is quite
simple: it is just k (π) . However, even with a full panel, we only observe accepted
offers. Moreover, given our sample we do not even see accepted offers except
for the first period and first period of the final job. Writing the full likelihood
even with this simple individual period likelihood requires additional work, but
is straightforward. In Appendix B, we derive the full likelihood function with the
missing data and show how we constructed a Simulated Maximum Likelihood
Estimator of the model parameters, and then in Appendix C we show that the
offer distribution k is actually non-parametrically identified (although we still
use a parametric form in estimation for precision).
6 Estimation Results
6.1 Wage Equation
The log wage equation for immigrant i in occupation j in time t is given by
w i j t = PolynomialExpansion (X i t , τct ) + εi j t
(12)
We have two wage observations for each person: the wages in their initial and
current job in the US. For precision purposes we use a second degree polynomial
expansion, so all cross-terms and squares were included along with direct effects. This approach necessarily makes for difficult-to-interpret estimates since
17
the marginal effects of any variable is a function of all other variables. Instead,
results from a low-dimensional version of the wage equation including mainly
direct effects can be seen in Table V, but we use the estimates from the full polynomial expansion in everything that follows.
This specification generates a distribution of marginal effects for demographics. For example, we allow for different effects of legal experience in the US
and illegal experience to account for both potential differences in the skill backgrounds of workers who arrive and live in the US illegally as well as the possibility
that they may receive less training or be more poorly matched with firms than legal immigrants. We find that estimated average effect of a year of legal US labor
market experience is about 50% higher than that of an illegal year (6% vs. 4%),
which reflects both per-existing skill differences as well as different experiences
in the US. Figure IV (a) shows the estimated distribution of the returns to one
year of legal experience and one year of illegal experience.
We also find that visa status at entry plays an important role as a proxy for
worker human capital. The effect of the dummy variable that is 1 if the worker
arrived on a work visa (e.g. H1B visa category for skilled workers) is one of the
best proxies for individual human capital, even conditional on education, and is
significantly more important than the cognitive tasks of the home job or English
skills. Figure IV (b) shows the estimated wage returns to switching from nonemployer-sponsored visa to employer-sponsored status. The graph shows both
the gain to getting a sponsor for those without one, and (for ease of comparison) the absolute value of the loss from not having a sponsor for those who do
have one. Presumably this reflects firm-specific human capital that the worker
may already have for the firm who sponsored the visa, since often workers with
employer-sponsored visas are already working for the particular firm who sponsors it in the immigrant’s home country.
6.2 Occupational Transition Parameters
We estimate multiple sets of the parameters relating immigrant demographics to the occupational transition process, given by equations (3), (4), (5), and
(6). The parameters of the job offer rates and the rate of job loss, our measures of
18
s O and s F from above, are shown in Table VI. Table VII reports the estimated parameters governing the shape of the job offer distribution as a function of characteristics. Almost none of the parameters have a direct economic interpretation,
and, while many are statistically insignificant, even those that are large and statistically significant are typically interacted with many other independent variables. The primary reason we include Tables VI and VII is to emphasize that we
estimate two sets of job offer rate parameters and four sets of job offer distribution parameters, depending on whether or not the immigrant is legal or illegal or
whether they are in their first job in the US. This necessarily hurts the statistical
precision of some of our estimates, but since we are depending heavily on identification on observable demographics, allowing a flexible functional form allows
for a good deal of heterogeneity in responses.
It is difficult to interpret the economic significance of the parameter estimates for the job offer process simply from the numbers themselves. Instead, we
put them in some understandable units. To do this, we vary one characteristic at
a time while holding all others constant and to see how a change in that factor
affects occupational outcomes over time. In Figure VI we show how four of the
most important observable demographics serve as proxies for immigrant skills.
In Figure VI, panels (a) and (b), education and English skills both proxy for skills
relevant to entering the US (as seen by the higher intercept in the first period)
and skills for finding better jobs over time (as shown by the steeper slope than
the baseline occupations). In Figure VI (c) and (d), on the other hand, having
an employer sponsored visa or a better home occupation is primary a proxy for
the quality of the job at entry and is not estimated to increase the occupational
transition rate in the US over time.
Of particular interest here are the parameters governing the different job offer distributions of legal and illegal immigrants. In Figure VII, we show what the
predicted occupation paths of immigrants who arrived and stayed in the US illegally would be if all their US experience were legal, keeping all other characteristics fixed. There are at two potential interpretations of these results. First, even
conditional on all other demographics, those who arrive illegally may have lower
levels of skills. Second, some characteristics of the illegal labor market in the US
19
may prevent them from moving up the occupational ladder as quickly as their
legal immigrant peers. We cannot distinguish between any combination of these
two explanations in our setup, but to our knowledge this is some of the first evidence on the career paths of otherwise comparable legal and illegal immigrants
to the US.
6.3 Model Fit
A comparison of the predicted occupational cognitive tasks between the model
and the data is shown in Figure V (a). For each immigrant we have up to two
occupation observations over potentially many years. To get their predicted outcomes, we simulated their whole model-predicted career path 100 times given
their pre-immigration characteristics and compared the predicted values to the
observed values for each year we have observations. Note we do not use any
within-US data on the immigrants for the model predictions: instead the model
generates both their initial job and career path based on pre-immigration characteristics.
The model fit is quite good, particularly because the average occupational
cognitive tasks in the data is non-monotonic over time. Looking at the picture
of the raw data may actually lead to skepticism that there is occupational upgrading for immigrant workers in the US: the average cognitive tasks doesn’t look
anything like the example average careers simulated from the model in Figure III.
In fact, it turns out that the observed double-humped cognitive tasks path over
time is strongly consistent with a model of monotonic occupational upgrading.
The model can fit the rapid growth of occupational tasks over the first 5 years
in the US, the rapid decrease between 5 and 15 years, and gets mixed results in
matching the slight (although not statistically significant) uptick in occupations
from 15-25 years.
The observed dip in occupations after 5 years in the US is simply because of
demographics – the same workers are not being compared across different time
periods. For the current job in the US, workers have varied years of experience,
depending on when they immigrated. They also have variations in the number
of years of illegal labor market experience, given that people who have been in
20
the US for a long period of time and just received a green card are more likely
to have worked in the US as an illegal immigrant. We split the sample based on
the number of years in the US, looking at immigrants with 10 or fewer years in
the US versus those with more than 10. These two groups are quite different
in terms of education, with 65% of the lower-experience group having attended
college versus 42% for the high-experience immigrants. In addition, the highexperience immigrants have a greater share of years of experience as an illegal
immigrant (50% of their US experience versus 11%).
We also allow for unobservable average differences in the skills of different
birth cohorts in estimation, and it may be a concern that this is a cheap way of
forcing Figure Va to match the dip in the data while the other observable demographics would not have been sufficient to match the shape of occupation
levels over time. To test this, we simply show the model fit from the estimated
parameters with the cohort effects set to 0 throughout the model; see Figure Vb.
Re-estimating the model without cohort effects would deliver an even better fit,
but this suffices to show that observable demographics that vary within-cohort
are sufficient to deliver the non-monotonic average cognitive tasks seen in the
data.
6.4 The Wage Gap
Wage assimilation is typically defined as the catch-up of immigrants to “comparable” natives; that is, natives with the same levels of education and labor force
experience. We create wages for comparable natives for each immigrant in our
sample using the Current Population Survey. We compute the average wages of
native workers conditional on age, years of work experience, and education. We
then can impute the “native” wage for each immigrant with the same levels of
those variables using the conditional averages from the natives. We purposefully
do not control for occupation since it is not a part of the typical wage gap calculation. Table VIII shows the wage regression coefficients used to impute the
comparable native wages for each immigrant.
Once we have conditional native wages imputed for immigrants, we can calculate the difference between immigrant wages and comparable native wages.
21
Figure VIII shows the evolution of the wage gap with experience in the US. The
top solid black line gives the average gap across the sample: natives earn about
35% more than immigrants on entry, and the gap falls to about 10% after 15 years
in the US labor force. For the other lines, we calculate the wage gap for different subgroups, using the estimates from the model to predict their occupation
choices and wages. While we use the model to “fill in” missing observations (we
do not observe the full careers of most workers in these subgroups), this can just
be considered data smoothing since we do not change any of the baseline parameters to form these wage gap measures.
The results for the subgroup wage assimilation simulation show that immigrant skills as proxied by demographic characteristics can dramatically change
the measured wage gap. First, restricting attention to only workers who have
the higher level of education effectively does not change the wage gap. This
may seem surprising since education (of course) has a significant relationship
with immigrant skills. But this is because education is one of the conditioning
variables on creating comparable native wages. Looking at only educated immigrants means they are more highly skilled than the average; however, their
comparable natives are also more highly skilled than average, leading to a small
net effect.
On the other hand, both employer sponsored visas and English skills play a
significant role in immigrant wage, even conditioning on education levels. The
bottom two lines in Figure VIII show that by restricting attention to only workers
with good English skills, the wage gap is still 20% at entry but falls to 0 after 7
years. For employer-sponsored visa immigrants, they start very close to natives
(only a 10%) wage gap, but the wage gap falls to 0 by 4 years of labor market
experience and is negative after that. However, the speed at which the wage gap
declines is similar for all the different skill subgroups. The interpretation of these
results is there is a significant amount of skill heterogeneity within immigrant
education groups, but that heterogeneity seems to largely be in terms of wage
levels but not growth rates. From a policy perspective, this suggests that further
restrictions on immigration based on finer measures of immigrant skills would
be useful to reduce the measured average wage gap in levels but cannot make
22
immigrants “like natives:” they will either have a wage gap at entry or their wages
will overshoot natives later.
7 Quantifying the Role of Occupational Upgrading
The perfect counterfactual to quantify the importance of occupational upgrading for wage assimilation would be to determine how much occupational
upgrading early in the career could be improved through labor market policies.
However, this is an impossible object to estimate given our data; we do not have
any idea what the effects of a program would be that helped immigrants find
better jobs since there is no such variation in our data. Instead, our approach
is to give an approximate upper bound for policy using the following thought
experiment: what would happen if immigrants were placed right away into the
occupation they would have after 25 years in the US labor market? We expect this
to be higher than the true potential gains from policy, since immigrants may be
gaining occupational-specific skills or knowledge that cannot be given instantaneously.
This counterfactual, placing immigrants in their long-term occupation immediately, is graphically shown by the top line in Figure IX (a). For comparison
we also run a non-model based counterfactual in which workers never upgrade
their occupation in the US in order to show how important observed occupational upgrading is for immigrant wage growth; this is the bottom line in Figure
IX (a).
Table IX gives the wages and wage gaps associated with the counterfactual
occupational paths, and Figure IX (b) shows the wages graphically. The dashed
line in the figure gives the average wages of comparable natives, while the other
lines show immigrant baseline wages as well as counterfactual wages. The results
show that initially, immigrants earn around $11 per hour, while comparable natives earn around $18. Placed in their long-run occupation, immigrants would
earn about $12.20, a reduction of the initial wage gap of around 20%. Of course,
since the counterfactual immigrants will (on average) remain in that occupation
throughout their career, their increase in wages relative to the baseline will de-
23
crease over time. After around 15 years the counterfactual and baseline wages
effectively converge since immigrants will have found jobs very close to their
long-run job even in the baseline. The overall earnings gap averaging over the
15 years after entry between immigrants and natives is 7% smaller in the counterfactual than the baseline.
A closer analysis of occupational upgrading reveals why the model does not
consider it the primary driver of wage assimilation. Figure X, panels (a) and (b)
show the counterfactual restricted to immigrants with high English skills and low
English skills, respectively. The initial wage gap is closed by 54% in the counterfactual for those with good English skills, much larger than the average effect for
the whole sample. Those with high English earn about 3% less than natives over
the first 15 years of their career. In the counterfactual when they are placed immediately at their long-run job, that earnings gap reverses and the immigrants
earn about 1% more than the natives. On the other hand, for those with low English skills, the counterfactual shown in Figure X (b) reduces the quite large wage
gap between those less skilled immigrants and natives by only 10% at entry, and
the earnings gap over the first 15 years falls from 28% to 26%. This is because
low-skilled immigrants see the least occupational growth in their careers; then
putting them in their long-run career is barely better than doing nothing.
Similarly, the same analysis holds to a lesser extent for home country occupation. Figure XI compares the effect of the counterfactual at the top 25% versus the
bottom 25% of our sample in terms of home occupations. As in the English language case, higher skilled immigrants see a larger effect from the counterfactual:
20% of the initial wage gap is closed for the high home occupation immigrants
but only 10% for the low home country occupation immigrants.
These results have important distributional consequences. Our model naturally generates a different prediction for the importance of occupational upgrading for each immigrant as a function of their characteristics. The distribution of
these estimated effects is shown in Figure XII. To generate this graph, for each individual in the sample we simulated their career many times under the baseline
and then under the counterfactual of being placed immediately in their longrun occupation. We then averaged within each worker to get an estimate of how
24
much that particular worker’s wage gap with their comparable natives is affected
by occupational upgrading. For example, an individual with a result of $0 means
their average wage was the same in the simulations whether or not she started in
her long-run job. The results from this exercise show that there is a left skew to
the results: for most immigrants, the effects are fairly modest, but there are many
who would receive a significant wage boost through this counterfactual.
However, as shown above in particular cases, this counterfactual primarily
helps workers who are already high-skilled. Also on Figure XII we show the average entry wages from the NIS data of workers at different responsiveness levels
to faster occupational upgrading. The higher the wage at entry, the more potentially helpful removing barriers to occupational upgrading would be. The average
immigrant being helped $0 by the counterfactual on average makes around $7 at
entry, while the average immigrant who is helped $7 is making around $15 at
entry. While our model says nothing about welfare, knowledge of these heterogeneous effects of occupational upgrading could help policymakers make decisions about the types of policies they are interested in. If the policymaker wants
to encourage high-skilled immigrants to get back to their full earning potential,
focusing on barriers to occupational upgrading may make a significant difference. But if the goal is to attempt to help the worst-off immigrants, there does
not seem to be much room in our counterfactual for significant effects of an occupational upgrading policy.
While we interpret these results as an upper bound for policy in our framework, potentially policies could move individuals above their baseline long-run
job; for example, occupational-specific training for a high cognitive task occupation. While we cannot evaluate that counterfactual without additional information, the model setup can potentially be used to evaluate any effects of any
policy that acts to change the occupational transitions of immigrants as long as
the distributions of potential changes are known.
8 Conclusion
In this paper, we quantified the role of occupational upgrading in the wage
25
assimilation process of immigrants to the US. To do this, we used panel data on
the migration histories, labor market histories, and demographics of immigrants
to the US from the New Immigrant Survey, which allowed us to see partial immigrant career paths. To deal with endogenous partial censoring of occupations
(since only accepted job offers are observed) and missing data (since we only
see the first and most recent job in the US), we created an econometric model of
skills, job offers and occupational transitions, and established non-parametric
identification of the functions linking worker demographics to the model’s offer
distributions. We then estimated the model on the NIS sample of immigrants
and compared the model-predicted wages of immigrants under different occupational upgrading paths with wage data on comparable natives from the Current Population Survey.
The results indicate that the effects of occupational upgrading depend heavily on pre-immigration characteristics. If workers were moved into their longterm job immediately, the initial wage gap between immigrants and natives would
fall by 20% and their earnings gap with natives over their first 15 years in the US
would fall by 7%. We interpret this as the upper bound that policy interventions
could achieve. The immigrants who are helped the most by faster occupational
mobility are those who are higher earners in the baseline; e.g. those with high
English skills or who started in better home country occupations see the highest
gains from moving immediately to their long-term job.
Our results have implications for both US immigration policy and future research into wage assimilation. For policy, rather than policies that look to help
immigrants find the right jobs, policies which specifically focused on increasing
the skills of low-skilled immigrants may have better distributional consequences
than focusing on job-to-job mobility. For future research, our results show that
the higher-skilled the immigrant, the higher estimated role of occupational upgrading in assimilation. Given that many data sets in the immigration literature
(including ours) have some selectivity of the sample, this result emphasizes that
effects of potential policies cannot be simply applied to immigrants of different
skill levels.
26
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27
Tables and Figures
Table I: Summary Statistics
Variable
Age
Percent male
Years living legally in the US
Years living illegally in the US
Percent with non-zero illegal experience
Fraction that have an employer sponsor
More than high school
High English skills
Sample Size
28
Mean
38.21
55.53%
4.39
2.01
18.74%
28.37%
60.53%
33.28%
4,018
Table II: Determinants of Tasks of Jobs in the US
Cognitive tasks of home job
Home cognitive skills * home GDP
(1)
Initial job
0.211∗∗∗
(0.0181)
0.00231∗∗∗
(0.000578)
Cognitive tasks of initial US job
Years of legal work experience
Legal years US squared
Years of illegal work experience
Illegal years squared
0.0969∗∗∗
(0.00587)
0.0408∗∗∗
(0.00594)
0.0409∗∗∗
(0.00615)
0.0281∗∗∗
(0.00692)
0.00105
(0.00505)
-0.000353
(0.000755)
0.0000182
(0.0000224)
0.239∗∗∗
(0.0100)
3144
0.265
Employer sponsored visa
English skills
More than 12 years education
Schooling in US
Male
Years experience at home
Home experience squared
Constant
Observations
Adjusted R 2
(2)
Current job
0.0400∗∗
(0.0161)
0.000859∗
(0.000503)
0.613∗∗∗
(0.0156)
0.00653∗∗∗
(0.00191)
-0.000197∗
(0.000119)
0.00317∗∗
(0.00150)
-0.000160∗∗
(0.0000768)
0.0336∗∗∗
(0.00537)
0.0266∗∗∗
(0.00526)
0.0229∗∗∗
(0.00565)
0.0345∗∗∗
(0.00620)
-0.00542
(0.00444)
0.000236
(0.000702)
-0.0000152
(0.0000224)
0.108∗∗∗
(0.0101)
2877
0.531
Notes: Standard errors in parentheses. ∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01
29
Table III: Task growth
Cognitive tasks of home job
Home cognitive skills * home GDP
Cognitive tasks of initial US job
Years of legal work experience
Legal years US squared
Years of illegal work experience
Illegal years squared
Employer sponsored visa
English skills
More than 12 years education
Schooling in US
Male
Years experience at home
Home experience squared
Constant
Observations
Adjusted R 2
(1)
Cognitive task growth
0.0317∗
(0.0162)
0.00102∗∗
(0.000504)
-0.375∗∗∗
(0.0158)
0.00685∗∗∗
(0.00194)
-0.000223∗
(0.000121)
0.00316∗∗
(0.00155)
-0.000150∗
(0.0000774)
0.0334∗∗∗
(0.00541)
0.0270∗∗∗
(0.00529)
0.0203∗∗∗
(0.00574)
0.0324∗∗∗
(0.00632)
-0.00509
(0.00448)
0.0000629
(0.000715)
-0.00000996
(0.0000226)
0.109∗∗∗
(0.0103)
2769
0.183
Standard errors in parentheses. p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01
30
Table IV: Characteristics in Wage Equation
Years legal experience
Years illegal experience
College education
Current legal/illegal status
Home occupation’s cognitive tasks
Labor market experience in home country
Visa status
English skills
Home country GDP
Gender
Birth year
31
Table V: Low-Dimensional Wage Regression
Cognitive tasks of job
Cognitive tasks of home job
Home cognitive skills * home GDP
Years of illegal work experience
Illegal years squared
Years of legal work experience
Legal years US squared
Legal US experience * home GDP
Home GDP
Employer sponsored visa
English skills
More than 12 years education
Legal immigrant
Years experience at home
Home experience squared
Constant
Observations
(1)
13.50∗∗∗
(0.591)
4.109∗∗∗
(0.915)
-0.147∗∗
(0.0689)
0.416∗∗∗
(0.0741)
-0.00861∗∗
(0.00356)
0.787∗∗∗
(0.0801)
-0.0295∗∗∗
(0.00439)
-0.00855∗
(0.00439)
0.0878∗∗
(0.0384)
5.016∗∗∗
(0.211)
2.707∗∗∗
(0.205)
1.234∗∗∗
(0.210)
0.886∗∗∗
(0.316)
-0.0396
(0.0257)
0.000169
(0.000779)
-0.0654
(0.586)
5433
Notes: Standard errors in parentheses. ∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01
32
Table VI: Job Offer Rates and Loss Parameter Estimates
Constant Term
College
Home Occupation
Home Occupation2
College × Home Occupation
Sponsor
English
Male
Cohort Effects
Home Country GDP
Home country occupation× Home GDP
Education× Home GDP
Probability of job loss
Notes: Standard errors in parentheses.
33
Parameter Estimates
Legal Immigrants Illegal Immigrants
-0.96
-0.61
(0.24)
(0.64)
0.14
0.26
(0.18)
(0.58)
-0.09
0.13
(0.78)
(2.23)
1.40
0.54
(0.72)
(2.12)
-0.11
-1.13
(0.33)
(0.95)
-0.06
(0.05)
0.10
0.26
(0.05)
(0.15)
-0.06
-0.72
(0.05)
(0.11)
-0.07
0.12
(0.02)
(0.06)
0.38
-0.11
(0.43)
(1.51)
-1.66
-0.10
(0.78)
(3.28)
0.17
0.005
(0.28)
(1.09)
0.17
Table VII: Job offer distribution parameter estimates
Initial job
Constant term
Education
Home occupation
Home occupation squared
Education * home occupation
Sponsor
English
Cohort effects
Male
Home country GDP
Home country GDP*home occupation
Home country GDP*education
Notes: Standard errors in parentheses
34
Legal
2.44
(0.18)
-0.48
(0.20)
0.07
(0.70)
-1.56
(0.69)
0.18
(0.39)
-0.39
(0.05)
-0.19
(0.05)
-0.10
(0.02)
-0.06
(0.04)
0.07
(0.38)
-0.06
(0.71)
0.08
(0.28)
Illegal
2.27
(0.81)
-0.81
(0.62)
-1.01
(2.56)
0.70
(2.18)
1.02
(0.94)
0.14
(0.17)
-0.06
(0.07)
-0.18
(0.13)
-0.015
(1.66)
-0.084
(3.13)
0.17
(1.18)
Current job
Legal
2.97
(0.18)
-0.36
(0.18)
-1.42
(0.62)
0.40
(0.58)
0.46
(0.32)
-0.35
(0.04)
-0.40
(0.03)
-0.07
(0.02)
-0.02
(0.04)
-0.24
(0.24)
-0.19
(0.46)
-0.26
(0.l9)
Illegal
2.17
(0.43)
0.11
(0.40)
0.58
(1.40)
0.20
(1.20)
-1.03
(0.72)
-0.13
(0.14)
0.15
(0.04)
-0.43
(0.09)
0.005
(1.01)
-0.010
(2.45)
0.005
(0.61)
Table VIII: CPS Wage Regressions
Dependent variable = wage
Education
7.14
(0.08)
Years experience
0.70
(0.01)
Experience squared
-0.012
(0.0003)
Constant
6.13
(0.12)
Number of observations 70,572
R-squared
0.14
Notes: Standard errors in parentheses.
Table IX: Counterfactual: Originally Placed in Long Run Occupation
Years
0
3
6
9
Average Wages
10.7
13.6
15.6
16.8
Counterfactual Wages
12.2
14.4
16.1
17.1
35
Native Wages
17.9
18.6
19.1
19.4
% Decrease in Wage Gap
21%
16%
11%
9%
Figure I: Home Country Occupation and US Occupations
36
Figure II: Model Example
(a) Example Career Path
(b) Observed Data from Example Career
37
Figure III: Effect of initial job
38
Figure IV: Estimated Population Distributions of Wage Returns
(a) Returns to Experience
(b) Returns to Employer Sponsor
39
Figure V: Model fit: occupations
(a) Model Fit
(b) Model Fit, Cohort Effects Set to 0
40
Figure VI: Effects of demographic characteristics on occupational outcomes
(a) Education
(b) English
(c) Employer sponsored visa
(d) Home occupation
41
Figure VII: Effects of illegal labor market experience on occupational outcomes
42
Figure VIII: The Wage Gap
43
Figure IX: Effects of occupational mobility
(a) Occupations
(b) Wages
Figure X: Effects of occupational mobility: English Skills
(a) High English Skills
(b) Low English Skills
44
Figure XI: Effects of occupational mobility: Home Country Occupation
(a) High Home Country Occupation
(b) Low Home Country Occupation
45
Figure XII: Heterogeneous Returns to Moving to Long-Run Job Immediately
46
For Online Publication:
A Forming the O*NET Task Measures
This process is identical to that used in Sanders (2014), but is included here for
completeness.
The following questions were taken from the “Work Activities” section of the
O*NET survey. Workers were asked to rate the importance of a broad set of activities in their job, from which we choose the activities most related to cognitive
skills:
• Getting Information
• Processing Information
• Analyzing Data or Information
• Making Decisions and Solving Problems
• Thinking Creatively
• Updating and Using Relevant Knowledge
• Developing Objectives and Strategies
• Organizing, Planning, and Prioritizing Work
We then took workers and occupational choices from the National Longitudinal
Survey of Youth 1979. We linearly projected wages onto worker characteristics
and survey responses for their chosen occupation in each year using the regression
£
¤
E Real Wagei t |Covariatesi t = β0i + β1 Urban/Rural Dummyi t +
β2 t + β3 t 2 + β4 Labor Market Experiencei t +
β5 Labor Market Experience2i t + β6 Num. Childreni t + β7 Marital Statusi t +
βC · Task Responsesi t
The regression is estimated using fixed effects, which allows for individualspecific intercept terms (the β0i ). We then formed the scores for each occupation
using the estimated coefficients from the wage equation,
τ̂C j = β̂C · Cognitive Task Responses in Occupation j
47
and normalized each score between 0 and 1 to get the final τC for each occupation. We constructed manual and interpersonal task scores similarly using responses to other task questions. All these regressions and scores are available
upon request.
48
B The Occupation Transition Process: SMLE Estimation
To derive the likelihood, it is easiest to begin by writing the likelihood of the
occupational history assuming we observed all jobs. We then deal with the missing data by integrating out the data we do not observe using Simulated Maximum
Likelihood. Assume for one individual (suppressing i and s notation) we see their
occupation in each period. Denoting the whole path of occupation for a worker
from time 1 (labor market entry in the US) to T (time of the survey) and using the
Markov structure of the model we have the likelihood of the path π0 → π1 → π2 ...
L (π0 , π1 , ..., πT ) = l 0 (π0 ) l (π1 |π0 ) l (π2 |π1 ) ...l (πT |πT −1 )
(13)
where l 0 is the likelihood of the initial observation and l is the conditional density
of observing a worker in occupation πt as a function of the previous occupation.
We treat unemployment as its own job with some arbitrary value of π below
the lower bound of the job offer distribution. The support of the job offer distribution is [0, 1], and we let πt = −1 if the worker is unemployed. This simply allows
us to unify the notation of employed and unemployed states since unemployed
workers will always accept an offer as all offers have higher π than unemployment.
The first component of the likelihood is the initial job offer. We assume each
worker gets a job offer in the first period, so the likelihood is just the density of
the time 0 offer pdf at the observed occupation:
49
l 0 (π0 ) = k 0 (π0 ) .
The later conditional likelihoods can be calculated from the occupational transition equation, given in equation (6). The model breaks down the likelihood
of transitioning between occupations πt −1 and πt , l (πt |πt −1 ) , into five different
cases depending if the worker moves to a higher productivity firm, lower productivity firm, unemployment, etc.:
1. A worker is employed at time t − 1 but unemployed at t . In this case, the
worker must have gotten fired, which happens with probability s F . We also
know that they did not get a new job offer in this period since all job offers
are accepted when
The probability that a worker does not
¡ unemployed.
¢
O
get a job offer is 1 − s . The likelihood in this case is
¢
¡
l (πt = −1|πt −1 6= −1) = s F · 1 − s O .
2. A worker is unemployed at both at the end of last period and at the end of
the current one. This worker must have not received an offer in period t ,
so the likelihood is
l (πt = −1|πt −1 = −1) = 1 − s O .
3. A worker moves a higher productivity firm. This case includes when a
worker moves to a firm from unemployment. If we see a worker move to a
higher productivity firm, we know that he got a job offer and we know exactly what the offer was. In this case, it does not matter whether or not the
worker was fired, since all that is relevant is that he received a higher job
offer, which he would accept regardless of whether or not he was fired. The
likelihood in this case is the probability of receiving a job offer multiplied
times the likelihood of receiving the specific offer that is observed:
l (πt > πt −1 |πt −1 , ) = s O · k (πt ) .
4. A worker moves to a lower productivity firm but is not unemployed. This
worker must have been fired, otherwise he would not have left his previous higher-productivity job. We also know that he received a job offer at
50
productivity level πt , so the likelihood is
l (−1 < πt < πt −1 |πt −1 ) = s F · s O · k (πt ) .
5. A worker stays at the same job as in the previous period. We know that he
was not fired, since the probability of getting a new offer at the same job
is 0. The likelihood of not getting fired is (1 − s F¡). He then
either did not
¢
O
get a new offer, which happens with probability 1 − s , or he got an offer
for a lower productivity job. The probability of getting an offer is s O and
the probability of it being lower than his current job is the cdf of the offer
distribution K (πt −1 ). The likelihood is then
¡
¢ ¡£
¤
¢
l (πt = πt −1 |πt −1 6= −1) = 1 − s F · 1 − s O + s O · K (πt −1 ) .
Unfortunately, the data does not contain a full record of occupations each year.
Instead, we have the initial and current jobs π0 and πT , and the durations (in
years) of both jobs, d 0 and d T respectively. Denote the first period of the final job
by K = T − d T . The likelihood of the observed data can be written as
L (π0 , πT , d 0 , d T ) = l 0 (π0 ) · l (πt = π0 |πt −1 = π0 )d0 −1 ×
¡
¢
Pr πd0 6= πd0 +1 × l (πK |π0 , d 0 ) · l (πt = πT |πt −1 = πT )dT −1
(14)
.
This reads as: in the first period the worker received the offer π0 and kept it for
d 0 − 1 periods. In the period after that, we know they moved jobs. The individual
then receives their offer in period K for their final job and stays there for d T − 1
periods without leaving.
Without the term l (πK |π0 , d 0 ), the first period of the final job, this would be
straightforward to calculate using the conditional likelihoods from above. However, l (πK |π0 , d 0 ) requires calculating the conditional distribution of observing
some job π in period K as a function of the last observed job π0 and duration
51
at the job d 0 while missing data on job transitions from periods d 0 to K . Direct
calculation of this requires evaluating a K − d 0 dimensional integral for each individual for each likelihood evaluation. Instead of direct computation we use
simulation-based estimation method.
The Simulated Maximum Likelihood (SMLE) estimator begins by writing down
the likelihood as if we observed the entire occupational history and then integrating out the missing data directly. We can transform the full likelihood into
the observed likelihood by integrating out over all the missing middle jobs. The
SMLE method notes that this integral can be written as E πK −1 ,...,πd0 +1 |πd0 [l (πK |πK −1 )],
the expected value of the conditional likelihood for period K with the expectation taken over the possible paths that led to πK . Since our model is cheap to
simulate, it is easy to start the model at d 0 with current job π0 and simulate the
job path forward until period K . Doing this S times for each individual’s data, we
¡
¢
can then calculate the value l πK |πSK −1 for each data point πK combined with
simulated job in period K − 1, πSK −1 . We know that as long as πSK −1 is drawn from
the correct conditional distribution, as S → ∞
S ¡
¢
1X
l πK |πSK −1 →p E πK −1 ,...,πd0 +1 |πd0 [l (πK |πK −1 )] .
S i =1
(15)
Using this, the SMLE estimator maximizes the calculated likelihood for the observed data points combined with the simulations used to eliminate the missing
data problem.
52
C Identification
Our econometric model of occupational transitions relates individual demographic characteristics X i to occupational productivity outcomes π j t through
the equations (3), (4), (5) and (6), where we assumed that the offer distribution
K (·) is a Kumaraswamy distribution with a parameter s π which has a single-index
form in demographics. We have not yet showed that we can actually recover
these parameters from our data. In this section, we do more than that: we show
that we can non-parametrically identify the offer distribution K (·). Our sample is
too small to use non-parametric estimators, but in estimation we used as flexible
functional forms as possible and in principle we could use increasingly flexible
functional forms as the amount of data increased.
First we show the job offer and firing rates are identified. For this section we
suppress the observable demographics X i ; we can repeat the argument for any
given X i . Consider a worker who is at job π0 in the initial period. We will observe
them at the same job next period only if they did not lose their job and if they
received an offer, it was lower than π0 . The probability of this event is
¡
¢¡
¡
¢
¢
Pr (π1 = π0 ) = 1 − s F s O + 1 − s O K (π0 ) .
(16)
Now consider workers who have π0 = 1, that is, the workers with the best jobs.
The probability of them getting an offer lower than 1 is 1, so K (1) = 1 and this
reduces to
Pr (π1 = π0 |π0 = 1) = 1 − s F .
53
This directly identifies s F , the probability of job loss. Intuitively, we have data
about how long it takes a worker to switch jobs, as well as a ranking of jobs. If we
look at individuals only in the highest type of jobs, the only model mechanism
for leaving this job is job loss since they will rarely get a better offer to make a
job-to-job move.
Once we have identified the probability of job loss s F , we can use a similar
argument to recover the probability of a job offer s O . Consider workers at π0 = 0,
that is, the workers with the worst jobs. Since we know the probability of an offer
above 0 is 1, K (0) = 0 and the probability of not moving jobs is
¡
¢
Pr (π1 = π0 |π0 = 0) = 1 − s F · s O .
Since we already know s F , this probability gives us s O . As above, if we look at
individuals only in the worst type of jobs who did not lose their jobs, the only
model mechanism for moving up is receiving an outside offer so we know all
upwards moves come with an offer and every time they stay in their job there was
not an offer. We are able to identify the relative frequency of job offers versus the
offer distribution, unlike in many versions of search models, because we assume
we have data on rankings of jobs, so we can ex ante identify workers who are
either unlikely or very likely to receive better offers.
Lastly, once we know s O and s F , solving for K (π0 ) in equation (16) gives
K (π0 ) = ¡
sO
Pr (π1 = π0 )
¢¡
¢−
.
1 − sO
1 − s F 1 − sO
(17)
The right hand side is simply data (Pr (π1 = π0 )) and known parameters. Given an
54
original job, we can now remove the correct proportion of workers who had either been fired or not received an offer and then use the proportion of remaining
workers who did not move to identify the probability of getting an offer below
that job. As long as workers are observed at every possible job in some period
(which will be true given the model setup), the full distribution of K can be traced
by varying π0 in equation (17).
For this identification argument we only required a limited part of the data:
the type of the first job and one observation in period 1 of whether the individual
remained in that job or not. The duration of the first job, the type of the final job,
and the duration of the final job are all not strictly required for identification but
increase the power of our estimators. Since the actual cross-section of workers is
relatively small, the additional power of knowing the first and final job durations
helps significantly for getting a reasonable amount of precision.
55