Interaction Between Human Capital Investment and
Search Intensity: Implications on Life Cycle Earnings
Profiles
Huju Liu
∗†
University of Western Ontario
Incomplete and Preliminary
May 22, 2006
Abstract
This paper develops a life cycle model of labor earnings, human capital accumulation,
and search intensity. The model allows for both human capital investment and search
intensity to be endogenous choices and analyzes the interactions between these two
forces. A key insight of the model is that human capital accumulation and job search
are reinforcing each other in the sense that both human capital investment and search
intensity are increased because of interaction. The preliminary results show that the
model is able to generate a concave life cycle earnings profile and imply a higher growth
in earnings over life cycle.
∗
I thank Professor Audra Bowlus for continuous guide and support. I also thank Professor Lance Lochner
and Professor Hiroyuki Kasahara for encouragement and valuable suggestions. I am also grateful to seminar
participants in the University of Western Ontario for valuable comments. I am responsible for all errors and
mistakes.
†
Correspondence: Department of Economics, Social Science Center, University of Western Ontario, London, Ontario. Email: hliu23@uwo.ca.
1
Introduction
The objective of this paper is to study the interaction between human capital investment
and search intensity over life cycle and to study the implications of this interaction to life
cycle earnings profile.
It is well documented that life cycle earnings profiles are increasing and concave.1 Figure
1 plots life cycle earnings profiles for high school graduates and college graduates in 1996
using samples from the Survey of Income and Program Participation (SIPP).
2
We can see
that earnings rise rapidly over the first 20 to 25 years of a career. Earnings stabilize as the
career progresses.
Mean Log Weekly Wages
6
6.5
7
7.5
Human capital investment and job search are widely acknowledged as two major driving
5.5
high school
college
17
21
25
29
33
37
41
Age
45
49
Fitted values
Fitted values
53
57
61
65
Figure 1: Life Cycle Earnings Profiles
forces to the above concave earnings profiles.3 Standard Human capital theory, represented
by Ben-Porath [1967] (hereafter BP), attributes the concave earnings profiles to individual
investment decision over life cycle. Human capital investment is a decreasing function of
human capital stock possessed. An individual takes advantage of lower opportunity costs
1
In this paper, I will focus only on full-time workers, which helps to get rid of the variations of labor
supply over time.
2
This figure is excerpted from Liu [2005].
3
See a recent survey by Rubinstein and Weiss [2004] for detailed discussions.
1
by investing more in human capital production in his early career. As time goes on, he
reduces human capital investment and reaps the return of rising human capital due to his
early investment.
Modern job search theory, represented by Burdett and Mortensen [1998] (hereafter BM),
focuses on the roles played by informational friction in the labor market. In presence of
friction, job offers are arrived not instantly as in human capital literature, but instead at
exogenous rates. Workers may not know exactly what wage each firm pays and job search
is costly and time consuming. This gives firms a certain degree of monopoly power. Hence,
firms, even if identical firms, may not pay the same wage rates to identical workers. That
is, in the presence of friction, there exists a non-degenerate wage offer distribution where
identical firms pay differently. Over time, workers climb up the job ladder, moving up from
low-paid jobs to high-paid jobs.
However, these two forces are unlikely to be isolated, but instead link to each other very
closely. Consider an environment where individuals are allowed to choose both human capital
investment and search effort. Individuals make a living by renting out their human capital
to firm they meet sequentially. Firms post different rental rates, unit price of human capital,
to hire workers. Earnings takes a multiplicative form between human capital and rental
rate. In this world, the return to job search is likely larger than it would be without human
capital investment. This is because human capital is also growing over time. Hence the
return to job search includes not only an increased value due to a higher outside offer on
current human capital level, but also an increased value due to both a higher outside offer
and growing human capital. Therefore, individuals would like to search more intensively
than they would if no human capital investment and everything else is equal.
Similarly, the return to human capital investment is also larger than it would be if there
is no job search. In human capital literature, every firm has to pay the same rental rate
which is equal to the marginal product of aggregate human capital in economy, if human
capital is perfectly substitutable. Individuals have no incentive to change jobs. However, in
a world where friction is present, firms may pay different rental rates. Hence in this world,
the return to human capital investment includes not only an increased value due to growing
human capital at current rental rate , but also an increased value of growing human capital
at a higher rental rate. Therefore, individuals would like to invest more in human capital
accumulation.
2
Essentially, human capital investment and job search are reinforcing each other in a
world where both choices are endogenous. This also likely have the following interesting
implications.
• Search intensity is increasing in human capital and decreasing in rental rate, since it
is more beneficial for individuals with more human capital to search and the chance of
getting better outside offers is declining with rental rate.
• Human capital investment is decreasing in both human capital and rental rate. Hence
human capital investment is different across different firms.
• Both search intensity and human capital investment are larger than they would be
without this interaction. This leads to a higher earnings growth over life cycle.
Previous attempts in existing literature to explore the interaction between human capital
accumulation and job search can be categorized into 3 groups. Exogenous job search and
human capital accumulation are assumed in the first group where job offer arrival rates are
constant over time and across firms and human capital grows exogenously. For example,
Bunzel et al. [1999] assume worker’s productivity is a linear function of experience with
constant a growth rate within a BM framework. This translates wages earned on the job
into a linear function of experience with initial wages offered by firms as an intercept. Since
the growth rate is constant over time and across firms, the distribution of wages earned
on the job is a direct transformation of distribution of initial wages offered by firms. The
estimate of growth is almost close to zero, which would imply wage growth over time is
almost the same before and after allowing for human capital growth, which is different from
the implication from the present paper. Omer [2004] assumes an exogenous and constant
growth rate for human capital as well as constant offer arrival rates. In his setting, the only
interaction between human capital accumulation and job search is that unemployed workers
would like to lower their reservation wages in order to get on jobs to accumulate human
capital. However, as will be shown in the present paper where endogenous search intensity
is also allowed, workers would like to not only lower their reservation wages but also search
more intensively in order to accumulate human capital on the job.
The second group includes those allowing for endogenous human capital accumulation
but with exogenous job search. One paper I am aware of is Rubinstein and Weiss [2004].
3
They only state a way of interaction similar to mine in terms of human capital accumulation
but without further exploration. No implications for search intensity are available from their
paper since job offer arrival rates are exogenous.
The only work I am aware of that allows for both human capital investment and search
intensity to be endogenized is Jovanovic [1979]. However, the present paper is still different
from his work in several dimensions. First, I focus on general human capital only since
my primary concern in this paper is that to what extent life cycle earnings profile can be
explained by the interaction between human capital investment and search intensity, given
many literature have found little on-the-job wage growth or tenure effect for wage growth.4
He focuses on the firm-specific human capital only since his primary concern is to relate
permanent job separations to firm-specific human capital. Second, the implications are
different due to different human capital specificity. With firm-specific human capital, human
capital investment is decreasing because of the interaction. And search intensity is also
decreasing in firm-specific human capital. However, the search intensity and human capital
are reinforcing each other in the present paper where human capital is completely general.
Third, he assumes all the match rent goes to workers by equating the rental rate of human
capital to worker’s marginal product. However, in the present paper, I will argue that firms
may not pay the rates equal to worker’s marginal product due to certain degree of monopoly
power arising from the market friction.
2
Model
In this section, general settings of the present model and worker’s problem are presented.
Firm’s problem is left in section 5.
2.1
2.1.1
General Settings
Model Environment
The human capital part of the present model is based on BP, Heckman et al. [1998], and
Hugget et al. [2004]. The search part is based on BM and Mortensen [2003].
4
Altonji and Shakotko [1987] find on-the-job wage growth about 0.7% per year and Altonji and Williams
[1997] find on-the-job wage growth about 1.1% per year.
4
Assume individuals are active in the labor market for T periods. They are born at
the beginning of period 1 and retire after period T , receiving a constant stream of income
thereafter. Assume individuals are income maximizers. Individuals make a living by renting
out their human capital stock to firms they meet sequentially. Individuals face a nondegenerate distribution of rental rates of human capital across firms, F (R), but do not know
exactly how much a particular firm pays when making decisions. There are two channels
through which they can potentially increase their income. One is to invest in human capital
accumulation while working. The other is to locate better job offers through job search.
Individuals make decisions at the beginning of each period. At period 1, all individuals
are born unemployed. Since human capital can only be augmented while working, the only
choice individuals have to make in period 1 is how much effort, s, is devoted to search,
which results in an arrival rate of job offers coming at the beginning of next period. Once
receiving a job offer Individuals have to decide whether to accept the offer immediately.
Simultaneously, they will decide time allocation between human capital production, i, and
output production, l, as well as search effort at that period if the job is accepted. Jobs are
also subject to exogenous destruction at a rate δ per period. The process continues until
individuals retire from the labor market.
2.1.2
Human Capital Production Technology
Assume human capital is completely general and perfectly substitutable. Hence individuals
are only different in the amount of human capital possessed. Also assume human capital
does not depreciate over time.
Assume a standard BP human capital production function, Q(h, i), where h is amount
of human capital devoted to human capital investment and i is the fraction of market time
allocated to human capital investment. In this paper, the production function Q(·) takes
the same specification as in Hugget et al. [2004]: Q(h, i) = a(hi)α , where α < 1 is a scalar
and a > 0 is individual learning ability and is assumed constant over time. Here, I do not
assume that a differs across individuals as Hugget et al. [2004] do, since my goal in this
paper is to examine life cycle profiles of human capital investment and search intensity for
a relatively homogeneous group of individuals, not the dispersion of earnings dynamics. In
this specification, i also can be thought of the proportion of human capital stock devoted to
human capital production. Assume the production function Q(·) is concave in both h and i.
5
The law of motion for human capital accumulation hence is h0 = h + Q(h, i), where h0
is human capital stock at next period, h and i are human capital stock and investment at
current period, respectively.
2.1.3
Search Intensity
There are several ways in literature to measure search intensity. For instance, Seater [1977]
and Jovanovic [1979] measure search intensity by the fraction of time devoted to job search.
Benhabib and Bull [1983] and Shimer [2004] measure search intensity by the number of
applications filled out and the number of job search methods used by a worker. Mortensen
[2003], Christensen et al. [2005], and Lise [2005] use search effort, a more abstract measure.5
In this paper, I adopt Christensen et al.’s way as the measure of search intensity. I try to
stress that search effort is really causing disutility or monetary costs for individuals, but not
an alternative for market time allocation.6
Assume that job offer arrival rate depends on individual search intensity. Let λ(s) be the
job offer arrival rate for an individual with search effort s. Assume λ(s) is an increasing
and concave function of s, with boundary conditions λ(0) = 0 and λ0s−→0 = +∞. In this
paper, λ(s) takes a linear specification: λ(s) = λs, where λ is an efficiency unit arrival rate.7
Assume that unemployed individuals and employed individuals have the same λ. This is
particularly useful in identifying parameter λ, since λ and s can not be separately identified
in data. However, they can be identified separately if we normalize the search intensity for
unemployed workers s0 to unity, since they are expected to search most intensively. Hence,
the search intensity for employed workers s1 can also be identified if we assume the same λ
for both the unemployed and employed.8 Since λs is the probability of a job offer arriving
at the beginning of next period, s is bounded above by 1/λ and below by 0.
Let c(s) be the disutility or monetary cost associated with search effort. Assume c(s) is
an increasing and strictly convex function of s, with boundary condition c(0) = c0s−→0 = 0,
5
6
An early version of Christensen et al. [2005] was summarized in Mortensen [2003].
The other reason for adoption of this measure is that information about measurement of search intensity
is not available in most of panel data, such as the Natioanl Longitudinal Survey of Youth(NLSY) and the
Panel Survey of Income Dynamics(PSID), which will be used in my estimation.
7
This is a standard and only specification so far in search literature where search intensity is endogenized.
See Mortensen [2003], Christensen et al. [2005], and Lise [2005].
8
See Mortensen [2003] or Christensen et al. [2005] for addressing this identification issue.
6
and twice differentiable. In this paper, c(s) takes the same specification as in Christensen
et al. [2005]
c(s) =
c0 s1+γ
,
1+γ
where c0 > 0 is a scalar and 1 + γ (γ > 0) is the elasticity of search cost with respect to
search effort.
2.1.4
Earnings
Individual make a living by trading their human capital to firms they meet sequentially.
Therefore, a worker with h, accepting a job offer R, investing i on human capital accumulation will earn e1 = Rh(1 − i) during that period. When he becomes unemployed, he receive a
stream of unemployment benefits which is proportional to his human capital, e0 = bh, where
b is a scalar and assumed to be constant over time.
2.2
9
Worker’s Problem
Consider an unemployed worker at period t with human capital h. Define Ut (h) as the
present value of expected lifetime income for this individual at the beginning of period t.
He receives bh as his income during that period. He has to decide the optimal amount of
search effort in order to make possible transition to employment the next period. With
probability λs0t , where s0t is the search intensity chosen at period t, he will receive a job
offer R randomly from the distribution F (R) at the beginning of next period and decide
whether to accept the offer. With probability 1 − λs0t , he will receive no offers and stay
unemployed. Hence the Bellman equation for this unemployed worker is:
Z
Ut (h) = max{bh − c(s0t ) + β(λs0t max{Ut+1 (h), Vt+1 (h, R0 )}dF (R0 )
s0t
+(1 − λs0t )Ut+1 (h))},
(2.1)
s.t
0 ≤ s0t ≤
1
,
λ
where β is a discount factor.
9
In practice, unemployment benefit is calculated as a fraction of individual previous labor income which
is correlated with individual human capital stock.
7
Define Vt (h, R) as the present value of expected lifetime income at the beginning of period
t for an working at a firm offering R with human capital h. His income during this period will
depend on his human capital investment, i.e., Rh(1−it ), where it is the amount of investment.
Search intensity s1t also will be decided in order to locate better outside options. As a result,
the next period with probability λs1t , he will receive a job offer R0 randomly and decide
whether to accept the offer. With probability δ, the match will exogenously be destroyed,
leaving him unemployed. With probability 1 − λs1t − δ, he will stay with his current firm.
Hence, The Bellman equations for this employed worker is:
Z
Vt (h, R) = max{Rh(1 − it ) − c(s1t ) + β(λs1t max{Vt+1 (h0 , R), Vt+1 (h0 , R0 )}dF (R0 )
it ,s1t
+δUt+1 (h0 ) + (1 − λs1t − δ)Vt+1 (h0 , R))},
(2.2)
s.t
0 ≤ it ≤ 1,
1
0 ≤ s1t ≤ ,
λ
h0 = h + a(hit )α .
Proposition 2.1. Ut (h) is continuous and increasing in h. Vt (h, R) is continuous, increasing
and concave in both h and R.
Proof. See the appendix.
Following the above proposition, we have the following reservation wage strategy.
Proposition 2.2. Let φt (h) be the reservation wage for unemployed workers with h, such
that Ut (h) = Vt (h, φt (h)). Hence for these unemployed workers, only wage offers that are at
least as good as φt (h) are acceptable. For employed workers working with firms offering R,
only wage offers that are at least as good as R are acceptable.
Utilizing the reservation wage strategy, the worker’s problem can be simplified as:
Z
Ut (h) = max{bh − c(s0t ) + βλs0t
(Vt+1 (h, R0 ) − Ut+1 (h)) dF (R0 )
s0t
φt+1 (h)
+βUt+1 (h)},
(2.3)
s.t
0 ≤ s0t ≤
1
,
λ
8
and
Z
(Vt+1 (h0 , R0 ) − Vt+1 (h0 , R)) dF (R0 )
Vt (h, R) = max{Rh(1 − it ) − c(s1t ) + βλs1t
it ,s1t
R
+βδ(Ut+1 (h0 ) − Vt+1 (h0 , R)) + βVt+1 (h0 , R)},
(2.4)
s.t
0 ≤ it ≤ 1,
1
0 ≤ s1t ≤ ,
λ
0
h = h + a(hit )α .
We can see that in equation (2.3), job search λs0t brings in a possible net gain in future
value whenever the offer R0 is at least as good as the reservation wage next period φt+1 (h),
which is captured by the 3rd term in the RHS. Similarly, in equation (2.4), the future value
includes not only the gain due to human capital investment it , even with the same firm,
Vt+1 (h0 , R), but also a possible net gain due to a better outside offer R0 attributed to onthe-job search s1t , which is captured by the 3rd term in the RHS. Hence the 3rd term in the
RHS of equation (2.4) really embodies the interaction between job search and human capital
investment in terms of future return.
3
Analysis
Optimality implies the following first order conditions for equations (2.3 and 2.4) respectively:
Z
0
c (s0t ) = βλ
(Vt+1 (h, R0 ) − Ut+1 (h)) dF (R0 ),
(3.1)
φt+1 (h)
where φt+1 (h) is the reservation wage at period t + 1 such that Vt+1 (h, φt+1 (h)) = Ut+1 (h),
Z
0
c (s1t ) = βλ (Vt+1 (h0 , R0 ) − Vt+1 (h0 , R)) dF (R0 ),
(3.2)
R
and
¶
Z µ
∂h0
∂Vt+1 (h0 , R0 ) ∂Vt+1 (h0 , R)
∂Ut+1 (h0 )
0
Rh = β
(λs1t
−
dF
(R
)
+
δ
∂it
∂h0
∂h0
∂h0
R
∂Vt+1 (h0 , R)
).
+(1 − δ)
∂h0
(3.3)
Equation (3.1) is used to solve the search intensity for unemployed workers, s0t . The LHS
of equation (3.1) is the marginal cost of search and the marginal return of search is on the
9
RHS. The job offer arrival probability is increased by λ if spending one more unit of time
or resource on search. Hence the probability of realization of net gain is also increased by
λ. Working seems more attractive than staying unemployed, if human capital accumulation
is allowed. One the one hand, workers receive constant compensation bh and see no growth
in human capital while unemployed. On the other hand, they may augment their human
capital and locate better outside offers while working. This encourages unemployed workers
to get out from unemployment as soon as possible by search more intensively or lower their
reservation wages. Hence s0t is higher and reservation wage φt+1 (h) is likely lower than they
would be without human capital growth, respectively, since human capital accumulation
makes working is more valuable. Meanwhile, workers with more human capital would like
to search more intensively since their opportunity costs of staying unemployed are higher.
Hence s0t is increasing in h.
Equations (3.2 and 3.3) together are used to solve s1t and it . On the one hand, the
marginal return of on-the-job search , the RHS of equation (3.2), is decreasing in R. Because
as R increases, the chance of accepting better outside offers is declining. Hence as R increases,
workers would like to reduce search intensity. On the other hand, search is more valuable for
individuals with more human capital. Hence as h increases, workers would like to increase
search intensity. To see how different search intensity is from it would be without human
capital growth, rewrite equation (3.2) to the following:
Z
0
c (s1t ) = βλ (Vt+1 (h0 , R0 ) − Vt+1 (h, R0 )) − (Vt+1 (h0 , R) − Vt+1 (h, R))
R
+ (Vt+1 (h, R0 ) − Vt+1 (h, R)) dF (R0 ).
(3.4)
In the present model, the first 2 terms inside the integral are both positive since the value
function is increasing in h and the difference of these two terms is also positive due to the
concavity of the value function. However, in a situation where human capital is constant
over time, these 2 terms would disappear. Hence the marginal return of search is higher than
it would be with constant human capital. This implies higher on-the-job search intensity
than it would be without human capital growth.
Human capital investment is decreasing in h, since the marginal cost of investment is
increasing in h and human capital production function is concave in h. As R increases,
the chance of accepting better outside offers is decreasing. Hence the return to human
capital investment is realized mostly likely at current rental rate. Therefore, human capital
10
investment is decreasing in R due to increasing marginal cost and decreasing marginal return.
To see how different human capital investment is from it would be without job search, rewrite
equation (3.3) to the following:
¶
µ
¶
Z µ
∂h0
∂Ut+1 (h0 ) ∂Vt+1 (h0 , R)
∂Vt+1 (h0 , R0 ) ∂Vt+1 (h0 , R)
0
dF (R ) + δ
−
−
Rh = β
(λs1t
∂it
∂h0
∂h0
∂h0
∂h0
R
0
∂Vt+1 (h , R)
).
(3.5)
+
∂h0
The first term on the RHS of equation (3.5) is greater than zero due to the concavity of V .
Imagine an environment where there is no job search. Individuals are not allowed to search
while unemployed and working. Individuals have to accept whatever offers they receive
randomly. Once on the job, they stay with the firm forever unless the match is exogenously
destroyed. Hence in this situation, the first term, would disappear. Therefore, the marginal
return of human capital investment would be smaller in the situation where job search is
not allowed.10 Hence, individuals would like to invest more on human capital accumulation
than they would without job search.
The ideas in this section can be summarized in the following proposition.
Proposition 3.1. The search intensity s0t , for unemployed workers, is increasing in human
capital h. The on-the-job search intensity s1t is increasing in h and decreasing in human
capital rental rate R. The human capital investment it is decreasing in both h and R.
Human capital accumulation and job search reinforce each other in the sense that both
search intensities s0t and s1t are greater than they would be without human capital growth
and human capital investment it is also greater than it would be without job search.
4
Numerical Exercises
In this section, a 5-period model is numerically solved. Simulations are also conducted based
on the decision rules numerically solved to examine life cycle profiles of search behavior,
human capital accumulation, and earnings.
10
Value functions also would be smaller in situation where no job search is allowed than they are with job
search.
11
4.1
Solve the Model
In this section, a 5-period model is numerically solved by backward induction. Start from the
last period T . It is rational for individuals not to engage in any investment activity at the last
period since they retire and receive a constant stream of income from period T +1 and on. For
simplicity, assume they will receive zero income after retirement. Hence at the last period,
UT (h) = bh, VT (h, R) = Rh, and the reservation wage is the same for everyone, φT (h) = b.
Given the value functions and the reservation wage at period T , the decision rules s0T −1 (h),
s1T −1 (h, R), and iT −1 (h, R) can be solved using 3 first order conditions, equations (3.1, 3.2
and 3.3). This will give us the value functions UT −1 and VT −1 and the reservation wages
φT −1 . General speaking, given the value functions Ut+1 (h) and Vt+1 (h, R) and reservation
wages φt+1 (h) at period t + 1, the decision rules at period t, s0t (h), s1t (h, R), and it (h, R),
and the value functions Ut (h) and Vt (h, R) can be solved. This procedure is repeated until
we get the solutions for all periods.
The parameters used in solving a 5-period model are listed in the following table.
β
0.7576
λ
δ
a
0.125 0.007 0.08
α
c0
γ
b
0.5
0.5
1
1.5
h
R
[1,10] [1,5]
F (R)
uniform
Assume individuals are attached to the labor market for about 40 years. Hence one period
in the model represents 8 years in the labor market. Let the annual interest rate r be 4%. β
is calculate as 1/(1 + 8r). a is taken from Heckman et al. [1998] which is an average estimate
across different skill groups. Assume initial human capital levels range from 1 to 10. The
rental rates of human capital range from 1 to 5 and are assumed to be constant over time and
uniformly distributed. The rest of the parameters are randomly chosen just for the purpose
of illustration.11
Figure 2 plots the value function V in both 3 dimensions and 2 dimensions. We can see
that V is continuous and increasing in both h and R and is strictly concave.
The on-the-job search intensity s1 and human capital investment i are plotted in Figures
3 and 4 respectively. The left panels of the figures are 3-D plots and the right panels of the
figures are corresponding contour plots. Hence it is verified that s1 is increasing in h and
decreasing in R and that i is decreasing in both h and R.
The numerically solved reservation wages are increasing in h at any period and increasing
11
I would expect the qualitative results derived from these numerical exercises are still valid even if another
sets of parameters are used, since the model behaves very nicely as shown in results.
12
40
50
0
80
9
30
120
11
10
0
60
10
8
70
100
50
40
7
90
60
80
80
20
70
30
h
v
6
60
4
20
30
20
40
10
3
0
10
50
40
5
40
30
20
8
5
6
2
3
2
h
1
2
0
1
20
10
4
4
60
10
1
R
1.5
2
2.5
3
R
3.5
4
4.5
Figure 2: Value function V
over time for each individual. And the reservation wages are smaller than they would be
without human capital accumulation. However, they are all roughly equal to 1.49 for all
periods and all individuals with different h. Hence in this regard, I think the results are
ambiguous. Maybe this is partly because the learning ability parameter a I choose is so
small that human capital is roughly constant over time. This needs further examinations.
4.2
Simulation Results
In this section, several simulations are conducted based on the decision rules solved in the
preceding section to examine how search intensity, human capital investment, and earnings
change over time, respectively. In particular, simulations are conducted for a group of 50
individuals with initial human capital equal to 2 and based on 100 replications.
The profile of search intensity for unemployed worker s0 over time, is plotted in the left
panel of Figure 5 and the profile of on-the-job search intensity s1 over time, is plotted in the
right panel.
We can see that both search intensities are decreasing over time and s1 is smaller than s0
at any period t.12 As time goes on, in the present model, human capital is growing which
12
Recall that all individuals are unemployed at period 1 and they also spend nothing on search at period
5. Hence periods 1 and 5 are not for comparison.
13
5
2.5
3
8
6
0.5
s1
1.5
2
3.5
5
4.5
9
1
4
10
2.
5
4
5
s1
0.5
1.5
h
3
2
3.
5
6
1
4
7
5
3
4
10
2
2
3
5
0
1
1
1.5
1
5
0.
2
1
1.5
2
2.5
3
3.5
4
4.5
5
0
1
h
0.5
1
1.5
2
2.5
R
3
R
3.5
4
4.5
5
Figure 3: On-the-job Search Intensity
10
−3
iv
x 10
9
8
00
0.0
0.0015
5
0.001
0.002
7
3
5
4
h
iv
6
4
1
0.00
3
1
0.001
5
2
2
5
3
1
4
105
h
0.002
0.0025
1
0.003
1.5
2
R
Figure 4: On-the-job Human Capital Investment
14
0.001
0.001
0.0
01
2
0
0
0.0005
0.0015
5
2
0.0005
2.5
0.0015
0.002
0.0025
3
3.5
R
4
0.0015
0.002
0.0025
4.5
5
encourages individuals to search more on one hand. On the other hand, individuals also
climb up the job ladder, moving from low-paid jobs to high-paid jobs, which discourage
them to search. It is really the interaction between these two forces, one positive the other
negative, that determines the profiles of search intensity over time. The profiles of search
intensity over time here implied by the present model is consistent with couples of important
empirical findings in the literature. One is that people change jobs very often in the first 10
to 15 years in the labor market and the frequency is declining over time as found by Topel
and Ward [1992]. The other is that estimates of job offer arrival rate for employed workers
are smaller than those for unemployed workers in most of the existing search literature using
a variety of data sets.13 In the context of the present model, the frequency of job changing is
declining over time can be explained by the declining search intensity over time. Job arrival
rate is smaller for employed workers than unemployed workers is because employed workers
search less intensively than unemployed workers, i.e., s1 < s0 .
The profiles of human capital investment and accumulation are plotted in the left panel
and the right panel of Figure 6, respectively. We can see that the human capital investment
is decreasing over time since human capital is growing over time and individuals moves from
low-paid jobs to high-paid jobs.
The profiles of on-the-job search intensity and earnings under two situations, with and
without human growth, are plotted in Figure 7 for comparison. The solid blue lines represent
the profiles with human capital growth. The dash green line represent the profiles without
human capital growth. We can see that from the left panel of Figure 7, search intensity with
human capital growth (solid blue line) is, at any period, greater than that without human
capital growth (dash green line). This leads to a higher job offer arrival rate and hence it
is more likely or frequently for employed workers to change jobs, clime up the job ladder
and end up with working at higher-paid firms in a world with human capital growth. This
joining with a growing human capital over time results in higher earnings over time as we
can see in the right panel of Figure 6.
13
For example, to name a few, Bowlus et al. [2001] using NLSY, Liu [2005] using SIPP, Postel-Vinay and
Robin [2002]using French data, and Bunzel et al. [1999] using Danish data.
15
1.6
0.45
1.4
0.4
0.35
1.2
0.3
1
s1
s0
0.25
0.8
0.2
0.6
0.15
0.4
0.1
0.2
0
0.05
1
1.5
2
2.5
3
t
3.5
4
4.5
0
5
2
2.5
3
3.5
t
4
4.5
5
3
3.5
t
4
4.5
5
Figure 5: Simulated Search Intensity over Time
−3
3
x 10
2.0035
2.003
2.5
2.0025
2
h
iv
2.002
1.5
2.0015
1
2.001
0.5
0
2.0005
2
2.5
3
3.5
t
4
4.5
5
2
2
2.5
Figure 6: Simulated Human Capital Accumulation over Time
16
0.45
4.5
hc
nhc
0.4
hc
nhc
0.35
0.3
earnings
4
s1
0.25
0.2
0.15
3.5
0.1
0.05
0
2
2.5
3
3.5
t
4
4.5
3
5
1
1.5
2
2.5
3
t
3.5
4
4.5
5
Figure 7: Profiles of On-the-job Search Intensity and Earnings, with and without Human Capital
Growth
5
Work in Progress
First, a non-degenerate distribution of rental rates for human capital is assumed to exist
in solving for worker’s problem. The question is whether this non-degenerate distribution
of rental rates can be supported by firm’s rational behavior. That is, do firms choose to
distinguish themselves by offering different rental rates? This needs to work out firm’s problem appropriately. The idea, in the sprit of BM and Mortensen [2003], is that the expected
profit flow per worker contacted is the same across all homogeneous (equally productive)
firms. When a firm decides how much he is willing to pay for 1 unit of human capital,
he should take into account that how likely a randomly contacted worker would accept the
offer and once accepted, how long the newly-formed match will likely last. This consists of
the expected profit flow per worker contacted which in equilibrium should be equal at all
possible rental rates. That is, firms should be indifferent by offering different rental rates. A
firm offering a higher rate would hire a worker more easily and quickly and retain the worker
more easily, but with lower profit per unit of human capital. A firm offering a lower rate
would earn a higher unit profit, but less likely to hire and retain a worker. Of course, the
probability of a worker willing to accept a offer and the probability of a worker willing to
stay with his current firm depend on the worker’s behavior at different human capital levels
17
and rental rates.
Second, the parameters of interest in the present model will be estimated using panel
data sets, such as the NLSY and the PSID. Information from panel data should include
employment status, job spells, unemployment spells, job transitions, wage or earnings and
so on. The life cycle profiles of search intensity, human capital investment, and earnings will
be reexamined based on the estimates.
6
Conclusions
This paper examines the interactions between human capital accumulation and job search
by allowing for both forces to be endogenous choices within a life cycle framework. The
model has several interesting implications. Individuals with more human capital would like
to search more intensively both on the job and off the job (being unemployed). Individuals
would like to reduce search intensity as they move from low-paid jobs to high-paid jobs.
Individuals would like to reduce human capital investment as they move from low-paid jobs
to high-paid jobs and they accumulate more human capital. Both human capital investment
and search intensity are higher than they would be without allowing for the interactions,
respectively.
The preliminary results show that the model implies a higher earnings profile and a
higher growth in earnings over the life cycle. It is really the interactions between human
capital accumulation and job search that contribute to both within job and between job
earnings growth, since they are reinforcing each other. Hence, any quantitative estimates of
relative contribution of each force to earnings growth could be misleading or not informative
without understanding the interactions between them. The model also is able to explain
why individuals with more human capital, like college graduates, have shorter unemployment
spells and more frequent job to job changes than those with less human capital, like high
school graduates.
7
Appendix
Available upon request.
18
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