Department of Economics
Working Paper Series
Education, Mobility and the College Wage Premium
14-001 Damba Lkhagvasuren
Concordia University and CIREQ
Department of Economics, 1455 De Maisonneuve Blvd. West, Montreal, Quebec, Canada H3G 1M8
Tel 514–848–2424 # 3900 · Fax 514–848–4536 · econ@alcor.concordia.ca · alcor.concordia.ca/~econ/repec
Education, Mobility and the College Wage Premium∗
Damba Lkhagvasuren†
Concordia University and CIREQ
January 17, 2014
Abstract
Motivated by large educational differences in geographic mobility, this paper considers
a simple dynamic extension of Roy’s (1951) model and analyzes it using new evidence
on net versus excess mobility and the individual-level relationship between mobility
and wages. According to the model, the dispersion of a labor income shock specific to
a worker-location match is greater for more educated workers and accounts for large
educational differences in mobility. In the model, labor mobility raises both the average
wage and the college wage premium, a prediction consistent with differences between
Europe and the U.S.
Keywords: mobility, wage structure, a dynamic Roy model, a labor income shock,
spatial mismatch, moving cost, local employment dynamics, excess versus net mobility,
gross mobility, college premium
∗
I thank two anonymous referees for detailed comments that greatly improved the paper. I also received
helpful comments from Árpád Ábrahám, Mark Bils, Paul Gomme, Jonathan Heathcote, Lutz Hendricks,
John Kennan, Seik Kim, Greg LeBlanc, Naci Mocan, Stephen Ross, Peter Rupert, Christopher Taber,
and the participants at various seminars and conferences, including the 2007 Midwest Macro Meeting, the
2009 Canadian Economic Association Conference, the 2009 Urban and Housing Conference at the Federal
Reserve Bank of Atlanta, the 2010 Economic Research Forum in Ulaanbaatar and the 2010 Econometric
Society Meeting. I gratefully acknowledge financial support from FRQSC grant 2014-NP-174520.
†
Department of Economics, Concordia University, 1455 Maisonneuve Blvd. W, Montreal, QC H3G 1M8,
Canada. Telephone: +15148482424 extension 5726. E-mail: damba.lkhagvasuren@concordia.ca.
1
Introduction
One of the most common patterns across local labor markets is higher geographic mobility
among more educated workers. For example, according to the U.S. census, among workers
who are older than 28, those with a college degree are twice as mobile relative to those who
have a high school diploma (see Table 1). Recent work by Machin, Pelkonen, and Salvanes
(2012) and Malamud and Wozniak (2012) shows that education has a large causal effect on
mobility. However, despite these empirical advances, the actual mechanism underlying the
impact of education on mobility is not well understood. This paper addresses the issue of
what makes more educated workers more mobile than otherwise observationally similar less
educated workers.
It is well known that gross migration flows are much larger than the corresponding net
flows.1 Moreover, as shown in Table 1, the net flows are too small to account for large educational differences in mobility. Therefore, any credible theory accounting for the positive relationship between mobility and education must allow for simultaneous in- and out-migration
at the local level. One such theory is that the spatial dispersion of an individual’s labor
income is higher among the more educated: the wage of a more educated worker could be
more responsive to where the person works and therefore the more educated person could
enjoy larger wage gains when moving across locations.2
To explore whether the spatial dispersion of labor income can account for large educational differences in labor mobility, I consider a simple dynamic model where worker
migration and wages are jointly determined. Following the long tradition of the literature
on sectoral selection and earnings, I build on the foundations of the Roy (1951) model of
sectoral choice. In particular, I start with the static two-sector Roy model considered by
McLaughlin and Bils (2001), who analyze the wage gap between movers and stayers across
industries. I extend their model to a stochastic dynamic setting with costly labor mobility
1
See, for example, Vanderkamp (1971), Coen-Pirani (2010) and Lkhagvasuren (2012).
Borjas, Bronars, and Trejo (1992b), Dahl (2002) and Kennan and Walker (2011) emphasize the importance of the idiosyncratic location match income effect for labor mobility.
2
1
across locations. In addition, I distinguish between two key components of individuals’ labor income: unobserved ability and an income shock specific to the worker-location match.
Workers in the same location are also subject to a common regional level shock, below referred to as a local technology shock. The local technology shock causes net migration, while
the worker-location match shock creates simultaneous in- and out-migration. So, in contrast
to the standard Roy model, which allows for only net mobility, the model considered in this
paper permits both net and excess labor mobility.3
In the model, the worker-location match shock and the local technology shock are persistent over time. This is motivated by the following two considerations. First, the literature
on labor income dynamics finds that labor income shocks are highly persistent over time
(see, for example, Hubbard, Skinner, and Zeldes, 1994 and Guvenen, 2009). Second, Bayer
and Juessen (2012) show that the persistence of migration incentives is essential in linking
individuals’ migration decision to data on geographic mobility.
I discipline the quantitative analysis of the model by using new evidence on mobility and
wages. Specifically, using the U.S. census data, I document that the share of net mobility in
overall mobility is lower among the more educated. I also show that the relationship between
mobility and wages is strikingly different between college- and high-school-educated workers:
(a) Among high-school-educated workers, recent in-migrants earn less than the incumbent
workers of the receiving localities; and (b) College-educated in-migrants earn more than their
incumbent counterparts.
It should be stressed that the previous studies on migration and wages report a negative
wage gap between movers and stayers (e.g., Borjas, Bronars, and Trejo, 1992a and Krieg,
1997). This is in sharp contrast with the above positive movers-stayer wage gap among
college-educated workers. These opposing results arise because earlier studies maintain that
mobility affects the wages of different educational groups in the same direction (see Section 2).
3
Analogous to Davis and Haltiwanger (1992), net mobility refers to the part of the worker flows that
account for the observed net migration across regions, while excess mobility is overall mobility minus the
net mobility.
2
According to the model, among high-school-educated workers, the spatial dispersion of
labor income, measured by the standard deviation of the worker-location match shock, is
approximately 6.6 percent of their overall labor income. For college graduates, the spatial
dispersion of labor income is much higher and amounts to 10.6 percent of their average
labor income. These numbers imply that market thickness decreases with education: for less
educated workers opportunities do not vary much across different local markets, whereas for
college-educated workers, different markets offer different opportunities. More important,
using counterfactual experiments, it is shown that the spatial dispersion of labor income
accounts for most of the educational differences in mobility.
One of the key issues of local labor market dynamics is who moves across local markets
(Topel, 1986). While there are a large number of studies describing movers by observable
demographic characteristics (see Greenwood, 1997, for a survey), little is known about the
composition of observationally identical movers. According to the model, among workers
with the same education, those with lower unobserved ability have lower moving costs.
Therefore, while regions experience above-average employment growth through higher inmigration of well-educated workers, these workers tend to have lower unobserved ability
than otherwise observationally identical non-movers.
To the best of my knowledge, this paper is the first attempt to provide a dynamic
perspective on the individual-level relationship between mobility and wages across different
educational groups. Indeed, without such a framework it seems difficult to have a consistent
description of labor flows and income. In this regard, the model shows that overall labor
mobility and the college wage premium are positively related, a prediction consistent with
higher labor mobility and a lower college wage premium in the U.S. relative to those in Europe
documented, respectively, by Rupert and Wasmer (2012) and Krueger, Perri, Pistaferri, and
Violante (2010). Normatively speaking, understanding how mobility and wages are jointly
determined in a multi-sector setting is important for the evaluation of labor market policies
that affect individuals’ job search across markets and thus labor market equilibrium, since
3
many policy instruments are closely tied to labor income.4
The paper also contributes to the recent debate on the magnitude of the moving cost.
By considering a rich set of factors, Davies, Greenwood, and Li (2001) and Kennan and
Walker (2011) estimate that the migration cost for an average high school graduate moving
between U.S. states is in the range of a few hundred thousand U.S. dollars. Recently, Bayer
and Juessen (2012) argue that ignoring the persistence of migration incentives leads to such
high costs. The the current paper is closely related to their work as it also considers a
two-location, stochastic dynamic model where a worker’s wage and migration decision are
jointly influenced by persistent idiosyncratic shocks specific to the worker-location match.
The current paper extends their work by explicitly allowing for spatial correlation of these
shocks. The results indicate that ignoring such correlation can also introduce a large upward
bias in the moving cost. More important, the current paper shows that the wage gap between
movers and stayers might be essential in measuring the moving cost and that the moving
cost differs substantially between educational groups.
The outline of the rest of the paper is as follows. Section 2 presents the main empirical
findings on the relationship between mobility, wages and education. Section 3 extends Roy’s
(1951) model to a dynamic stochastic setting with costly mobility and persistent shocks.
Section 4 shows that the model can replicate main features of data on mobility and wages.
Section 5 conducts numerical experiments to quantify the impact of the key elements of the
model on labor mobility. Section 6 evaluates the impact of mobility on the average wage
and the college wage premium. Section 7 draws together the conclusions of the paper. The
appendix provides further details of the data and the model.
2
Facts
In this section, I present key empirical findings using Integrated Public Use Micro Samples
(IPUMS) of the census 1980-2000 (Ruggles, Alexander, Genadek, Goeken, Schroeder, and
4
For studies on how labor mobility affects the aggregate labor market equilibrium, see Lucas and Prescott
(1974), Lee and Wolpin (2006), and Lkhagvasuren (2012).
4
Sobek, 2010). First, I document that while the level of mobility is higher among the more
educated, the share of net mobility (excess mobility) in overall mobility declines (increases)
with education. Second, I show that the relationship between mobility and wages exhibits
strikingly different patterns across educational levels.
To focus on labor mobility that is not affected by schooling and retirement, I consider the
age range between 28 and 64 years. The main sample includes white male employees who
are not in the armed forces and who have worked between 20 and 80 hours per week and
at least 17 weeks a year, but it excludes self-employed and unpaid family workers. I restrict
the sample to workers with a high school or college education. For high school education,
I consider 12 years of education (Grade 12 according to Ruggles et al., 2010). For college
education, I consider a bachelor’s degree.
2.1
Mobility
The U.S. census records respondents’ current state of residence and the state in which they
resided five years ago. Therefore, an individual’s mobility status is obtained for a five-year
interval. The main geographic units considered in the empirical analysis are census divisions.
For brevity, census divisions will be referred to as regions for the remainder of the paper. Let
in
denote the number of people who in-migrate to region j between t − 1 and t. Let Nj,t
Nj,t
denote the number of people in region j at time t. Then, the economy-wide gross mobility
P in
rate at time t is given by mt = j Nj,t
/Nt , where Nt is the total number of workers in the
P
entire economy, i.e., Nt = j Nj,t . The upper panel of Table 1 shows that college educated
workers are twice as mobile relative to those who have a high school diploma.
Next, I show that net migration driven by regional-level effects alone cannot account for
large educational differences in mobility. For this purpose, I break gross mobility down into
two components: net mobility and the excess reallocation. As in Davis and Haltiwanger
out
(1992), net mobility is given by the average of |min
j,t − mj,t |/2 across locations (i.e., across
out
js), where min
j,t and mj,t are the in- and outmigration rates of region j. Excess mobility
5
Table 1: Mobility and Wages
data moments
high school
college
both
gross mobility, m
0.044
0.099
0.063
net mobility, δ
0.008
0.012
0.009
18.2%
12.1%
14.3%
81.8%
87.9%
85.7%
-0.092
(0.002)
0.044
(0.002)
-0.023
(0.002)
share of net mobility,
δ
m
× 100%
share of excess mobility, (1 −
δ
)
m
× 100%
the mover-stayer wage gap, γ
Notes: This table is based on mobility across census divisions at a quinquennial frequency.
The labels high school and college denote, respectively, 12 years of education and a bachelor’s
degree. The label both refers to the full sample containing the both educational groups.
The mover-stayer wage gap refers to the estimated log wage difference between movers and
stayers using equations (1) or (2). The standard errors of the estimated coefficients are in
parenthesis.
is gross mobility minus the net mobility. Table 1 shows that net mobility denoted by δ
constitutes a small fraction of overall mobility for each educational group. Also, the share of
net mobility in overall mobility decreases with education. What is more important is that
net mobility is too small to account for the large educational differences in mobility. This
serves as the main motivation of the paper for considering a worker-location match shock
that generates simultaneous in- and out-migration at the local level.
2.2
Wage gap between movers and stayers
Given the subsample of workers with education level s, consider the following regression:
wi,t,j = γdi,t,j + Gs (ai ) + αt + αj + i,t,j ,
(1)
where wi,t,j is the log hourly wage of person i in location j in year t, di,t,j is a dummy for
whether the person has recently migrated to region j, Gs (ai ) is a quartic polynomial of the
person’s yearly age ai , and αt and αj denote, respectively, the year and location effects.
6
The hourly wage rates are calculated as the ratio of labor income to hours worked per year.
Table 1 displays the results from the regression run separately for each educational group.
The wage differences between movers and stayers are highly significant for each educational
group. More important, among high-school-educated workers, in-migrants earn less than
the incumbent workers of the receiving localities, whereas college-educated in-migrants earn
more than their incumbent counterparts.5
Next, for a comparison purpose, I measure the wage gap between movers and stayers using
a common age-earnings profile for different educational groups as in the previous literature
(e.g., Borjas et al., 1992a and Krieg, 1997). Consider the following regression for the log
hourly wage wi,t,j using entire sample:
wi,t,j = γdi,t,j + ϕcoli + G(ai ) + αj + αt + i,t,j ,
(2)
where coli is a dummy for whether the person has a college degree and G(ai ) is a quartic
polynomial of the person’s yearly age, while the variables di,t,j , αt and αj are as in equation (1). Using equation (2) for the full sample containing the both educational groups,
I obtain −0.023 for γ. First, this number is much smaller (in absolute terms) than those
obtained above by applying equation (1) to each educational group. Second, the common assumption that mobility affects the wages of different educational groups in the same direction
masks massive differences between these groups in how mobility and wages are related.
3
Model
In this section, I propose a parsimonious model of regional mobility that is flexible enough to
replicate the above features of the data. I build on McLaughlin and Bils (2001), who study
wage differences between inter-industry movers and stayers using Roy’s (1951) framework.
5
Appendix A.1 addresses a possible bias resulting from the timing of mobility and shows that the above
wage gaps remain robust.
7
I extend their model to a dynamic setting that allows for a persistent labor income shock,
unobserved ability and moving costs.
For ease of notation, I present the model for only one educational group while keeping
in mind that the parameters can differ between the groups. It should be stressed that the
main goal of the paper is not only to construct a flexible model to replicate the data pattern,
but also to examine whether the spatial dispersion of the labor income shock can account
for the educational differences in mobility.
Given the significant difference in the mover-stayer gap between the educational groups,
I assume fully directed mobility in that workers know their initial wage at their destination
before leaving their current location. However, directed mobility, along with persistent
location-match shocks, generates a large state space in the dynamic programming problem.
To reduce the computational load while focusing on the prototype of dynamic problems
with an explicit relationship between mobility and wages at the individual level, I consider a
two-location Roy model. Thus, regarding the modeling choice, my analysis can be compared
with that of McLaughlin and Bils (2001) and Bayer and Juessen (2012), who use two-sector
models to analyze worker mobility among many industries and locations. Appendix A.2
provides a further discussion on the importance of directed mobility.
3.1
Setup
The economy is composed of two islands denoted by 0 and 1. The islands are inhabited by
a large number of workers. Time is discrete and workers are infinitely lived. Workers can
differ by their permanent unobserved ability µ. There are two ability levels: µ ∈ {µ` , µh },
where µ` = −σµ and µh = σµ for some σµ > 0. The cost of moving between the islands can
differ by ability. Let C(µ) denote the moving cost of workers with ability µ.
Each worker’s productivity is subject to a stochastic idiosyncratic shock. The magnitude
of the shock depends on where the person resides. Let (e0 , e1 ) denote these labor income
shocks. The pair of shocks is drawn for each person at each period. The stochastic process
8
governing the dynamics of e0 and e1 will be introduced shortly.
The productivity of workers on island 0 is subject to a common stochastic shock z,
which is referred to as a local technology shock. This shock is governed by the stationary
transition function Pr(zt < z 0 |zt−1 = z) = Q(z 0 |z) given by the following autoregressive
process: zt = %zt−1 + εt , where 0 < % < 1, and εt is a zero-mean random variable. Let σz
denote the unconditional standard deviation of the local technology shock zt .
Each period consists of three stages. In the first stage, individuals observe their labor
income shocks (e0 , e1 ) along with the local technology shock, z. In the second stage, after
observing these shocks, individuals choose their location. In the last stage, production takes
place and workers are paid their wages. Depending on whether the person works on island
0 or 1, the current log wage is given by
w0 = z + µ + e 0
(3)
w1 = µ + e1 ,
(4)
or
respectively. The flow utility of a local resident of island j ∈ {0, 1} is given by wj , whereas
that of a current in-migrant of the island is wj − C(µ). Workers’ time discount factor is β.
3.2
Labor income shock
The labor income shocks e0 and e1 are correlated across time and locations and given by the
following autoregressive process:


 e0,t = ρe0,t−1 + u0,t

 e1,t = ρe1,t−1 + u1,t ,
9
(5)
where the innovations (u0,t , u1,t ) are drawn from a bivariate normal distribution such that
Var(u0,t ) = Var(u1,t ) = σu2 and Corr(u0,t , u1,t ) = R. Let σe denote the unconditional standard
p
deviation of the labor income shocks, e0,t and e1,t , i.e., σe = σu / 1 − ρ2 .
Let us consider the following decomposition:


 u0,t = ζt + ξt

 u1,t = ζt − ξt ,
(6)
where ζt and ξt are independent zero-mean transitory shocks. Then, by repeatedly substituting for the lagged values of e0 and e1 in equation (5), one can write


 e0,t+1 = yt+1 + xt+1 = ρ(yt + xt ) + ζt+1 + ξt+1

 e1,t+1 = yt+1 − xt+1 = ρ(yt − xt ) + ζt+1 − ξt+1 ,
(7)
where xt and yt are independent shocks. According to this decomposition, xt and yt are
AR(1) processes with the common persistence ρ. Moreover, xt is the part of the income
shock specific to where the person works. Let σx denote the standard deviation of xt :
σx = Std(xt ). For the remainder of the paper, σx is referred to as the spatial dispersion
of the labor income shock. Below I will argue that σx is much higher for college-educated
workers than for high-school-educated ones and thus accounts for the large mobility gap
between the two groups.
3.3
Value functions
Now I specify the value functions associated with individuals’ mobility decision and characterize the model’s solution. Given the flow utility, an individual’s mobility decision is
determined by the local technology shock z and the location-specific component x, subject
to the moving cost. Moreover, the component y in equation (7) does not affect the wage
gap between movers and stayers. Therefore, I define the expected lifetime utility using the
10
values of x and z.
Let Uj (z, x, µ) denote the lifetime utility of a worker who worked in the previous period on
island j ∈ {0, 1}. Also, let F (x0 |x) be the transition function Pr(xt < x0 |xt−1 = x) associated
with the autoregressive process of xt . Then, for a worker who worked in the previous period
on island j, the lifetime utility of staying in the current location is given by
ZZ
Sj (z, x, µ) = wj (z, x, µ) + β
Uj (z 0 , x0 , µ)dQ(z 0 |z)dF (x0 |x),
(8)
where
wj (z, x, µ) = (1 − j)z + (1 − 2j)x + µ
(9)
for each j ∈ {0, 1}. If the person moves from island j to island 1 − j, the lifetime utility is
ZZ
Mj (z, x, µ) = w1−j (z, x, µ) − C(µ) + β
U1−j (z 0 , x0 , µ)dQ(z 0 |z)dF (x0 |x).
(10)
Finally, the maximized lifetime utility of the worker is given by
Uj (z, x, µ) = max{Sj (z, x, µ), Mj (z, x, µ)}.
3.4
(11)
Measures and flows
Let τ ∈ {1, 2, 3, · · · } denote the number of periods a person has worked in their current
location since his last move. Suppose that, at the end of period t, there are φj,t (x, µ, τ )
workers who have worked in their current location j for τ periods and whose ability and
current productivity are, respectively, µ and x.
11
3.4.1
Law of motion for measures
For each quadruplet (j, x, µ, τ ), the measure of workers after the realization of the idiosyncratic shocks of t + 1 is given by
Z
ψj,t+1 (x, µ, τ ) =
φj,t (x̃, µ, τ )
∂F (x|x̃)
dx̃,
∂ x̃
(12)
where x̃ has the same domain as x. Now let Dj denote the decision rule governing whether
a worker in location j stays in her current location at time t:


 1 if Sj (zt , x, µ) ≥ Mj (zt , x, µ),
Dj (zt , x, µ) =

 0 otherwise.
(13)
where zt is the local technology shock at time t. Then, for each (x, µ), the number of workers
moving from j to 1 − j at time t + 1 is given by
n1−j,t+1 (x, µ) =
X
(1 − Dj (zt+1 , x, µ))ψj,t+1 (x, µ, τ ).
(14)
τ
Given these notations, the measure of workers at the end of period t + 1 is given by


 nj,t+1 (x, µ)
φj,t+1 (x, µ, τ ) =
 D (z , x, µ)ψ

j
j,t+1 (x, µ, τ
t+1
if τ = 1,
(15)
− 1) if τ ≥ 2
for each quadruplet (j, x, µ, τ ).
3.4.2
Equilibrium measures
Given these measures, the total number of workers in region j at time t is
Nj,t =
XXZ
τ
µ
12
φj,t (x, µ, τ )dx.
(16)
Let the total population in the economy be normalized to 1: for any t,
N0,t + N1,t = 1.
(17)
Below in the empirical implementation of the model, the length of a unit period is one year.
Therefore, in accordance with how mobility is measured in Section 2, individuals with a
tenure of up to five years are considered recent in-migrants. Thus, the number of the recent
in- and out-migrants of region j are
in
Nj,t
=
5 XZ
X
τ =1
φj,t (x, µ, τ )dx
(18)
φ1−j,t (x, µ, τ )dx.
(19)
µ
and
out
Nj,t
=
5 XZ
X
τ =1
µ
Solving the model amounts to finding an equilibrium stream of workers, {φ0,t (x, µ, τ ),
φ1,t (x, µ, τ )}∞
t=1 for each (x, µ, τ ) to satisfy equations (12) to (17), subject to the sequence of
the local technology shock {zt }∞
t=1 and the initial measures {φ0,0 (x, µ, τ ), φ1,0 (x, µ, τ )} for
all (x, µ, τ ).
3.5
Interdependence of mobility and wages
For the remainder of the section, I discuss how mobility and wages are interrelated in this
simple model. I start with a much simplified version of the model and re-introduce the key
elements of the model to show their impact on mobility and wages.
3.5.1
Labor income shock and gross mobility
Suppose for now that workers move costlessly between the two islands. Let the labor income
shocks, e0 and e1 , be purely transitory, i.e., ρ = 0. Also, let the local technology shock z be
permanently zero. Then, workers whose labor income shocks satisfy e0 > e1 or, equivalently,
13
Figure 1: A Roy Model with Unobserved Ability and Costless Mobility
µ + e1 6
q
µh
rB
rA
w1A
q
µ`
45◦
w0A
µ`
µh
µ + e0
Notes: The figure illustrates an economy in which there is no regional shock (i.e., z is
permanently zero) and individuals move costlessly. Each worker is described by a point in
the graph. The iso-probability contours reflect the distribution of the income shocks (e0 , e1 )
for each ability level. For example, point A is more likely to describe low ability workers
whose shock on island 0, e0 , is much lower than his or her shock on island 1, e1 . Similarly,
point B is more likely to describe high ability workers whose e0 is much higher than his or
her e1 . Workers whose shocks lie above the 45 ◦ line will work on island 1 and those whose
shocks are below the line will work on island 0. For example, if the worker described by
point A works on island 0, his or her wage will be w0A . However, if the same person works
on island 1, the wage will be much higher at w1A . Thus, the person will choose island 1.
x > 0 will decide to work on island 0, whereas those who have e0 < e1 or, equivalently, x < 0
will work on island 1 (see Figure 1). Despite the large gross mobility, net mobility will be
zero. Moreover, since the moving cost is zero and the shocks are transitory, there will be no
wage gap between movers and stayers.
3.5.2
Local technology shock and net mobility
Now let us introduce a positive permanent technology shock to island 0. Suppose that the
permanent shock is realized at the beginning of period t. Then, during period t, there will
be a gap between the two flows: the number of workers moving from island 1 to island 0 will
14
be larger than the number of workers moving in the opposite direction. Workers whose labor
income shocks satisfy e0 + z > e1 or, equivalently, 2x > −z will decide to work on island
0, whereas those who have e0 + z < e1 or, equivalently, 2x < −z will work on island 1. So,
there will be net mobility during period t. Since the technology shock z is permanent and
the idiosyncratic shock x is transitory, net mobility will be zero starting from period t + 1.
3.5.3
Persistence of a labor income shock
Clearly, with costless mobility (C(µ) = 0) and the transitory idiosyncratic shock (ρ = 0),
there will not be any wage gap between movers and stayers. However, if the labor income
shock becomes persistent (ρ > 0), local residents draw from a better income distribution
than new in-migrants do. Consequently, the incumbents of each island will have a higher
wage than its new residents, on average. Section 5.3 illustrates this effect numerically.
3.5.4
Moving cost
Now suppose that a worker incurs a fixed moving cost c0 . For simplicity, let the local
technology shock z be permanently zero and the labor income shocks, e0 and e1 , are again
transitory. Clearly, a higher moving cost will imply lower mobility for a given level of the
spatial dispersion of the income shock (i.e., for a given level of σx ). Thus, one can generate
the same level of mobility using different pairs of values of σx and c0 . In other words, one
can obtain the same level of mobility by using a lower spatial dispersion of labor income
shock and a lower moving cost or by using a higher spatial dispersion of labor income shock
and a higher moving cost. However, the two cases will have a different implication along two
dimensions.
First, the wage gap between movers and stayers will be higher in the latter case (i.e.,
when σx is higher) since the moving cost amplifies the selection effect along labor income
shocks. Second, once the local technology shock is introduced, net mobility (excess mobility)
will be higher (lower) in the former case. Because, for a given level of gross mobility, a lower
15
Figure 2: A Roy Model with Unobserved Ability and Costly Mobility
µ + e1 6
I0
%
%
%
%
I1
%
µh
,
,
,
q
%
%
%
,
,
%
,
%
,
,
%
%
µ`
%
q
,
,
,
%
,
%
,
,
,
µ`
µh
µ + e0
Notes: The figure illustrates an economy in which there is no regional shock (i.e., z is
permanently zero), but the moving cost is non-zero. In this figure, the moving cost is
higher for high ability workers. Individuals who are indifferent between working on island 0
and moving to island 1 are aligned along the line denoted by I0 . Similarly, those who are
indifferent between staying on island 1 and moving to island 0 are aligned along the line
denoted by I1 . If a worker is initially on island 0 and then draws a pair of shocks above the
line I0 , he or she will move to 1. Analogously, if a resident of island 1 draws shocks below
the line I1 , that person will move to island 0. Also, see notes to Figure 1.
spatial dispersion of labor income shock means that more workers are indifferent between
moving and staying and thus more workers respond to the technology shock while raising
the share of net mobility. Hence, the relative magnitude of excess versus net mobility is
intimately related to the spatial dispersion of labor income and the mover-stayer wage gap.
3.5.5
Heterogeneous moving costs
In addition to the above selection effect, another dimension through which moving cost can
affect the wage gap between movers and stayers is unobserved ability. Specifically, for a
given level of mobility, one can obtain a substantial wage gap between movers and stayers
by making workers of a certain ability level more mobile than the rest of the workers (see
16
Figure 2). Therefore, in order to relate the wage gap between movers and stayers to labor
mobility quantitatively, one has to allow for different moving costs for different ability groups.
It should be stressed that a negative mover-stayer wage difference does not necessarily
mean lower moving costs among lower ability workers. Indeed, Section 5.3 shows that one can
obtain the above data patterns by imposing the same moving costs on different ability groups.
However, such an assumption implies an implausibly low moving cost and an extremely high
persistence of a labor income shock for high school graduates.
4
Empirical implementation
Here the model is analyzed quantitatively using the key features of wage and mobility,
including those documented in Section 2.
4.1
Numerical method
Although the model is simple, its solution requires highly intensive computation due to the
large state space capturing heterogeneous moving costs and the persistence of both the local
technology shock and the labor income shock. The numerical solution requires five state
variables for each educational group when implemented. Moreover, the simulation of the
model brings a further computational load for the following two reasons. First, generating
small net mobility requires a large number of agents and a very fine state space along x.
Second, measuring the wage gap between movers and stayers requires that the wages and
mobility of all agents be simulated simultaneously while keeping track of each individual’s
past and present location. Given these considerations, I combine discretization of state
variables with value function iteration. The location-specific shock x and the local technology
shock z are approximated by finite state Markov chains using the method of Rouwenhorst
(1995).6 In order to have sufficiently fine grids for x and z, each of the two shocks is
6
As Galindev and Lkhagvasuren (2010) show, the method of Rouwenhorst (1995) outperforms the other
commonly used discretization methods for highly persistent AR(1) shocks.
17
approximated by a 51-state Markov chain.
To simulate the model, I first generate the sequence of the local technology shock for T =
4, 000 periods. For the initial measures {φ0,0 (x, µ, τ ), φ1,0 (x, µ, τ )}, I assume that workers
of each ability group are distributed equally between the two locations, their within-sector
distribution over idiosyncratic productivity x is given by the zero-mean normal distribution
with variance σx2 and locational tenure τ of each person is 1. Given the initial measures and
the sequence of the local technology shock, I then simulate the sequence of the measures
for T = 4, 000 periods. I discard the first 10 percent of the observations in order to remove
the effect of the initial measures, and use the rest to compute the moments. The simulated
moments are highly accurate in that doubling the number of periods (i.e., setting T = 8, 000)
does not have a meaningful impact on the moments.
4.2
Parameters
The period length chosen for the numerical simulation is one year. The time discount factor
β is set to 0.952 (=1/1.05), which reflects an annual interest rate of 5 percent. Following
Ciccone and Hall (1996), local productivity is calibrated using the gross domestic product of
the U.S. states released by the Bureau of Economic Analysis. Using the annual per-worker
gross state product series from 1974 through 2004, the productivity of each census division
is generated by taking the state employment share as the aggregation weight. Given these
series, local productivity is defined as the logarithm of per-worker gross domestic product
of a division minus the logarithm of per-worker gross domestic product of the U.S. For an
average division, the standard deviation and annual autocorrelation of the deviation of local
productivity from its linear trend are 0.021 and 0.769. These numbers are used for σz and
%, respectively.
Disagreement exists in the literature over the magnitude of the persistence of a labor
income shock (e.g., Hubbard et al., 1994; and Guvenen, 2009). However, a common finding
between these studies is that the persistence of the labor income shock does not differ sub18
Table 2: Benchmark Parameterization
parameters
high school
college
β
%
σz
ρ
σµ
σx
c`
0.952
0.769
0.021
0.829
0.442
0.066
0.851
($28,491)
1.199
($40,143)
same
same
same
0.805
0.500
0.106
0.929
($46,747)
1.064
($53,540)
ch
description
time discount factor
persistence of the regional shock
standard deviation of the regional shock
persistence of the labor income shock
standard deviation of unobserved ability
spatial dispersion of a labor income shock
moving cost of a low ability worker
moving cost of a high ability worker
Notes: The amounts in parenthesis are the moving costs as expressed in the year 2000 USD.
stantially across educational groups. As benchmark, I use Guvenen’s (2009) estimates that
ρ is 0.829 and 0.805, for high-school- and college-educated workers respectively.7
Individuals are equally divided between the two ability levels. So, the individual-specific
permanent effect in the log-residual wage is symmetrically distributed, which is a common
assumption among the empirical studies of labor income processes. The dispersion in unobserved ability, σµ , is calibrated using the wages of male household heads in the Panel Study of
Income Dynamics (PSID) for 1968 through 1997. Specifically, using the data, first I calculate
the wage rank of each individual for each year while controlling for age and education. Then
I construct the mean wage rank of each person over the sample period (see Appendix A.3).
The parameter σµ is chosen so that the variation in the mean wage rank in the data matches
the variation in the mean wage rank in the model. This yields the following values of σµ for
high school and college graduates, respectively: 0.442 and 0.500.
Let c` and ch denote moving costs associated with the ability levels µ` and µh : c` = C(µ` )
7
As mobility and the income shock are correlated, there is a certain gap between the persistence parameter
ρ and the autocorrelation of the realized values of labor income. However, experimentation shows that this
gap is negligibly small for a wide range of the parameter space. The reason is that (i ) a considerable part
of labor income is driven by the common component y in equation (7) and (ii ) the selection effect along the
location-specific component x is much smaller compared to the dispersion of both x and y.
19
and ch = C(µh ). Given the rest of the parameters, these two costs are chosen by targeting
the mobility rate m and the mover-stayer wage gap γ. The only remaining parameter is σx ,
which measures the spatial dispersion of the labor income shock. The parameter is chosen
by targeting net mobility, δ. Below, it is shown that for a given level of gross mobility, δ
and σx are indeed inversely related. For the remainder of the paper, the current calibration
is referred to as the benchmark model.8
4.3
Predictions
The parameters of the benchmark model are displayed in Table 2. The targeted data moments are presented in column (i) of Table 3 while the associated simulated moments are
summarized in column (ii). The model is able to capture the key features of mobility and
mover-stayer wage differences across educational groups. The spatial dispersion of labor
income differs considerably between the two groups. The value of σx implies that the spatial
dispersion is approximately 6.6 percent of labor income of high school graduates. However,
for college graduates, it amounts to 10.6 percent of their labor income. This means that for
high school graduates, employment opportunities do not vary much across different markets,
whereas for college-educated individuals, different markets offer different opportunities.
The moving cost relative to labor income does not differ much between the two educational groups. Using the 2000 IPUMS sample, I estimate that annual labor income of the
two educational groups is US$ 33,480 and US$ 50,320. These numbers imply that the actual
moving cost of US$ 28,491 - 40,143 for high school graduates and US$ 46,747 - 53,540 for
college graduates, as expressed in the year 2000 dollars.9 These costs are much lower than
8
To a certain extent, the current calibration can be interpreted as choosing c` , ch and σx by minimizing a
weighted distance between the observed and simulated values of m, γ and δ. However, there is an important
difference between the current calibration and the standard minimum distance (MD) estimation (e.g., Altonji
and Segal, 1996). Because of the discrete space described in Section 4.1, here the moments (and thus the
weighted distance) tend to respond to parameters in a stepwise manner, especially in the limit as changes in
the parameters go to zero. Nevertheless, one can see the overall impact of the parameters on the simulated
moments using the numerical experiments in Sections 5 and 6.
9
In addition to these dollar amounts, the nature of the moving cost could also differ between the educational groups. For example, Machin et al. (2012) argue that certain components of the moving cost, such as
credit constraints and lack of information, might be more important for less educated workers.
20
Table 3: Model Predictions
moments
High school graduates
(i)
(ii)
data
BM
gross mobility, m
net mobility, δ
mover-stayer wage gap, γ
moments
0.044
0.008
-0.092
0.044
0.008
-0.092
College graduates
(i)
(ii)
data
BM
gross mobility, m
net mobility, δ
mover-stayer wage gap, γ
0.099
0.012
0.044
(iii)
σxcol
(iv)
C col
0.098
0.010
-0.005
0.045
0.009
0.018
(iii)
σxhs
(iv)
C hs
0.099 0.038
0.012 0.008
0.044 -0.002
0.097
0.010
-0.028
Notes: Column (i) displays observed data moments, while column (ii) provides the same
moments generated by the benchmark (BM) model. Column (iii) describes a restricted version of the model economy in which the spatial dispersion of labor income of an educational
group is replaced by that of the other group. Column (iv) describes a restricted version of
the model in which moving costs of an educational group are replaced by those of the other
group.
21
those estimated by Davies et al. (2001) and Kennan and Walker (2011), but comparable
with an estimate of US$ 34,248 by Bayer and Juessen (2012) for a typical move between
U.S. states.
Within each educational group, individuals with lower unobserved ability have lower
moving costs and move more frequently than those with higher ability. So, movers have
lower unobserved ability than otherwise observationally identical non-movers. In Section 2
it was documented that high-school-educated movers earn less than their non-migrant counterparts and that college-educated workers earn more compared with the college-educated
non-movers. The quantitative results offer the following explanation for these data patterns.
For high-school-educated workers, the mover-stayer wage gap is negative due to the lower
moving costs of lower ability workers. However, for college-educated workers, this negative
effect is offset by the positive selection effect of their more volatile location-match shock.
In the current model, moving costs reflect both the direct and psychological costs of traveling long distances to take a job. The prediction that workers with lower unobserved ability
(thus lower income) have lower moving costs could be linked to homeownership. Specifically,
these low-income individuals are more likely to be renters (Callis and Kresin, 2013) and thus
may not incur the costs associated with selling or buying new houses when moving across locations. Also, since the incomes of the married couples are positively correlated (Jacquemet
and Robin, 2012), the spouses of the low-income individuals could be less attached to their
current labor market (Mincer, 1978). Moreover, long distance moves may take a substantial amount of time and this time cost could be larger for higher ability workers. While
all these effects could produce heterogenous moving costs across ability groups, more direct
investigation to the impact of the housing price, spousal income and the time cost is clearly
desirable.
22
4.4
Local dynamics
As a further test of the model, I evaluate its prediction for the local labor force fluctuations.
The reason is that, in the model, the volatility of the local labor force is governed by the
spatial dispersion of labor income, the key parameter in the current paper. For example, if the
spatial dispersion, σx , is too high, the model will generate a negligibly small local fluctuation
for a given level of gross mobility. Therefore, examining local dynamics will indicate whether
the spatial dispersion of labor income in the benchmark model is reasonable.
Since the model does not distinguish between employment and unemployment, I evaluate
the model’s performance by using both the local labor force and employment. In the model,
the local series are constructed by setting the share of high school (college) graduates to 0.664
(0.336), the value obtained from the main sample. The results are reported in Table 4. It
shows that the model performs reasonably well in replicating the persistence of the local labor
force and employment growth. The volatility of the local labor force is slightly lower than
those observed in data. The main reason for this discrepancy is that the model ignores the
labor force participation decision of incumbent workers and thus generates lower volatility.
Nevertheless, the model accounts for the most of the shifts in the local labor force and
employment. This is consistent with Borjas et al. (1992b), who argue that due to low
fertility, internal migration has become the most dominant source of shifts in the local labor
force. According to the model, the volatility of employment and the labor force is higher
among more educated workers. So, more educated workers are more responsive to the local
market conditions (Wozniak, 2010). These results suggest that the model performs well
along local fluctuations, even though the above moments were not targeted in calibration.
5
Numerical experiments
In this section a set of numerical experiments is conducted to illustrate how the spatial
dispersion and moving costs affect educational differences in mobility.
23
Table 4: Local Dynamics
Moments
volatility, Std(∆nt )
persistence, Corr(∆nt−1 , ∆nt )
data
all-emp all-lf
0.013 0.010
0.415 0.664
benchmark model
all
hs
col
0.0067 0.0060
0.539 0.523
0.0083
0.530
Notes: ∆nt denotes the log annual change of the local labor force or local employment at
year t. The columns all-emp and all-lf summarize the data moments calculated using the
employment and labor force series of 1976-2011 provided by the Bureau of Labor Statistics
while controlling aggregate effects by subtracting the log growth of the aggregate series.
5.1
Role of the spatial dispersion of labor income
As mentioned earlier, the moving cost relative to labor income do not differ much between
the two educational groups. This suggests that the difference in the spatial dispersion of the
labor income shock, σx , might account for a substantial part of educational differences in
mobility. To examine whether this is the case, the benchmark models of the two educational
groups are simulated while switching their spatial dispersion parameters. The results are
shown in column (iii) of Table 3. When the benchmark model of high school graduates
is simulated while using the spatial dispersion of labor income of college-educated workers,
their mobility becomes virtually the same as the observed mobility of college graduates. At
the same time, when the spatial dispersion of labor income of college-educated workers is
replaced with that of high school graduates, the mobility of the college graduates declines
and becomes almost equal to the observed mobility of high school graduates. So, the spatial
dispersion of labor income shocks accounts for the bulk of the educational differences in
mobility.10
At the same time, an average mover in the model performs better than before as the
selection effect is now stronger. Comparing the benchmark model and the results of the
numerical experiment, it can be seen that, with all other parameters held constant, an
10
This finding can be related to the view that that professional job market operates on a national basis
and that unskilled job market tends to be more localized (e.g., Heckman, Layne-Farrar, and Todd, 1996).
24
increase in the spatial dispersion raises the wages of in-migrants relative to those of the
incumbents. Therefore, the spatial dispersion of labor income is not only important for
understanding labor mobility, but also accounts for a considerable share of the mover-stayer
wage gap. Moreover, it is important for understanding why the mover-stayer wage gap
increases with education.
As discussed in Section 3.5, net mobility relative to overall mobility declines as the spatial
dispersion of the labor income shock, σx , goes down. Comparing the mobility rate m and
the spatial dispersion σx of different educational groups shows that holding all else constant,
an increase in the spatial dispersion σx raises the wages of in-migrants relative to those of
the incumbents. Therefore, the observed positive relationship between education and the
mover-stayer wage gap is consistent with a higher spatial volatility among more educated
workers. Moreover, the mobility rate m is a highly convex (increasing) function of σx . This
is because of the strong non-linearity of the tail distribution function of the labor income
shock.
5.2
Impact of moving cost
Next, I evaluate the impact of the moving cost on mobility and the mover-stayer wage gap.
For this purpose, I simulate the benchmark model for each educational group while using
the moving cost (relative to labor income) of the other educational group. By simulating the
model with different moving costs, this experiment also shows how sensitive the simulated
moments are to the parameters and how the key elements of the model are important for
understanding both mobility and wages.
The results reported in the last column of Table 3 show that small differences in the
relative moving costs indeed do not have much impact on the overall mobility. The table also
illustrates that the moving cost and and the wage differences between movers and stayers are
intimately related. Comparing the columns of the table, one can see that a higher moving
cost is associated with a higher mover-stayer wage gap. Also, an increase in the spatial
25
dispersion raises the wages of in-migrants.
5.3
Homogeneous moving cost
For the remainder of the section, I argue that while it is possible to generate the negative
mover-stayer wage gap among high school graduates by imposing the same moving cost on
different ability groups, such a restriction requires highly implausible parameter values. I
simulate the model by setting ch = cl = c while choosing σx , ρ and c to replicate the key
moments considered in the benchmark calibration.
The results are displayed in Table 5. Despite the restriction, the model is able to generate
the observed data patterns including the negative wage gap between movers and stayers
among high school graduates. However, it requires highly implausible parameter values for
high school graduates. First, there is an extremely large gap between the moving costs of
high school and college educated workers: the moving cost of college graduates is almost 30
times higher than that of high school graduates.
Second, the moving cost of high school educated workers is implausibly low. Specifically,
their moving cost is 5 percent of their annual income, or approximately US$ 1,640. This
is unreasonably low compared with moving costs estimated in the literature. For example,
Bayer and Juessen (2012) estimate that the moving cost to be US$ 34,248 for a typical move
between U.S. states. Davies et al. (2001) and Kennan and Walker (2011) find even higher
inter-state migration costs for high school graduates. Keeping in mind that moves between
census divisions must be more costly than interstate moves, the moving cost of high school
graduates in Table 5 is roughly one or two orders of magnitude smaller than those in the
literature.
Third, there is also an extremely large gap in the persistence of the labor income shock
between the two educational groups. This is in sharp contrast with the existing studies
which find that the persistence of labor income shocks does not differ substantially across
educational groups (e.g., Hubbard et al., 1994; Guvenen, 2009).
26
Table 5: Model with Homogeneous Moving Cost
high school
σx
ρ
c
c̃
m
δ
γ
0.210
0.993
0.049
$1,640
0.044
0.008
-0.092
college
description
0.149
0.935
0.849
$42,722
Parameters
spatial dispersion of a labor income shock
persistence of a labor income shock
moving cost
moving cost expressed in the year 2000 USD
0.099
0.008
0.044
Moments
mobility
variation of mobility across regions
wage difference between movers and stayers
Notes: This table summarizes a version of the model in which the moving cost is the same
between different ability groups. The other parameters are at their benchmark values.
6
The college wage premium
One of the key predictions of the model is that the overall impact of mobility on wages
differ by education. Specifically, because of their higher spatial dispersion of labor income,
more educated workers enjoy larger wage gains from mobility. A particularly interesting
implication in this regard is that labor mobility can have a substantial impact on the college
wage premium, the additional average wage a college graduate earns relative to a high
school graduate.11 To quantify this effect, I consider a version of the model where mobility
is prohibited.
Let ∆whs (∆wcol ) denote the change in the log mean wage of high school (college) graduates when the moving costs of the benchmark model are replaced by prohibitive moving
costs. Table 6 displays these changes implied by the model. When mobility is prohibited,
the overall wage of high school graduates decreases by 0.97 percent, while that of college
graduates decreases by 4.40 percent, i.e., ∆whs = −0.0097 and ∆wcol = −0.044. Thus, the
11
Here I consider the impact of mobility on the economy-wide college premium. For the variability of the
skill premium across local markets, see Armenter and Ortega (2011) and Hendricks (2011).
27
Table 6: Impact of Prohibitive Moving Cost
the average wage of high school graduates
-0.97%
the average wage of college graduates
-4.4%
the average wage of all workers
-2.4%
the college wage premium
-12.0%
Notes: This table shows that mobility raises both the average wage and the college wage
premium.
overall wage gain from mobility for college graduates is more than four times higher than
that for high school graduates, in percentage terms. Moreover, given the share of the two
educational groups measured in Section 4.4, the prohibitive moving cost lowers the average
wage of all workers by 2.4 percent.12
What fraction of the observed college premium do these mobility effects account for?
Let Pobs denote the observed college premium. In the absence of mobility, the college wage
premium becomes
Pexp = (1 + Pobs )(1 + ∆wcol ) − (1 + ∆whs ).
(20)
Hence, the fraction of the college premium resulting from mobility is
π=
∆whs − ∆wcol
Pobs − Pexp
=
− ∆wcol .
Pobs
Pobs
(21)
Including a dummy variable for a college degree into equation (1) and using the main sample,
I find that Pobs = 0.408. Combining this value with those of ∆whs and ∆wcol , the fraction
of the college wage premium explained by mobility is 12 percent, i.e., π = 0.12. Conversely,
the prohibitive moving cost decreases the college premium by 12 percent (see Table 6).
Recall that the current analysis focuses on long distance moves between census divisions.
12
It should be made clear that the counterfactual experiment is conducted in a partial equilibrium setting.
Specifically, it ignores the negative dependence of labor productivity on local employment, a common equilibrium element used in modeling local labor markets (e.g., Lucas and Prescott, 1974; Coen-Pirani, 2010;
Lkhagvasuren and Nitulescu, 2013). However, the impact of such an equilibrium effect might be small in
an economy where net mobility, which drives local employment fluctuations, is much smaller than excess
mobility.
28
Therefore if one includes shorter distance moves, such as inter-city or residential moves,
the effect of mobility on the college premium will be higher than those measured above.
However, since shorter distance moves are less costly, the marginal impact of an inter-city
or residential move on the college premium will be less than that of long distance moves
considered in this paper. At the same time, a higher frequency of shorter distance moves
(Greenwood, 1997) may raise the overall impact of such moves on the average wage and the
college wage premium.
An important implication of the above finding is that shifts in the moving cost can affect
the college wage premium. Then a natural question is whether part of the large differences
in the college premium across countries could be attributed to labor mobility differences
between these countries. Indeed, differences between Europe and the U.S. support this novel
hypothesis. For example, Krueger et al. (2010) show that an average European country has
a substantially lower college premium relative to the U.S., while Rupert and Wasmer (2012)
find that geographic labor mobility is much lower in Europe than in the U.S.
7
Conclusions
I extended the standard Roy (1951) model of locational choice into a dynamic stochastic
setting while allowing for both net and gross mobility. I analyzed the model using key
patterns of micro data on mobility and wages, including new evidence on the variability of
mobility across regions and the wage gap between movers and stayers. The model makes
a strong prediction that the dispersion of the individual-location match shock is larger for
more educated workers and accounts for the bulk of educational differences in mobility. So
for more educated workers, different markets offer different opportunities, whereas for less
educated workers, opportunities do not differ much across locations.
According to the model, among workers with the same education, those with lower unobserved ability have lower moving costs and thus move more frequently than otherwise
29
observationally identical non-movers. Numerical experiments suggest that the wage gap between movers and stayers might be key to quantifying dynamic multi-sector models. In the
model, mobility raises both the average wage and the college wage premium, a prediction
consistent with the differences between Europe and the U.S.
By allowing for a spatial component in a persistent labor income shock, the model establishes a link between two important branches of the literature: labor mobility and labor
income dynamics. Specifically, higher mobility and a higher spatial dispersion of labor income among more educated workers suggest that, on average, their income is generated at
a higher cost. Therefore, focusing solely on the statistical or time series properties of labor
income shocks introduces an important oversight regarding the the welfare impact of the
idiosyncratic income shifts.
In this paper, labor income is assumed to follow an exogenous process specific to the
worker-location match. Therefore the paper is silent about the underlying forces driving
the spatial dispersion of labor income. In this regard, an interesting exercise would extend
the analysis by examining whether within-region industry compositions affect geographic
mobility. Moreover, an extension of the model that allows for risk aversion and housing
markets could be used to examine whether the recent housing market contraction raised the
idiosyncratic income risk, especially among the well educated. Future research along these
dimensions may contribute to our understanding of the role of mobility for the labor market.
30
A
Appendix
A.1
Timing of mobility
As previously mentioned, the U.S. census records individuals’ current state of residence and
the state in which they resided five years ago. However, it does not record when exactly
during the past five years the respondents moved if they did. On the other hand, it records
labor income and work hours by calendar year. Therefore the measured wage of a mover is
not necessarily the actual wage the person received at the current location. For example,
consider an individual who worked in region A during the first nine months of the previous
calendar year and in region B for the remainder of that year. Suppose that the person’s
hourly wage was $20 in A and $28 in B. For simplicity, let the person’s monthly hours of
work remain constant throughout the previous calendar year. Then, the measured hourly
wage for this newly arrived worker is (9 × $20 + 3 × $28)/12 = $22, which is much lower
than $28, the actual hourly wage in the new location. This suggests that there can be a
potential bias introduced by inconsistency between the point in time at which workers move
and the time period over which their annual labor income is recorded.
To examine whether the bias is substantial, I measure the wage differences between
movers and stayers using Current Population Survey (CPS), 1980-2009 (King, Ruggles,
Alexander, Flood, Genadek, Schroeder, Trampe, and Vick, 2010) while imposing the same
sample restrictions used for the U.S. census data. Specifically, since the CPS records individuals’ mobility at annual frequency, it allows us to measure the wage differences between local
residents and those who moved within the last year. I find that the wage gap γ measured by
equation (1) are -0.096 and 0.054 for high school and college graduates, respectively. (The
standard errors of these coefficients are 0.011 and 0.013.) Since these numbers do not differ
significantly from those obtained in Section 2, the bias introduced by inconsistency between
the point in time at which workers move and the time period over which their labor income
is recorded is negligible.
31
A.2
Modeling choice
In the model there are two locations. While it is straightforward to introduce more locations,
it will sharply increase the number of states in the dynamic programming problem. With two
locations, as discussed in Section 4, the solution of the model results in a dynamic stochastic
problem with five state variables for each educational group. Since the number of state
variables associated with the individuals’ decision problem increases geometrically with the
number of locations, having more locations introduces a much heavier computational load.
As in Kennan and Walker (2011), one can reduce the computational load by assuming
that individuals do not know their wage at a new location, but in order to find out their
wage in another location, it is necessary to move there. Under such an assumption, some
individuals move, at a high cost, to poorly matched areas and stay there. Given the focus of
the paper, this creates two issues. First, the assumption typically implies that the wages of
newly arrived workers are less than those of the local residents. Thus, it is unclear how one
can capture different mover-stayer wage gaps of different educational groups. Second, the
literature on labor income dynamics (Hubbard et al., 1994; Guvenen, 2009) suggests that
the labor income shock is quite persistent. Therefore in the presence of the highly persistent
wage, it might be too strong an assumption that workers move to areas without knowing
their wage.
Since I focus on the relationship between wages and mobility, I consider Roy’s framework,
which is inherently a model of directed mobility, while considering two locations. This allows
us to focus on the prototype of the economic problems with the combination of directed
mobility and a persistence location match shock. It should be noted that, in the absence of
a local technology shock, the model can be viewed as one of many islands. Suppose that there
are N islands. Consider an individual who stays on island 1 and whose labor income shock
for the location is e1 . Also, let the labor income shocks the person draws for the remaining
islands be {e2 , e3 , · · · , eN }. Then, the same mobility decision and wages are obtained by
restricting var(e0 ) = var(e1 ) and Corr(e0 , e1 ) = R, where e0 = max{e2 , e3 , · · · , eN }.
32
A.3
Variation of ability
In this appendix I estimate the variation of unobserved ability, σµ , using individuals’ wages
over their life-cycle in the PSID, as in Moffitt and Gottschalk (1994). To reduce the impact
of outliers in the small subsamples of each educational group, I consider a wage rank statistic.
Given the residual wage of the Mincerian regression, let ri,t denote the rank of person i in
the sample at time t. Let r̄i denote the mean rank of the person over the sample period.
Then, rit − r̄i can be considered as the shifts in rank due to the effects not captured by
permanent ability. If most of the wage variation across individuals at a given point in time
is explained by their unobserved ability, the overall shifts in rit − r̄i will be much smaller
across individuals. Thus, the effect of the permanent component relative to that of the
Stdi (r¯i )
.
non-permanent component can be captured by k = Ei (Std
t (rit −r̄i ))
I measure the wage rank rit using the annual hourly wage rate of the male heads of
households in the PSID for 1968 through 1997. The sample includes those between 28
and 64 years of age while excluding those in the Survey of Economic Opportunity, which
oversamples poor households. I also restrict the sample to those whose income is recorded
for more than twenty years (i.e., Ti ≥ 20). Given these selection criteria, I obtain that
k = 1.583 for high-school-educated workers and k = 1.516 for college graduates. Now,
consider the following decomposition of the log wage variance: σw2 = σµ2 + σ2 , where σ2 is
the variance of the non-permanent component of the log wage. Setting σµ /σ to k, one can
p
write that σµ = σw k 2 /(1 + k 2 ). Using the year 2000 sample, σw , is 0.522 and 0.599 for high
school and college graduates, after controlling for age, education, year and regional effects.
These numbers, along with the values of k, imply that σµ is 0.442 and 0.500 for the two
groups.
33
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