ï»¿ WPS6035
Policy Research Working Paper 6035
Workersâ€™ Age and the Impact of Trade Shocks
Erhan ArtuÃ§
The World Bank
Development Research Group
Trade and Integration Team
April 2012
Policy Research Working Paper 6035
Abstract
Do trade shocks affect workers differently because of simulation of counterfactual trade-liberalization policies
their age? This paper examines the issue by estimating in the metal manufacturing sector, the paper shows that
the lifetime mobility of workers based on the sectors trade shocks affect workers with higher mobility costs
in which they work. Using U.S. data, the paper shows more, for both winners and losers of the policy shocks.
that mobility costs rise with a workerâ€™s age and years of But the effects taper off over a workerâ€™s lifetime, especially
experience, but stay the same regardless of his or her when they are close to retirement.
education level. In addition, using a general-equilibrium
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contacted at eartuc@worldbank.org.
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Produced by the Research Support Team
Workersâ€™ Age and the Impact of Trade Shocks
Erhan ArtuÂ¸1
c
April, 2012
Abstract
Do trade shocks aï¬€ect workers diï¬€erently because of their age? This paper examines the
issue by estimating the lifetime mobility of workers based on the sectors in which they work.
Using U.S. data, the paper shows that mobility costs rise with a workerâ€™s age and years of
experience, but stay the same regardless of his or her education level. In addition, using
a general-equilibrium simulation of counterfactual trade-liberalization policies in the metal
manufacturing sector, the paper shows that trade shocks aï¬€ect workers with higher mobility
costs more, for both winners and losers of the policy shocks. But the eï¬€ects taper oï¬€ over a
workerâ€™s lifetime, especially when they are close to retirement.
JEL Classiï¬?cation: F1, D58, J2, J6
Keywords: Trade Liberalization, Sectoral Mobility, Labor Market Equilibrium.
1
The views in this paper are the authorâ€™s and not those of the World Bank Group or any other institution.
Artuc: The World Bank, Development Economics Research Group (Economic Policy), 1818 H St NW
Washington DC, 20433, USA. Email: eartuc@worldbank.org. I would like to thank Leora Friedberg and John
McLaren for their valuable comments, Turkish Academy of Sciences (TUBA) and Scientiï¬?c and Technological
Research Council of Turkey (TUBITAK) for their ï¬?nancial support between 2007-2010, and Jane Zhang for
her editorial comments. All errors are mine.
1
1 Introduction
One of the key policy questions in the international trade literature is the distributional
eï¬€ects of trade shocks. Policy makers need to know who are the winners and losers from trade
liberalization in order to develop eï¬€ective compensation programs and address ineï¬ƒciencies.
Recently, economists have started to use structural models to study trade policy, with a
special emphasis on labor market dynamics and general equilibrium eï¬€ects, to focus on issues
that cannot be addressed with reduced form methods. The main motivation for structural
estimation is running counterfactual policy simulations, such as trade liberalization, using
estimated theoretical parameters.
Most of the frontier research on structural estimation of labor market parameters requires
solution of agentsâ€™ optimization problem, naturally from the agentsâ€™ perspective. In order to
solve workersâ€™ optimization problem, the econometrician has to know the exact distribution
of expected aggregate shocks as perceived by agents, a popular special case being the per-
fect foresight assumption2 . This is a fundamental challenge for international trade research
because trade policy, by its nature, is a shock that changes agentsâ€™ expectations about the
future dynamically.
The trade barriers have been changed very frequently by policy-makers, in most cases
being reduced and in some cases being increased. Sometimes, a new trade policy is announced
in advance, but in many other cases it appears as a shock-therapy. As new information
arrives regarding the trade policy, agents update their expectations about future wage and
employment outcomes in diï¬€erent sectors.
For example, when the Multi Fibre Agreement ended in 2005 after the establishment
of the World Trade Organization, the original plan was to abolish textile quotas. This
important change in the global trade policy had already been public information for many
years. After the arrival of this new information, probably prior to the establishment of the
WTO, agents updated their expectations about wages and employment prospects in the
2
Some prominent examples are Keane and Wolpin (1997), Lee and Wolpin (2006) from the labor literature,
Dix-Carneiro (2011) from the trade literature.
2
textile industry. It is safe to assume that both physical and human capital investments in
textiles had declined signiï¬?cantly before 2005 in many countries, excluding China. Later
on, however, the EU announced that they were imposing new quotas, causing an increase in
trade barriers once more. Possibly, agents had updated their expectations several times as
they learned more about the planned policy change. It is not possible to know when workers
and employers changed their expectations and how much they changed them, since we do
not have survey data on expected future wages.
Another sector that was subject to trade shocks is the metal manufacturing sector, in
particular the steel industry. In 2002, the US administration announced that they would
impose a 3 year temporary safeguard to protect the domestic steel industry, under Section
201 of the US Trade Act of 1974. According to news, this announcement raised hopes in
the textile industry to receive a similar protection. Meanwhile, there were discussions about
the US automotive industry and whether it was hurt due to the increase in steel prices,
a major input for car production. Shortly after, WTO ruled against this decision asking
the US to lift the temporary protection. Although initially the US was expected to appeal
this ruling, in 2003 the temporary barrier was lifted voluntarily, 2 years before the scheduled
time. Because of high uncertainty in metal tariï¬€s, it is practically impossible to parameterize
workersâ€™ and manufacturersâ€™ expectations about labor market outcomes in the metal sector:
new information arrives frequently and changes expectations dynamically.
Identiï¬?cation of workersâ€™ expectations is a challenge for any research that relies on struc-
tural estimation of labor market parameters, such as migration, education choice, occupa-
tional mobility, sectoral mobility, etc. Just like trade shocks, other policy and macroeconomic
shocks can also aï¬€ect workersâ€™ expectations. Our contribution is studying distributional ef-
fects of trade liberalization, one of the key questions in the international trade research that
is usually addressed via reduced form regressions, in a setting that allows unspeciï¬?ed ï¬‚uc-
tuations in workersâ€™ expectations due to policy and macroeconomic shocks. Diï¬€erent from
the previous research, our main focus is the eï¬€ect of trade shocks on diï¬€erent age groups.
3
Although reduced form econometrics provides useful insights on the distributional eï¬€ects
of trade shocks, structural estimation is the only known method to address certain important
issues, such as adjustment dynamics, general equilibrium eï¬€ects, and counterfactual policy
simulations, despite the challenges we mentioned earlier.
In this paper, we study the impact of trade liberalization along the life cycle of work-
ers from diï¬€erent skill and experience groups without imposing any strong restrictions on
workersâ€™ expectations in the estimation stage. Therefore our estimation strategy, which is
described fully in Artuc (2012), is applicable to environments that are subject to aggre-
gate uncertainties. The econometrician does not need to know the distribution of aggregate
shocks due to changes in trade policies, labor market policies, ï¬?nancial crises, technological
progress, etc. We investigate how age interacted with education and experience aï¬€ects the
mobility of workers, and report the increase in mobility costs as workers get older. Then,
we show that workersâ€™ mobility determines loss and gain from trade shocks, and provide a
general picture of welfare changes across diï¬€erent worker subgroups.
To illustrate the connection between mobility and diï¬€usion of gains from trade, imagine
that all workers were perfectly mobile across sectors. Then, all workers would be unanimously
better oï¬€ or worse oï¬€ after a policy shock thanks to factor price equalization. If workers
were immobile and attached to their original sectors, then there would be distinct winners
and losers from free trade. In that case, workersâ€™ sectors would determine their gain and loss.
In reality, mobility costs probably lie between these two extremes and vary across groups.
A major source of variation in mobility has to do with the age of aï¬€ected workers, causing
diï¬€erences in their position towards free trade. For example, the Pew Global Attitudes
survey, conducted in 2002, shows that young people are more enthusiastic about free trade
compared to older people.
After the empirical exercise we conduct using the Current Population Survey and the
1979 cohort of the National Longitudinal Survey of Youth (henceforth CPS and NLSY re-
spectively), we calibrate production, input demand and consumption demand functions to
4
set a general equilibrium framework with the estimated sectoral choice parameters. Finally,
we simulate a hypothetical trade liberalization in the metal manufacturing sector (which
has been especially vulnerable to trade shocks in the past) to analyze gradual adjustment
of labor, wages and prices in all sectors in response to the trade shock. The counterfactual
trade shock is a surprise reduction in protective trade barriers in the metal manufacturing
sector, reducing metal prices. Wages, labor allocations, service sector price, gross ï¬‚ows of
workers and sectoral outputs adjust endogenously during a transitional period, following the
policy shock.
One important question is why old workers are less mobile than young workers. Following
the previous literature we can give several diï¬€erent answers to this question: For example,
Borjas and Rosen (1980) attribute decreases in mobility with age to the increase in wages
with tenure. The decrease in mobility with age can be attributed to speciï¬?c human capital
as in Topel (1991), better job match as in Jovanovic (1979) or implicit contracts as in
Lazear (1979). Groot and Verberne (1997) suggest that the decrease in mobility with age
can be partially attributed to non-ï¬?nancial reasons. Possible non-pecuniary reasons are the
likelihood of owning a house, having a spouse working in the same location, old workersâ€™
relatively lower education levels or shorter time horizon. Other examples are Davidson et
al (1994) and Falvey et al (2010), who model employment prospective and training costs in
relation to age of workers respectively. Since it is impossible to model all these important
factors explicitly, we allow sectoral mobility costs of workers to change over their life-cycle
with age, experience and education.
The most closely related work to ours is Artuc, Chaudhuri and McLaren (2010), (hence-
forth ACM). They introduce an empirical dynamic discrete choice model, a new direction
for trade research, to study trade shocks without imposing restrictions on workersâ€™ expecta-
tions. However, their estimation strategy fails when there are more than a few worker types
or small sectors. They can identify only a limited number of theoretical parameters. As it is
incredibly diï¬ƒcult to ï¬?t such a compact model to data, they report imprecise and possibly
5
overestimated values for the structural moving cost parameters.
In this project, unlike ACM, we focus on distributional eï¬€ects of trade shocks on disag-
gregated worker groups and provide a much sharper picture. We utilize a diï¬€erent estimation
strategy which allows small sectors (such as metal), detailed worker heterogeneity and a large
number of structural parameters without imposing distributional assumptions on workersâ€™
expectations. This new estimation strategy can successfully pin down a much richer set of
theoretical parameters with more precision, without adding any computational burden. In
fact, we show that workersâ€™ optimization problem can conveniently be collapsed to two linear
equations, which are easy to estimate, without sacriï¬?cing from worker heterogeneity3 .
It is possible to consider two main lines of quantitative research on labor market eï¬€ects
of trade liberalization: First, research that is conducted via reduced form estimation. Re-
search based on reduced form estimation utilizes natural experiments to identify eï¬€ects of
free trade on import competing sector workers. This type of research usually contains rich
worker heterogeneity and focuses on distributional eï¬€ects4 . The second type is general equi-
librium models that are inspired from macroeconomics or structural labor economics (which
requires calibration or estimation of theoretical parameters). General equilibrium models
allow counterfactual policy simulations and focus on labor market interactions based on the-
ory. Diï¬€erent from reduced form regressions, they require strong assumptions on workersâ€™
expectations and the distribution of aggregate shocks5 .
Our paper is an intuitive combination of reduced form analysis and general equilibrium
models. The model we present here is a general equilibrium model, and we estimate theoret-
ical parameters; from this perspective it is structural. On the other hand, we employ linear
regressions (Poisson and IV) to estimate structural parameters which are almost exclusively
3
The main econometric analysis here can be conducted using standard statistical software, and can be
applied to many other discrete choice problems, such as migration, occupational mobility, education choice,
etc.
4
Two well-known examples are, Pavcnik, Attanasio and Goldberg (2004) and Ravenga (1992); Slaughter
(1998) provides a survey of this literature.
5
Among others, some prominent examples are Cosar (2011), Cosar et al (2011), Dix-Carneiro (2011),
Kambourov (2009) and Ritter (2009).
6
used in reduced form analysis. The linear regressions we employ allow us to be agnostic
about aggregate policy and macroeconomic shocks in the estimation stage, but at the same
time we run counterfactual simulations as we recover theoretical parameters.
In the next section, we specify the theoretical model, followed by an introduction of the
estimation strategy. Then, we discuss data issues and present empirical results. Finally, we
conclude after discussing the counterfactual trade simulations.
2 Model
Consider an economy with N industries, where workers choose a sector to work dynami-
cally in each period to maximize their present discounted expected utility. The industries are
indexed with i âˆˆ {1, 2, .., N }. We divide workers in each sector into economically relevant
subgroups; a workerâ€™s subgroup is deï¬?ned by the state vector s âˆˆ S. The state vector s in-
cludes workersâ€™ age, education, endogenous sectoral experience status and unobserved type.
The state variable age can take six values, age âˆˆ {26, 33, 40, 47, 54, 61}. Since our main fo-
cus is age, we consider binary variables for the other elements of state space. The education
variable is denoted as edu âˆˆ {noc, col}, standing for non-college and college educated respec-
tively, while the sectoral experience variable is denoted as exp âˆˆ {in, ex}, inexperienced and
experienced respectively. Finally, we consider two unobserved types denoted as Ï„ âˆˆ {I, II}.
The state of a worker is his current industry i and the vector
s = [age, edu, exp, Ï„ ]ï¿¿ . (1)
At period t, a worker with state vector s receives an instantaneous utility in sector i,
denoted as
i,s i,s
ui,s = wt + Î·t ,
t (2)
i,s i,s
where wt is the wage and Î·t is a non-pecuniary utility common to all type s workers in
i,s
sector i. The wage for a type s worker in sector i, wt , is a function of the aggregate state
7
of the economy, denoted as Î¾t , where
i,s
wt = W i,s (Î¾t ) .
The aggregate state variable, Î¾t , captures all industry, macroeconomic and policy shocks.
The workers are rational, hence any new information that updates expectations for this
aggregate state variable is a surprise. More formally, Îµw = Et+1 W i,s (Î¾t+n ) âˆ’ Et W i,s (Î¾t+n ) is
a mean zero iid shock for n â‰¥ 1. This assumption applies to all random variables in our
model. For the estimation purposes, we do not need to specify a functional form for W i,s (Î¾t ),
so we deï¬?ne this function in the next subsection when we focus on general equilibrium aspects
of the model.
i,s
The non-pecuniary utility component, Î·t is distributed iid with mean Î· i,s . A rational
Â¯
worker chooses his sector after taking instantaneous utility, ui,s , and the stream of expected
t
future utilities into consideration. Workers can expect changes, trends and ï¬‚uctuations in
wages due to policy, sectoral and macroeconomic shocks. Hence expected future values of
the aggregate state variable, Î¾t+n , can ï¬‚uctuate over time. The econometrician does not
need to know or quantify the expectations of workers.
We establish that a worker pays a moving cost, C ij,s + ï¿¿j , if he decides to switch from
t
sector i to sector j. This moving cost has two components, a ï¬?xed component C ij , and an
individual speciï¬?c random component ï¿¿j . Note that, ï¿¿j is diï¬€erent for every worker as it is
t t
individual speciï¬?c (but we omit the agent index). The ï¬?xed component C ij is equal to zero
for stayers, so Ctij,s = 0 if i = j, otherwise it is expressed as
C ij,s = C 1,age,edu + 1exp C 2 + 1Ï„ C 3 , (3)
where C 1,age,edu is the component changing with age and education of workers. 1exp is the
indicator function which is equal to one when sectoral experience status is â€™exâ€™, i.e. when the
worker has sectoral experience, zero otherwise. Hence, the workers with sectoral experience
8
pay an additional moving cost, C 2 , when they move. 1Ï„ is an indicator function which is
equal to one when Ï„ = II and zero otherwise, resulting in an additional C 3 units of moving
cost for the unobserved type II workers.
The idiosyncratic individual speciï¬?c moving costs shock ï¿¿j is drawn from extreme value
t
type I distribution with scale parameter Î½ and location parameter âˆ’Î½Î³, where Î³ is the Eulerâ€™s
constant.
We deï¬?ne exogenous transition probabilities between states. Following Artuc (2006), a
similar methodology was also used by ACM to introduce limited heterogeneity. We assume
that the probability of moving from one age group to the next group is 1/k, where k is the
diï¬€erence between two age groups. In our case k=7, since we consider age clusters of seven
years such as 26, 33, 40, etc. We assume that workers gain sectoral experience if they stay in
their sector as they move up to the next age group6 . Experience is lost if a worker changes
sectors. Workersâ€™ education and unobserved type do not change over time. Let us denote the
probability of switching from state s to state sï¿¿ as Ï€ ij (s, sï¿¿ ) for a worker moving from i to j.
Artuc (2006) shows that this approach provides a reasonable approximation of continuous
state space.
i,s
Timing of the events is as follows: 1. Agents learn values of wt at time t when they
learn Î¾t . They also update their expectations about future shocks, Et Î¾t+n for n âˆˆ {1, 2, 3, . . . }
when they receive new information. 2. Then, at the end of period t, they learn the random
component of their â€œmoving cost,â€? ï¿¿j , for every j = 1, .., N , and choose the next period
t
sector (based on expected stream of future wages and moving costs). 3. Agents pay the
moving cost, C ij,s + ï¿¿j , where j is the chosen sector. 4. Period t + 1 starts, and the cycle
t
repeats itself.
Workersâ€™ objective is to maximize their present discounted utility ï¬‚ows following the
Bellman equation
6
This is a binary variable, therefore only workers do not already have experience can gain additional
experience.
9
ï¿¿ ï¿¿
Vts = max Vti,s , (4)
i
alternative-speciï¬?c values are deï¬?ned as
ï¿¿ ï¿¿
ï¿¿ j,sï¿¿
Vti,s = i,s
wt + i,s
Î·t + Et max Î² Ï€ ij (s, sï¿¿ ) Vt+1 âˆ’ C ij,s âˆ’ ï¿¿j
t , (5)
j
sâˆˆS
where the expectation is taken with respect to all random variables including Î¾t+n for
n â‰¥ 1 (which can change with anticipated or realized policy shocks).
For the estimation purposes, we consider that expectations of agents are unknown to
the econometrician, i.e. we do not know Et wt+1 . For example, if there is a future shock,
such as a trade shock, we do not need to assume whether the agents know it or not, when
they learn about it, or how it aï¬€ects wages. We only impose a certain distribution for
the individual shock, ï¿¿i . The distribution of other random variables is only needed for the
t
simulations, not for the estimation. We are agnostic about the distribution of random shocks
and workersâ€™ expectations, and unlike most of the other structural discrete choice models,
we do not attempt to calculate values by backwards solution or iteration (for estimation
purposes). We explain how we estimate the model without distributional assumptions in the
next section.
The value function, then, can be re-arranged as
i,s i,s ï¿¿ i,s
Vti,s = wt + Î·t + Î² Vt+1 + â„¦i,s ,
t (6)
where
ï¿¿ ï¿¿
ï¿¿ i,s
Vt+1 = i,s
Ï€ ij (s, sï¿¿ ) Et Vt+1 , (7)
sâˆˆS
and
10
N
ï¿¿ ï¿¿ï¿¿ ï¿¿ ï¿¿
â„¦i,s
t = âˆ’Î½ log exp ï¿¿t+1 âˆ’ Î² Vt+1 âˆ’ C ik,s 1 .
Î²V k,s ï¿¿ i,s (8)
k=1
Î½
See Artuc (2012) for the derivation of the equations above. Using the value functions,
we can easily derive gross ï¬‚ows of workers (thanks to McFadden (1973)). The probability of
a type s worker to move from sector i to sector j is equal to
ï¿¿ï¿¿ ï¿¿ ï¿¿
exp ï¿¿ j,s ï¿¿ i,s
Î² Vt+1 âˆ’ Î² Vt+1 âˆ’ C ij,s 1
Î½
mij,s
t = . (9)
N
ï¿¿ ï¿¿ï¿¿ ï¿¿ ï¿¿
exp ï¿¿ k,s ï¿¿ i,s
Î² Vt+1 âˆ’ Î² Vt+1 âˆ’ C ik,s 1
Î½
k=1
The equations (9) and (6) are pivotal for our estimation strategy.
Aggregate Economy
To be able to simulate workersâ€™ response to trade shocks, we need to deï¬?ne labor demand
i,s
equations, more speciï¬?cally wt = W i,s (Î¾t ). In this section, we deï¬?ne production functions
and derive wage equations from them. Note that the equations we derive in this section are
only required for simulations, and they do not play any role in the main estimation strategy.
The number of type s workers in sector i at time t is deï¬?ned as Li,s . Then, the distribution
t
of workers at time t + 1 can be expressed as
N
ï¿¿ï¿¿
ï¿¿
Lj,s =
t Li,s mij,s Ï€(s, sï¿¿ )
t t (10)
i=1 sâˆˆS
We assume that any 61 years old worker moving up to the next age group is retired, he
receives a lump-sum payment and exits the labor force, and is replaced by a 26 years old
worker.
The production functions are Cobb-Douglass and they require skilled labor, unskilled
labor, capital and intermediate inputs from all sectors. Some of the output is consumed
by workers and some of it is used as input for production. In each sector, there is a large
number of competitive employers oï¬€ering workers their marginal product. We assume that
11
units of human capital possessed by type s worker for production of i sector output is equal
to hi,s .
i
We deï¬?ne production functions for i sector output yt as
ï¿¿ ï¿¿ bi ï¿¿ ï¿¿ bi N
ï¿¿ noc
ï¿¿ col
ï¿¿ ï¿¿b i ï¿¿ ï¿¿ ï¿¿b i
i
yt = B i Li,s hi,s
t Li,s hi,s
t Ki K ji
qt j
, (11)
sâˆˆS noc sâˆˆS col j=1
where S col is the subset of S that includes only college educated workers (henceforth
skilled), and S noc is the subset that includes only non-college educated workers (henceforth
unkilled), bi , bi , bi , and bi are the Cobb-Douglass shares of unskilled labor, skilled labor,
noc noc K j
ji
capital and sector j input to produce sector i output respectively. qt denotes the j-sector
input used in i-sector output. We assume that capital, K i , is ï¬?xed.
The consumer price index is deï¬?ned as
N
ï¿¿
Ïˆt = (pi )Î¸i ,
t (12)
i=1
where pi is the price and Î¸i is the consumption share of the sector i output (with an
t
underlying Cobb-Douglas utility function).
Then the real wage equations are
i,s ï¿¿ ï¿¿ pi
t bi y i
wt = hi,s ï¿¿ noc ti,s i,s , (13)
Ïˆt sâˆˆS noc Lt h
and
i,s ï¿¿ï¿¿ ï¿¿ï¿¿ pi
t bi y i
wt = hi,s ï¿¿ col ti,s i,s , (14)
Ïˆt sâˆˆS col Lt h
for unskilled and skilled labor respectively, where sï¿¿ âˆˆ S noc and sï¿¿ï¿¿ âˆˆ S col . Note that the
i,s
wage, wt , is a function of labor allocation matrix, Li,s , and the price vector, pi . There-
t t
fore, the aggregate state variable, Î¾t , consists of labor allocations and prices for simulation
purposes.
12
Thanks to the Cobb-Douglass nature of production and utility functions, we can deï¬?ne
the expenditure functions as
N
ï¿¿ï¿¿ ï¿¿ ï¿¿ï¿¿ j
Âµi
t = b j + Î¸i bj + bj + b j yt p j ,
i noc col K t (15)
j=1
where Âµi is the expenditure on sector i product.
t
Finally, we close the model by deriving an equilibrium price equation over the transition
for non-traded goods,
i
Âµi ytâˆ’1
t
pi = pi
t tâˆ’1 . (16)
Âµi
tâˆ’1 yt
i
Note that the equations we derive in this subsection, Aggregate Economy, are not relevant
for the estimation strategy, but they are used for simulations. In the next section we describe
the basic estimation strategy.
3 Estimation Strategy for the Workersâ€™ Problem
Artuc (2012) explains the estimation strategy in detail. The optimization problem of
workers can be expressed with two linear equations, which can be estimated easily with
standard statistical software.
Step 1: Flow Equation
We denote number of type s workers in sector i at time t as Li,s . Then, the number of
t
ij,s ij,s
type s workers moving from sector i to sector j, denoted with zt , is equal to zt = Li,s mij,s .
t t
After multiplying (9) with Li , we get
t
Î² Ëœ j,s 1 Î² Ëœ i,s ï¿¿ ï¿¿
ij,s
zt = exp[ Vt+1 âˆ’ Ctij,s âˆ’ Vt+1 + log Li,s t (17)
Î½
ï¿¿ N Î½ Î½ ï¿¿
ï¿¿ ï¿¿ï¿¿ ï¿¿ ï¿¿
Ëœ k,s Ëœ i,s ik,s 1
âˆ’ log exp Î² Vt+1 âˆ’ Î² Vt+1 âˆ’ Ct ].
k=1
Î½
13
This equation can be considered as a Poisson pseudo maximum likelihood regression
with a destination dummy for sector j, origin dummy for sector i, and a bilateral resistance
dummy for the moving cost7 . This log-linear regression can be expressed as
ï¿¿ i,s ï¿¿
ij,s ij,s
zt = exp Î±t + Î»j,s + Î´t 1(iï¿¿=j) + eij,s ,
t t (18)
i,s
where Î±t is the coeï¬ƒcient of origin dummy, Î»j,s is the coeï¬ƒcient of destination dummy,
t
ij,s
1(iï¿¿=j) is an indicator function equal to one when i ï¿¿= j and zero otherwise, Î´t is the moving
cost coeï¬ƒcient, and eij,s is the regression residual.
t
The regression coeï¬ƒcients can be interpreted as:
Î² Ëœ j,s
Î»j,s =
t V + Î›t ,
Î½ t+1
ij,s C ij,s
Î´t =âˆ’ ,
Î½
and
ï¿¿ N ï¿¿ï¿¿ ï¿¿
Î² Ëœ i,s ï¿¿ ï¿¿ 1ï¿¿
i,s
Î±t = âˆ’ Vt+1 âˆ’ log exp Ëœ k,s Ëœ i,s
Î² Vt+1 âˆ’ Î² Vt+1 âˆ’ C ik,s + log(Li,s ) âˆ’ Î›t ,
t
Î½ k=1
Î½
where Î›t is an unidentiï¬?ed constant common to all j = 1, .., N .
Note that at this step we estimate Î»i,s , which is simply equivalent to the expected value
t
of type s workers in sector i at time t. Unlike most of the dynamic structural estimation
methods, we do not calculate values by backwards solution, but we estimate them from
data. Therefore, all expectations of agents, however they aï¬€ect estimated values, are fully
taken into consideration. If new information arrives about a future event, the workers simply
ï¿¿ i,s
update Vt+1 , which is an estimated parameter. This gives us the convenience of being agnostic
7
Gourieroux et al (1984) introduced Poisson pseudo-maximum likelihood regression, Cameron and Trivedi
(1998) is an excellent source on its applications and Santos Silva and Tenreyro (2006) is an inï¬‚uential paper
that popularized this approach in trade research.
14
about workersâ€™ expectations and distributions of aggregate shocks.
After recovering the moving cost parameters and expected values in this step, we recover
distributional and ï¬?xed utility parameters in the second step, as discussed in the following
subsection.
Step 2: Bellman Equation
In this section, we re-write the Bellman equation that characterizes the optimization
problem of workers using the estimated parameters from Step 1. After multiplying (6) with
Î²/Î½, and aggregating it over possible states and moving all terms to the left hand side, we
get
ï¿¿ ï¿¿
Î² ï¿¿ i,s Î² ï¿¿ ij ï¿¿ ï¿¿ ï¿¿
ï¿¿ Î²ï¿¿ ï¿¿ ï¿¿ ï¿¿
ï¿¿
Et V âˆ’ i,s i,s
Ï€ (s, sï¿¿ ) wt+1 + Î·t+1 âˆ’ ï¿¿ i,s
Ï€ ij (s, sï¿¿ ) Î² Vt+2 + â„¦i,s = 0. (19)
Î½ t+1 Î½ sâˆˆS Î½ sâˆˆS t+1
We plug in the estimated coeï¬ƒcients from Step 1 to construct the second step regression
ij
equation. Note that Î»j corresponds to the expected value expression, Î´t corresponds to
t
the moving cost expression. One important missing parameter is the option value, â„¦i . Let
t
i,s
Ï‰t = â„¦i,s /Î½, thus
t
ï¿¿ ï¿¿
i,s i,s
Ï‰t = âˆ’Î»i,s âˆ’ Î±t + log Li,s .
t t
Finally, we replace the expressions in (19) with Ï‰t and Î»j , and take its diï¬€erence between
i
t
sectors, thus
ï¿¿ ï¿¿ ï¿¿ ï¿¿ ï¿¿ ï¿¿
i,sï¿¿ j,sï¿¿ j,sï¿¿
Et [ Î»i,s âˆ’ Î»j,s âˆ’ Î²
t t Î½
i,s
Ï€ ij (s, sï¿¿ ) wt+1 + Î·t+1 âˆ’ wt+1 âˆ’ Î·t+1
sâˆˆS
ï¿¿ ï¿¿ ï¿¿
ï¿¿ (20)
ij ï¿¿ i,s j,sï¿¿ i,sï¿¿ j,sï¿¿
âˆ’Î² Ï€ (s, s ) Î»t+1 + Ï‰t âˆ’ Î»t+1 âˆ’ Ï‰t ] = 0.
sâˆˆS
The equation (20) can be interpreted as a linear regression equation and no assumptions
are needed on agentsâ€™ expectations for it to hold, except rationality. This is due to the fact
15
that agents do not make any systematic mistakes. Naturally, residuals of the regression
may be correlated across observations within the same time period, this creates bias in
the estimated standard errors. Clustering, as described in Artuc (2012), solves this problem.
Another potential problem is the correlation between the residuals and other variables. Since
residuals capture arrival of new information, lagged variables can be used as instruments
because past variables should be uncorrelated with surprise shocks.
i
We take values of Î»i and Ï‰t from the ï¬?rst step regression and the transition matrix Ï€
t
is already deï¬?ned exogenously. The remaining parameters Î², Î½, and Î· i,s can be estimated
Â¯
using the Instrumental Variables method.
Our estimation strategy is related to ACM, Hotz and Miller (1993) and Arcidiacono and
Miller (2011). The method herein is signiï¬?cantly more eï¬ƒcient compared to ACM, both
econometrically and computationally. Unlike ACM, it can handle rich heterogeneity, small
sectors, and a large number of structural parameters. Arcidiacono and Miller (2011) is based
on the conditional choice probability (henceforth CCP) method introduced by Hotz and
Miller (2011) and an expectation maximization algorithm (henceforth EM). Unlike theirs, our
method does not use maximum likelihood, it is based on orthogonality conditions. Therefore
it does not require parameterization of aggregate shocks, which is a non-trivial convenience
when the economy is subject to shocks that are diï¬ƒcult to model (such as the trade shocks
in the metal and textile sectors). See Artuc (2012) for a detailed comparison.
4 Data
For estimation of the workersâ€™ problem, we use the 1979 cohort of the NLSY and CPS.
The CPS sample is from 1983 to 2001 and constructed in a way similar to ACM: We use
white males, who are between 23 and 64, and who worked at least 26 weeks in a given year.
We have a minimum of 11,857 and a maximum of 20,211 individuals in our ï¬?nal sample
between the years 1984 and 2001 (sample size changes every year). In CPS, the reported
mobility rates are 5 monthsâ€™ mobility rather than annual mobility, we correct the transition
probabilities. CPS is a repeated cross section, so agents are not followed over years. This
16
prevents us from being able to construct work history, thus the sectoral experience parameter
can not be estimated. The work history is also required to identify unobserved heterogeneity.
NLSY is widely used for estimation of occupational choice models, since it follows individ-
uals over years and provides detailed information on work history. The sectoral experience
variable can be easily constructed from NLSY. Initially, NLSY has 12,686 individuals in
the sample, consisting of 6,403 males and 6,283 females. The individuals in our sample are
between 14 and 21 years old as of 1979.
Following the previous research, we only use white males. We also take individuals with
missing observations out, since their sectoral experience can not be calculated correctly.
After this data cleaning procedure, we end up with 1,190 individuals in the sample.
Neal (1999) reports that there are coding errors in NLSY79 regarding occupations. A
similar error is also present for industry codings. In order to minimize this problem, we use
the following method of Neal (1999): Whenever a sector change is reported, we require the
worker to change his employer as well, otherwise it is considered as a coding error and the
original sector is kept.
NSLY follows individuals annually until about age 40, so we can not identify parameters
for older individuals in the model. Only years 1991-1993 have suï¬ƒcient number of obser-
vations to include both experienced and inexperienced workers at the same time, as most
of the individuals in our sample are too young to have suï¬ƒcient sectoral experience before
1991. We do not have enough observations for college graduates, as the metal sector is a
quite small and unskilled labor intensive sector. Because of these data problems, we only
estimate the ï¬?rst step equation for non-college graduates with NLSY.
First, using CPS, we estimate a special case of the model without sectoral experience
and unobserved heterogeneity. Then, using NLSY, we estimate parameters of the general
model for only unskilled workers who are less than 37 years old. Fortunately, we are able to
see the complete picture when we combine estimates from both datasets, as the changes in
worker mobility across diï¬€erent subgroups are fully identiï¬?ed.
17
The industries are aggregated into 4 main sectors: 1. â€œManufâ€?: Manufacturing and
Agriculture (tradable sector), 2. â€œMetalâ€?: Metal Manufacturing (sector subject to policy
change), 3. â€œServiceâ€?: Service except Trade (non-tradable sector), and 4. â€œTradeâ€?: Whole-
sale and retail trade (another non-tradable sector). The industries are aggregated mainly
in two groups, tradable and non-tradable. Since â€œwholesale and retail tradeâ€? is a relatively
large industry, we consider it as a separate sector apart from service.
Table 1 summarizes the distribution of workers across sectors, age, sectoral experience
and education groups in both NLSY and CPS samples. Note that the sectoral experience
variable is not available for the CPS sample and the NLSY sample includes individuals only
up to age 40. Manufacturing and agriculture workers (henceforth manuf.) are approximately
27%, metal workers are about 4%, service workers except trade workers (henceforth service)
are about 49% and ï¬?nally wholesale and retail trade workers (henceforth trade) are close to
20% of the total sample (see Panel A). Panel B shows age distribution and Panel C shows
sectoral experience distribution in the sample. As illustrated in Panel D, about 40% of
workers have college education in the sample.
Table 2 shows example transition probabilities from diï¬€erent age groups, education
groups and sectors. Panel A presents probabilities of sector change for workers with no
college education while Panel B shows it for those with at least one year of college educa-
tion. The eï¬€ect of education on probability of sector change is ambiguous. However, it is
clear that the probability of sector change is decreasing with age for both education groups.
Panel C shows transition probability from one sector to another. As one would expect, the
probability of moving out of a larger sector is lower than the probability of moving out
of a smaller sector, and the probability of moving into a larger sector is higher than the
probability of moving into a smaller sector.
5 Regression Results
We have two data sets, CPS and NLSY, for the estimation. CPS is missing the sectoral
experience and work history variables, while NLSY has enough observations for only limited
18
number of types and a short time-series. Therefore, we consider two separate regressions
for the two data-sets we have in hand. In the next section, when we run counterfactual
simulations, we demonstrate how we use results from both regressions in the same simulation.
Estimation with CPS
Since we do not observe sectoral history, neither unobserved heterogeneity nor sectoral
experience is included. This means that we have to impose two restrictions in order to make
the model identiï¬?able with the CPS data: C 2 = 0 and C 3 = 0. Henceforth, we call this
version of the model the â€œconstrained model.â€?
The restrictions imply that workersâ€™ sectoral experience and unobserved type have no
aï¬€ect on mobility costs. For the ï¬?rst step regression (the ï¬‚ow equation), we correct the
mobility rates reported in CPS to annual rates. Then, we run Poisson pseudo maximum
likelihood regression using (18). For the second step (the Bellman equation), we use time
lagged variables as instruments and run IV regression using (20). We normalize the average
wage in the economy to one. Since we can not identify the discount parameter, Î², we assume
that Î² = 0.95. The estimation procedure is explained in detail in Artuc (2012).
The regression results are reported in Table 3. We ï¬?nd that the moving cost parameter,
C 1,s /Î½, is increasing with age and is between 2.62 and 4.5, signiï¬?cant at the 99% level for all
types. The moving cost does not seem to vary much across education groups. The variance
parameter, 1/Î½, is about 1.67 and also signiï¬?cant at the 99% level. We ï¬?nd that the mean
of the ï¬?xed utility parameter for the metal sector, Î· i,s , is negative and signiï¬?cant at the 99%
Â¯
level for unskilled workers. Also, the mean ï¬?xed utility parameter for the trade sector, Î· i,s ,
Â¯
is positive and signiï¬?cant at the 95% level for skilled workers.
ACM report that the common moving cost parameter for all types, C 1,s , is equal to 6.56
when Î² = 0.97 and 4.7 when Î² = 0.90, relative to the annual average wages normalized
to one. They ï¬?nd that the variance parameter, Î½, is equal to 1.88 and 1.22 respectively.
Diï¬€erently, we use Î² = 0.95 and report parameters divided by the scale parameter v. If
we convert our results to make them consistent with ACM, the estimated moving cost is
19
between 1.57 and 2.69. Note that these are implied mean moving costs faced by agents, not
moving costs paid by those agents who actually move. Because of the random components of
the moving cost, the actual moving cost paid may be small or negative for movers. Thanks
to the new estimation strategy, we are able to estimate a model with much richer worker
heterogeneity, with a larger number of structural parameters and with a higher eï¬ƒciency
compared to ACM.
As we discussed in the introduction, it is diï¬ƒcult to pin down the moving cost parameter
precisely following ACMâ€™s estimation strategy due to the sparsity in workersâ€™ choice prob-
ability matrices, especially when there is heterogeneity. In addition to loss of precision due
i,s
to the sparsity problem, omission of the ï¬?xed utility parameter, Î·t , also causes the moving
cost parameter to be overestimated. We ï¬?nd that workers receive a disutility from working
in the metal sector due to a negative Î· i,s , therefore ï¬‚ows out of the metal sector are much
Â¯
larger than what its relatively high wages would imply. If the ï¬?xed utility parameter is not
included in the model, then the model can only be made to ï¬?t to the data by imposing high
variance, Î½, for the individual shock, ï¿¿i and high moving costs, C 1,s , simultaneously. When
both Î½ and C 1,s are large simultaneously, correlation between outï¬‚ows and wage diï¬€erences
becomes weaker, as the data imply (i.e. workersâ€™ decisions are random). With the inclusion
of Î· i,s , however, the wages and outï¬‚ows are not required to be highly correlated. Even if the
wages are high in a sector, workers still may not choose it if the ï¬?xed utility for that sector
is negative. Thus, ACM report much higher moving costs compared to us, possibly due to
their omission of the ï¬?xed utility parameters.
Estimation with NLSY
With NLSY, we estimate the model for workers with no college education and who are
less than 37 years old. The age restriction is due to the nature of the data as its name
implies, also since the metal sector is small and unskilled labor intensive, we do not have
enough observations to include workers with college education in our sample. Our main goal
is to estimate the moving cost parameter that captures sectoral experience, C 2 , and the
20
extra moving cost paid by the unobserved type II workers, C 3 .
First, we run the regression without types, hence imposing that C 3 = 0. The results are
reported in the ï¬?rst row of Table 4. We ï¬?nd that C 1,s /Î½ is equal to 2.68 for young workers
who are less than 30 years old, similar to what we ï¬?nd with CPS data. We ï¬?nd that C 1,s /Î½
is equal to 3.09 for the workers between 30 and 36, and with less than seven years of sectoral
experience. We ï¬?nd that (C 1,s + C 2 )/Î½ is equal to 4.38 for the workers who are older than
30 years and with more than 7 years experience. All estimates are signiï¬?cant at the 99%
level.
The workers are divided into two unobserved types. In reality, if there is a continuum
of types with diï¬€erent moving costs, then allowing two types of workers is equivalent to
discretizing a continuous distribution into two pieces. Ideally, we would like to discretize
into ï¬?ner grids but it is not possible given the available data. Therefore, we consider two
types, and impose the restriction that C 3 /Î½ = 1, then estimate C 1,s /Î½ and C 2 /Î½, while we
calculate the mass of each type with an EM loop. Although it is theoretically possible with
very detailed data, we can not estimate C 1,s /Î½ and C 3 /Î½ separately without a restriction,
since we do not have enough observations of workers with diï¬€erent work histories. It is
possible to try diï¬€erent values for C 3 /Î½ and change the distance between the centers of mass
of the grids; we ï¬?nd that the weighted average of moving costs C 1,s /Î½ and C 2 /Î½ is robust to
diï¬€erent speciï¬?cations.
The EM loop converges to a distribution with 50% type I and 50% type II. We report
the estimated moving costs for type I workers in the second row of Table 4. Since we impose
C 3 /Î½ = 1, the moving costs for type II workers are exactly one unit larger than type I
workers, which are reported in the third row.
6 Simulations
In the previous section, we estimated parameters of the workersâ€™ optimization problem.
In order to simulate the model, we need to parametrize wage equations, or in other words the
labor demand functions. Thanks to the Cobb-Douglass nature of the production functions, it
21
is straightforward to calculate its parameters using input-output tables. Also, consumption
shares give the consumer price index weights, Î¸i . We use Bureau of Economic Analysis
input-output and consumption share tables to calculate the parameters of the labor demand
equations8 . The calculated parameters are reported in Table 5.
Unlike the estimation step, we need to deï¬?ne all aggregate shocks for the simulations.
We assume that there is an unexpected shock-therapy trade liberalization in the metal man-
ufacturing sector which decreases the metal output price 50%9 . As we discussed previously,
it is practically impossible to model the exact liberalization process in the metal sector as
the trade policy has been changing dynamically. Our simulation exercise is an illustrative
counterfactual. We normalize initial prices to one. After the metal sector trade shock, prices
in the tradable sectors adjust endogenously over the transition, while non-tradable sectorsâ€™
output prices stay constant. Thanks to uniqueness of the equilibrium, and the concavity of
relevant equations, the simulations are straightforward: After we guess initial values for Vti,s
and Li,s for t = 1, 2, .., T , we calculate wi,s , then implied Vti,s and Li,s by the wage ï¬‚ows
t t
using equations presented in the Model section. Using an arbitrarily weighted average of the
initial and implied values and labor allocations, we update the guessed values. We repeat
this procedure recursively until we reach a ï¬?xed point and make sure that the economy
reaches free trade steady state before time T . We omit the details because the simulations
are easy to replicate.
We consider two diï¬€erent speciï¬?cations. Simulation I uses the restrictions we imposed to
estimate the model with CPS (i.e. the constrained model). Hence, we assume that C 2 = 0
and C 3 = 0. Therefore, we directly use the estimated parameters from CPS for Simulation
I. However, Simulation II uses estimates from both NLSY and CPS simultaneously.
First, note that the model with C 2 = 0 and C 3 = 0 imposed as a constraint is called
8
The ï¬?xed capital, K i , is normalized to unity.
9
This 50% price decrease is approximately equal to the change in steel price in the US between 1980 and
1998. Since the US uses about 10% of word metal output, a metal sector liberalization would not aï¬€ect
world price signiï¬?cantly. We experimented with an alternative speciï¬?cation where world price is determined
endogenously and found that the qualitative implications are unchanged.
22
the â€œconstrained model.â€? The estimation procedure outlined in the econometric section of
the paper for the CPS can estimate only the constrained model. However, for any set of pa-
rameters for the â€œunconstrainedâ€? model, one can generate simulated data and estimate the
parameters of the constrained model on the simulated data. A reasonable way of calibrating
the model is to ï¬?nd parameters for the unconstrained model that generate simulated data
that generate estimated parameters for the constrained model that are close to the parame-
ters for the constrained model estimated from the â€œactualâ€? data. That is the approach taken
for Simulation II.
The parameters for Simulation II, that give the same estimates as the actual data, are
reported in Table 6. We ï¬?nd that the second step (the Bellman equation step) regression
results are almost unchanged. Therefore, we understand that the restrictions we impose
on the moving costs in the ï¬?rst step do not bias the second step results. Note that the
restrictions we impose for the CPS estimation essentially aggregate types, i.e. unobserved
type I, type II, experienced and inexperienced workers are clustered into a single type. In
panel D of Table 6, we present weighted averages of moving costs based on age and education
level, which are directly comparable to the numbers presented in Panel A of Table 3. We
show that aggregation is not a signiï¬?cant source of bias, causing only 6 % to 14% diï¬€erence
between estimates of the aggregated and the disaggregated models.
In Table 7, we present steady state labor allocations and wages for CPS, Simulations I and
II. Although we do not attempt to match them in the simulations, the implied distributions
are close to the actual data.
In Figures 1 to 5, we present the results for Simulation I. For the sake of clarity, we only
illustrate the sector averages because there are 12 types of workers in Simulation I and 48
types of workers for Simulation II. Since the results for Simulation II are almost identical
to these, we omit them. In Figure 1, we show how workers react to the 50% drop in metal
price. After the price drop, real wages decrease causing an increase in outï¬‚ows from the
metal sector. We ï¬?nd that 25% of the metal workers leave their sector within one year after
23
the shock, and this number reaches 45% in the long run.
When metal workers leave their sector, the output decreases as seen in Figure 2. Note that
metal sector output is used as an input in the manufacturing sector, so the manufacturing
sector grows signiï¬?cantly after this trade shock. In Figures 3 and 4, we show the change in
unskilled and skilled workersâ€™ wages respectively. We ï¬?nd that the metal sector wage drops
signiï¬?cantly as expected, while the manufacturing sector wage increases due to the decrease
of the metal price as an important input. After this initial change, the metal sector wage
increases as workers leave their sector, but can not catch up with the original wage.
In Figure 6, we report the change in workersâ€™ present discounted value based on their age
and skill level. Since metal is an unskilled labor intensive sector, workers without college
education are more hurt in the metal sector compared to workers with college education.
Skilled workers beneï¬?t more in the manufacturing sector. The unskilled workers, especially
young workers, are almost unaï¬€ected. We ï¬?nd that young workers in the metal sector are
not as hurt as the middle aged workers. Initially, the impact of trade shocks increases with
age, but since the time horizon gets shorter this eï¬€ect is diminished for workers who are older
than 50 years. We ï¬?nd that workers are split based on their sectors, and other factors are
not important as workersâ€™ sectors. All metal workers are worse oï¬€, while all manufacturing
workers are better oï¬€ regardless of their education and experience level.
In Figures 7 to 9, we report welfare results for Simulation II. In Figure 7, worker types
are aggregated and the weighted averages of welfare changes for workers from diï¬€erent age
and education groups are reported. Surprisingly, Figures 6 and 7 are almost identical. So we
ï¬?nd that aggregating workers (as in Simulation I) does not aï¬€ect the welfare implications of
the model. Since studying welfare changes after the policy shock is our main interest, we can
conclude that Simulation I is less informative compared to Simulation II since it has fewer
worker types, but it is not necessarily biased.
Figures 8 and 9 show that as the moving cost increases, either with sectoral experience or
unobserved type, the impact of trade shocks on workers increases in both directions. Workers
24
with higher moving costs are hurt more in the metal sector, as they are less likely to leave
their sector and suï¬€er from the lower wages. Intriguingly, the workers with higher moving
costs beneï¬?t more in the manufacturing sector. Because workers with higher moving costs
are less likely to leave manufacturing, and more likely enjoy higher wages in the long run
compared to others. The manufacturing workers with lower moving costs are more likely
to end up in the metal sector; this decreases the change in their expected welfare relative
to the workers with higher moving costs. This result can be generalized for age as well:
As workers get older their moving costs increase and the impact of trade shocks increases.
However, at the same time workersâ€™ time horizon gets shorter; this decreases the impact
simultaneously. The second eï¬€ect starts to dominate after workers reach age 50. Therefore,
in general, large moving costs magnify the impact of trade shocks for both winners and losers
(with an exception of workers who are close to retirement).
7 Conclusion
We estimate a dynamic model of labor mobility using US data, CPS and NLSY. We
ï¬?nd that moving costs increase with age and experience, but are unchanged with work-
ersâ€™ education level. Then, we simulate a counterfactual trade liberalization in the metal
manufacturing sector using the estimated labor mobility model and calibrated production
function parameters in a general equilibrium setting. We consider two alternatives with
diï¬€erent levels of heterogeneity and ï¬?nd that aggregating worker types does not change the
welfare implications of the model.
We show that trade shocks aï¬€ect workers with higher mobility costs more, for both
winners and losers of the policy shocks. In the metal sector, workers with higher moving
costs are hurt more, while in the manufacturing they beneï¬?t more. But the eï¬€ects are
non-monotonic and they taper oï¬€ over a workerâ€™s lifetime, especially when they are close
to retirement. We also ï¬?nd that a workerâ€™s sector is the main determinant of how he is
aï¬€ected; this shows that moving costs are large enough to cause signiï¬?cant wage diï¬€erentials
across sectors, in contrast with models that have perfect labor mobility and factor price
25
equalization.
The estimation strategy herein is more eï¬ƒcient and easier to implement compared to
ACM. It can handle rich heterogeneity and allows estimation of workersâ€™ expected values
without solving their optimization problem explicitly. This feature of our method is especially
important when it is diï¬ƒcult to parameterize workersâ€™ expectations due to policy shocks.
This new method can be easily applied to other discrete choice problems, such as migration,
occupational choice, education choice, and others.
26
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28
Table 1 - Distribution of Workers
Panel A: Sectors
Sector NLSY CPS
Manuf 27.5% 27.2%
Metal 3.8% 3.3%
Service 50.1% 52.9%
Trade 18.6% 16.6%
Panel B: Age
Age NLSY CPS
23 to 29 56.6% 17.1%
30 to 36 44.4% 23.3%
37 to 43 NA 21.5%
44 to 50 NA 17.0%
51 to 57 NA 13.1%
58 to 64 NA 7.9%
Panel C: Sectoral Experience
Experience NLSY CPS
1 to 7 78.9% NA
8 to 14 21.1% NA
Panel D: Education
Education NLSY CPS
No-college 59.9% 59.4%
College 40.1% 40.6%
Table 2 - CPS Transition Probabilities
Panel A: Non-College Graduates
Age Manuf Metal Service Trade
23 to 29 0.067 0.076 0.055 0.090
30 to 36 0.041 0.050 0.032 0.061
37 to 43 0.030 0.035 0.021 0.041
44 to 50 0.022 0.035 0.017 0.036
51 to 57 0.018 0.016 0.014 0.026
Panel B: College Graduates
Age Manuf Metal Service Trade
23 to 29 0.065 0.085 0.039 0.104
30 to 36 0.041 0.065 0.019 0.060
37 to 43 0.032 0.048 0.015 0.046
44 to 50 0.033 0.046 0.011 0.042
51 to 57 0.025 0.050 0.010 0.033
Panel C: Transition Matrix
Manuf Metal Service Trade
Manuf 0.963 0.002 0.025 0.011
Metal 0.019 0.954 0.020 0.007
Service 0.011 0.001 0.977 0.011
Trade 0.017 0.002 0.039 0.943
Table 3: Regression Results with CPS
Panel A: First Step, Moving Cost (C1/!)
No-college College
Age Estim SE Estim SE
23 to 29 2.62 (0.04) 2.66 (0.04)
30 to 36 3.19 (0.04) 3.34 (0.04)
37 to 43 3.57 (0.04) 3.64 (0.04)
44 to 50 3.84 (0.04) 3.78 (0.05)
51 to 57 4.14 (0.05) 4.10 (0.06)
58 to 64 4.50 (0.07) 4.19 (0.10)
Panel B: Second Step, Variance Parameter (1/!)
Estim SE
1.67 (0.51)
Panel C: Second Step, Average Fixed Utility ("/! )
No-college College
Sector Estim SE Estim SE
Manuf 0.00 NA 0.00 NA
Metal -0.34 (0.07) -0.17 (0.12)
Service 0.02 (0.07) 0.08 (0.11)
Trade 0.10 (0.09) 0.35 (0.16)
Table 4: Moving Cost Estimates with NLSY, Non-College (C/!)
Age 23 to 29, Exp<7 Age 30 to 36, Exp<7 Age 30 to 36, Exp>7
C1/! C1/! C1/!+C2/!
Type Estim SE Estim SE Estim SE
Both 2.68 (0.11) 3.09 (0.15) 4.38 (0.19)
I 2.21 (0.07) 2.96 (0.16) 3.88 (0.26)
II 3.21 NA 3.96 NA 4.88 NA
Table 5 - Calibration of Production and Utility Functions
Panel A: Cobb-Douglas Production Function Input Shares
Manuf Metal Service Trade
Labor-Noc 0.10 0.18 0.16 0.21
Labor-Col 0.08 0.07 0.21 0.16
Capital 0.13 0.13 0.29 0.27
Manuf 0.35 0.07 0.08 0.04
Metal 0.05 0.29 0.01 0
Service 0.24 0.19 0.23 0.3
Trade 0.05 0.07 0.02 0.02
Panel B: Cobb-Douglas Production Function Constant
Manuf Metal Service Trade
B 2.10 0.33 2.17 0.91
Panel C: Cobb-Douglas Utility Function Shares
Manuf Metal Service Trade
! 0.4 0 0.6 0
Panel D: Units of Human Capital, Unskilled Labor Input (No-College)
Age Manuf Metal Service Trade
23 to 29 1.00 1.00 1.00 1.00
30 to 36 1.19 1.14 1.21 1.23
37 to 43 1.32 1.24 1.32 1.38
44 to 50 1.40 1.30 1.38 1.43
51 to 57 1.39 1.29 1.35 1.41
58 to 64 1.30 1.29 1.26 1.30
Panel E: Units of Human Capital, Skilled Labor Input (College)
Age Manuf Metal Service Trade
23 to 29 1.00 1.00 1.00 1.00
30 to 36 1.27 1.27 1.35 1.35
37 to 43 1.48 1.50 1.57 1.60
44 to 50 1.61 1.69 1.67 1.68
51 to 57 1.66 1.68 1.71 1.67
58 to 64 1.63 1.67 1.65 1.49
Table 6: Parameters for Simulation II
Panel A: Moving Cost (C1/")
Age No-college College
23 to 29 2.29 2.37
30 to 36 2.60 2.75
37 to 43 2.89 2.98
44 to 50 3.10 3.07
51 to 57 3.33 3.34
58 to 64 3.60 3.37
Panel B: Average Fixed Utility (!/" )
Sector No-college College
Manuf 0.00 0.00
Metal -0.31 -0.11
Service 0.02 0.08
Trade 0.10 0.36
Panel C: Other Parameters
(1/") 1.67
C2/" 0.91
Panel D: Implied Average Moving Cost (C1/")
Age No-college College
23 to 29 2.79 2.87
30 to 36 3.69 3.89
37 to 43 4.06 4.19
44 to 50 4.31 4.31
51 to 57 4.58 4.61
58 to 64 4.89 4.66
Table 7: Simulated Wages and Labor Allocations
Labor Allocations
Manuf Metal Service Trade
Data 27.26% 3.36% 52.73% 16.65%
Simulation I 27.88% 3.35% 51.27% 17.50%
Simulation II 27.80% 3.39% 51.38% 17.43%
Average Wages
Manuf Metal Service Trade
Data 1.02 0.97 1.05 0.89
Simulation I 1.00 0.97 1.07 0.87
Simulation II 1.00 0.96 1.06 0.87
Figure 1: Percent Change in Labor Allocation
5
0
âˆ’5
âˆ’10
âˆ’15
% ! Workers
âˆ’20
âˆ’25
âˆ’30
âˆ’35
Manuf
âˆ’40 Metal
Service
Trade
âˆ’45
âˆ’2 0 2 4 6 8 10
time
Figure 2: Percent Change in Output
10
0
âˆ’10
% ! Output
âˆ’20
âˆ’30
âˆ’40
Manuf
Metal
Service
Trade
âˆ’50
âˆ’2 0 2 4 6 8 10
time
Figure 3: Average Wages (Noâˆ’College)
0.95
0.9
0.85
0.8
Normalized Wage
0.75
0.7
0.65
Manuf
0.6
Metal
Service
Trade
0.55
âˆ’2 0 2 4 6 8 10
time
Figure 4: Average Wages (College)
1.4
1.3
1.2
Normalized Wage
1.1
1
0.9
0.8 Manuf
Metal
Service
Trade
0.7
âˆ’2 0 2 4 6 8 10
time
Figure 5: Average Values
18.5
18
17.5
Present Discounted Value
17
16.5
16
15.5 Manuf
Metal
Service
Trade
15
âˆ’2 0 2 4 6 8 10
time
Figure 6: Age, Education and Welfare Change (Simulation I)
0.2
0
âˆ’0.2
Change in Value
âˆ’0.4
âˆ’0.6
Metalâˆ’noc
Manufâˆ’noc
âˆ’0.8
Metalâˆ’col
Manufâˆ’col
26 33 40 47 54 61
age
Figure 7: Age, Education and Welfare Change (Simulation II)
0.2
0
âˆ’0.2
Change in Value
âˆ’0.4
âˆ’0.6
Metalâˆ’noc
Manufâˆ’noc
âˆ’0.8
Metalâˆ’col
Manufâˆ’col
26 33 40 47 54 61
age
Figure 8: Age, Experience and Welfare Change (Simulation II)
0.2
0
âˆ’0.2
Change in Value
âˆ’0.4
âˆ’0.6
Metalâˆ’in
Manufâˆ’in
âˆ’0.8
Metalâˆ’ex
Manufâˆ’ex
26 33 40 47 54 61
age
Figure 9: Age, Unobserved Types and Welfare Change (Simulation II)
0.2
0
âˆ’0.2
Change in Value
âˆ’0.4
âˆ’0.6
Metalâˆ’I
Manufâˆ’I
âˆ’0.8
Metalâˆ’II
Manufâˆ’II
26 33 40 47 54 61
age