Discussion Paper No. 658

JOB SEARCH, BARGAINING, AND
WAGE DYNAMICS
Shintaro Yamaguchi
The Eighth ISER-Moriguchi Prize (2006)
Awarded Paper

April 2006

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, JapanJOB SEARCH, BARGAINING, AND WAGE DYNAMICSSHINTARO YAMAGUCHIA BSTRACT. What are the sources of rapid wage growth during a worker’s early career? To address
this question, I construct and estimate a model of strategic wage bargaining with on-the-job search
to explore three different components of wages: general human capital, match-specific capital, andbargaining position. Workers search for alternative job opportunities on the job and accumulate
human capital through learning-by-doing. As the workers find better job opportunities, the current
employer has to compete with outside firms to retain them. This between-firm competition improves
the outside option value of the worker, which results in wage growth on the job even when productivity remains the same. The model is estimated by a simulated minimum distance estimator and datafrom the NLSY 79. The parameter estimates are used to simulate counterfactuals. Through thesesimulations I find that only 60% of the observed wage growth reflects the accumulation of generalhuman capital. The growth match-specific capital through job changes accounts for about 20%. The
improved bargaining position explains the remaining 20% of the wage growth. The results suggestthat labor market frictions explain a larger part of wage growth than previously considered in theliterature.

1. I NTRODUCTION
Wages of young workers grow rapidly. For example, a typical male high-school graduate in the
U.S. can expect 55% of wage growth during the first ten years of his permanent transition to thelabor market. This early wage growth accounts for about two thirds of the entire wage growthover the lifetime. Given that new entrants to the labor market can look forward to about 40 yearsof work, this fact implies that a major part of wage growth occurs in a relatively short period oftime. The objective of the paper is to empirically understand the sources of wage growth of young
workers.
One standard interpretation is based on the accumulation of human capital. Workers learn skills
more quickly while they are young. The rapid wage growth can be interpreted as a direct consequence of the rapid accumulation of human capital. Another explanation is job turnover. Young
Date: April 9, 2006.
Address: Department of Economics, University of Wisconsin, 1180 Observatory Drive, Madison, WI 53706, URL:
www.ssc.wisc.edu/~syamaguc, Email: syamaguchi@wisc.edu. I am grateful to my advisors John Kennan, Maurizio Mazzocco, and Bruce Hansen for guidance and support. I have also benefited from comments by
Jonathan Hore, Daiji Kawaguchi, Rasmus Lentz, Salvadore Navarro, Shiv Saini, Hisatoshi Tanaka, Nori Tawara,
James Walker, Jason Wu, and seminar participants at Bank of Japan, ISER at Osaka, McMaster, Midwest Econometrics Group, Search Theory Workshop, Statistical Institute, Penn State, Western Ontario, Wisconsin, and York. This
paper is awarded the 8th ISER-Moriguchi Prize. Financial support from Christensen Award in Empirical Economics
is gratefully acknowledged. All remaining errors are mine.
1

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workers change jobs frequently. Workers start their careers without detailed knowledge about thenature of their jobs or where they can find better jobs. They gradually find a better place to work.
Wages grow when a worker finds a better job and switches from the current job to a new job.
Topel and Ward (1992) find that about a third of early career wage growth can be explained byjob switching. This paper considers another source of wage growth: the value of outside optionof workers. This effect can increase wages even when a worker stays with the same employer andproductivity remains the same.
In my model employed workers are occasionally contacted by firms other than the current employer. When the value of the offer is better than that of the current employment contract, theworker wants to quit the current job to accept the offer. However, the current employer may bewilling to pay the worker a higher wage to retain him. In this way, offers from outside firms improve the bargaining position of a worker when he renegotiates wages with the current employer.
Wages can grow due to an increase in outside option value, even when productivity remains thesame. A worker is in a position of renegotiation, because rent from a match exists due to search
frictions. Workers do not have alternative job opportunities in hand, while firms are not able toimmediately find new workers that replace the current employees. Finding an alternative partner
who is as good as the current partner is more difficult when agents are heterogeneous, because theagents similar to the current partner can be scarce in the market. This labor market friction is asource of the rent from a worker-firm match.
Understanding the sources of wage growth is important for active labor market policies. If alarge fraction of wage growth is due to the labor market frictions, policies that attempt to accelerate matching process will have significant effect on individual wages. Public Employment
Services that assist job search not only reduce unemployment, but also enhance the wage growthof employed workers.
To consider the effects of outside option value, match quality, and human capital accumulation
on wages, I develop and estimate a model of on-the-job search with strategic bargaining. The modelis based on a continuous-time search model in which unemployed and employed workers searchfor jobs that are characterized by idiosyncratic match quality. On the one hand, employed workers
accumulate human capital through learning-by-doing. On the other hand, they occasionally receive
job offers from new potential employers. When the match quality with a new potential employer ishigh enough, a bargaining game begins among three-players: the worker, the current employer, anda new potential employer who attempts to recruit him. In this three-player bargaining, a worker
first bargains with a firm that is strategically chosen by the worker. He then bargains with theother firm if the bargaining with the first firm is not successful. The worker exploits these multiple
job opportunities and uses a firm as a threat in bargaining with another firm. Wages grow overthe duration of a job, not only because workers accumulate human capital, but also because theyreceive job offers, which improves their value of outside option.

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My work is related to the paper by Postel-Vinay and Robin (2002) that analyzes wage dispersion
in France using a model of on-the-job search with counteroffers. Although their model has somesimilar features to my model, they focus on wage distribution in a stationary equilibrium, instead ofwage dynamics. To address the question of sources of wage growth, my model departs from theirprevious contributions in two ways. First, the model allows for productivity growth of workers
through learning-by-doing. The productivity growth contributes to wage growth, because it increases not only the value of a match, but also the value of outside option such as unemployment.
The intuition is that experienced workers are more likely to get employed and that they would havehigher value of a match if they are employed. My empirical results suggest that the growth ofworker productivity actually explains the largest part of wage growth. Second, wage renegotiation
following idiosyncratic productivity shocks is considered in this paper. The model by Postel-Vinay
and Robin (2002) does not predict any wage decreases on the job and it assumes exogenous destruction of a match. In contrast, in my model productivity shocks may cause a wage decrease on
the job and a separation endogenously occurs if a match becomes inefficient due to negative productivity shocks. The price of these extensions is that an explicit solution to the equilibrium wage
and its distribution are too complicated to be derived analytically because of nonstationarity. I use
a numerical solution for simulation and estimation of the model. These extensions are important
to match the observed dynamics of wages and worker flows.
The main contribution of the paper is to empirically explore the effect of bargaining position
on wages of young workers. The structural parameters of the model are estimated by a simulated
minimum distance estimator using a sample of white male high school graduates from the National
Longitudinal Survey of Youth 1979. To quantify the effect of labor market frictions on wages,
the parameter estimates are used to simulate two counterfactuals. In the first simulation, labormarket friction is shut off so that workers are able to find the best matches immediately. In theabsence of frictions, wage growth is solely driven by the accumulation of human capital. In thissimulation, wages grow by 30% during the first ten years of their careers, which implies that
only about 60% of the observed wage growth reflects the accumulation of human capital. In thesecond simulation, human capital does not grow so that wage growth is driven by finding a better
match and improving the value of outside option. In particular, on-the-job wage growth is solely
explained by the improved value of outside option. In this simulation, wages grow on the job by
10% and the overall wage growth rate is 20% in the first ten years, which implies that the improved
value of outside option can account for about one fifth of the observed wage growth. The resultsfrom two counterfactuals indicate that labor market frictions explain a larger part of wage growththan previously considered in the literature.
The plan of the paper is as follows. The following section reviews the related literature. The
theoretical model is presented in section 3. Section 4 describes the data. The estimation strategy
is detailed in section 5. The estimation results are discussed and the estimates are used for wage

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decomposition in section 6. Section 7 concludes. Proofs and technical details are gathered inappendices.

2. R ELATED L ITERATURE
2.1. Theoretical Work. There is an extensive literature on labor market matching models withon-the-job search. Burdett and Mortensen (1998) develop a model in which firms post wages
and workers search while working. The firms that post low wages experience high quit rates andvice versa, because workers switch jobs when they meet a better-paying employer. They showthat equilibrium wage dispersion occurs with homogeneous workers and firms. Notice that thismodel assumes that firms have all the power to set wages and that they do not have information
on workers’ alternative job opportunities. The first point is revisited by Shimer (forthcoming).
He considers a wage bargaining game in a similar setting rather than assuming that wages areposted. Shimer (forthcoming) finds that the equilibrium wage dispersion still occurs when wages
are bargained, rather than being posted. The model differs from these papers in that firms know
workers’ alternative job opportunities and thus, equilibrium wages differ within a firm. I derive
wage growth on the job as well as wage growth when workers changes jobs.
Dey and Flinn (2005) and Cahuc, Postel-Vinay, and Robin (2005) consider bargaining models
with on-the-job search that are similar to ours. Dey and Flinn employ the axiomatic Nash bargaining solution. Cahuc et. al. find the same equilibrium outcome as Dey and Flinn using analternating offer game. Because their models are to explain the equilibrium distribution of wages(and health insurance), they are restrictive for the study of wage dynamics. To match the observed
patterns of wage dynamics and labor mobility, I depart from these prior contributions by allowing
for general human capital accumulation and wage renegotiation following productivity shocks.
Kiyotaki and Lagos (2005) consider a model in which both workers and firms look for otherpotential partners after they have already formed a match. They explore worker and job flows
and find that their modified competitive matching equilibrium achieves the efficient allocation ofworkers and firms. One important assumption here is that a firm employs at most one worker. On
the contrary, I allow firms to employ more than one worker. Unlike their model, workers are notdemoted or laid off when firms meet a new worker in my model.
This paper is also related to the papers that study intra-firm multilateral wage bargaining. Stoleand Zwiebel (1996a) are one of the first to present such a model in which one firm and many
employees independently bargain over wages. Their main finding is that the firm employs moreworkers than the efficient level, in order to lower the bargaining position of each worker. If workers
are heterogeneous, the workers with relatively scarce skills have better bargaining positions. Thisapproach focuses on bargaining inside the firm and thus, it is well suited to study organizational
structure (see Stole and Zwiebel, 1996b.) In contrast, I focus on the interactions with potential employers outside the firm. The bargaining position of a worker is characterized by job opportunities

JOB SEARCH, BARGAINING, AND WAGE DYNAMICS

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outside the incumbent firm, rather than his situation inside the firm. I argue that my approach iswell suited for my objective to study wage growth over the career, because one important featureof the labor market for young workers is high job turnover. My model directly considers the link
between job search and bargaining.
2.2. Empirical Work. There are a number of empirical papers that study wage growth. Topeland Ward (1992) estimate the ‘pure’ wage gain from job changes; they find that job changes canaccount for about 30% of early-career wage growth. They estimate on-the-job wage growth rate
and use it to construct counterfactual wage growth that the worker could have if he remains inthe same firm. The difference between the actual wage and the counterfactual wage is the ‘pure’
wage gain from the job change. However, they do not analyze the components of on-the-job wage
growth. I depart from their contribution in that I further decompose on-the-job wage growth into
the human capital effect and the bargaining effect.
Many papers that try to decompose on-the-job wage growth focus on the returns to tenure,instead of bargaining. Topel (1991), Altonji and Shakotko (1989), Abraham and Farber (1987),
and some others attempt to measure the returns to tenure. There is still an on-going debate about
the magnitude of the returns to tenure. One important lesson from this debate is that the regression
based approaches are mostly biased and it is very difficult to find a consistent estimator for returns
to tenure using only wage data and records of job change. Labor participation, job change, andwages are all simultaneously determined and there must be additional information to distinguishthe returns to tenure from other components of on-the-job wage growth. One possible solution
is to use a fully specified model. Abowd and Kang (2002) and Buchinsky et al. (2004) study inthis direction. My approach is closer to Abowd and Kang (2002) and Buchinsky et al. (2004) inthe sense that I use both the variation in the data and the theory for identification. It is true that
their models are more flexible than ours, but the model captures the important features of wage
and job mobility data, and it explains explicitly why and how wages grow. I differ from theserecent contributions in that I emphasize the economic interpretation, rather than the statisticaldecomposition.
3. T HE M ODEL
3.1. Setup. I consider the labor market for infinitely lived ex ante heterogeneous workers and ex
post heterogeneous firms. Both the workers and the firms are risk neutral, have the same interest
rate r, and have complete access to the capital market. Workers are heterogeneous with respect toinnate ability γ0 and general human capital h. Innate ability is fixed for each individual’s lifetime,
while general human capital grows with work experience. Both are precisely observed by all agentsin the economy.
Unemployed workers receive utility value b, including both pecuniary and non-pecuniary unemployment benefits, and meet a firm at a rate of λ0 . Employed workers receive a flow wage payment

JOB SEARCH, BARGAINING, AND WAGE DYNAMICS

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w and produce a flow output y. They are also contacted by firms other than the current employer at
a rate of λ. When a worker is contacted by a firm, match quality θ and an idiosyncratic shock to thematch θ are drawn from distributions with CDFs F and G, respectively. Both θ and θ are bounded
above θM AX , θ,M AX and below θM IN , θ,M IN . All workers and firms precisely observe the valuesof the match quality θ and the idiosyncratic shock θ . The accumulation of match-specific human capital is captured by a stochastic growth of match quality. This modeling saves the amountof computation because no additional state variable such as tenure is used, although an alternative(and more common) way is that match-specific capital grows with tenure. The match quality grows
from θ to θ+ (θ) at the Poisson rate of δ1 (θ). The idiosyncratic shock changes occasionally at the
Poisson rate of δ.
Firms are ex post heterogeneous in the sense that match quality varies across firms. However,they are ex ante homogeneous because neither workers nor firms know their match quality until
they meet. A match is exogenously destroyed at a rate δ0 due to family problem, health problem,and etc.
General human capital is accumulated through learning-by-doing while workers are employed
and it does not depreciate. This implies that human capital does not change while workers are
unemployed. Hence I have h(t + a) ≥ h(t) ∀a > 0 where t is the index for time and equality
holds only when workers are unemployed from period t to period t + a. I also assume that humancapital does not grow once it reaches a certain level h̄ < ∞.
The output y produced by a worker-firm match is strictly increasing in innate ability γ0 , generalhuman capital h, match quality θ, and idiosyncratic shock to the match θ . For example, theproduction function can take a multiplicative form y = exp(γ0 + γ1 h + γ2 h2 ) · θ · θ where γ1 > 0and γ2 < 0.
The assumption that all workers meet firms at the same rate and draw match quality from thecommon distribution may seem restrictive, because high-skilled workers should receive more job
offers and face a better distribution of job opportunities. This observation is plausible and it is also
true in the model. The intuition is that I distinguish between meeting rates (λ and λ0 ) and offer
rates. In the model, the high-skilled workers receive more job offers than the low-skilled workers
when they meet the same number of firms. Firms are less likely to employ unskilled workers
because they are unproductive. Moreover, high-skilled workers face a better distribution of job
opportunities, even though all workers have the common match quality distribution F . To see this,consider the distribution of productivity of a match, rather than the distribution of match quality.
The distribution that high-skilled workers face is better than that for low-skilled workers in thesense of first order stochastic dominance because the productivity is increasing in innate ability

JOB SEARCH, BARGAINING, AND WAGE DYNAMICS

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and human capital. For example, if the production technology is additive in workers’ skill andmatch quality, workers’ skill shifts the productivity distribution to the right.1
3.2. Wage Bargaining.
3.2.1. Bilateral bargaining between an unemployed worker and a firm. Unemployed workers receive unemployment benefit b and meet a firm at the Poisson rate of λ0 . When an unemployedworker meets a firm, the match quality θ and idiosyncratic shock θ to the match are randomly
determined. The worker and the firm bargain over an employment contract given all relevant information such as skill and match quality. Once the contract is signed, the firm pays a constantflow of wage w and the worker supplies flow of labor service until the contract is renegotiatedor separation occurs. The contract is renegotiable with mutual consent. Also, workers can quit a
job and firms can fire workers at any time (employment at will.) The contract also expires whenthe employee negotiates an employment contract with a third party firm. This assumption implies
that the worker cannot be re-employed by the current employer under the current contract when
he bargains with a third party firm and the bargaining fails. This assumption does not imply thatworkers are fired because of a bargaining with outside firms, but it does imply that the incumbent
firm is not bound by the existing contract. As it will be shown below, in equilibrium the worker
bargains with outside firms only when he actually leaves the current employer. There is also atechnical reason for the assumption, which will be discussed in subsection 3.2.2.
I use a strategic approach to describe the bargaining process, rather than employing an axiomatic
Nash bargaining solution. One advantage of this approach is that it clarifies the bargaining process.
The bargaining environment is similar to Binmore (1987) in the sense that the proposer of an offer
at each bargaining round is randomly chosen by nature. The worker and the firm are allowed toquit bargaining to look for another partner. However, to do so, the agent must wait for the offerfrom the other agent. The bargaining might break down into disagreement at the Poisson rate s
because of exogenous factors such as the worker’s family emergency. For simplicity, I assume
that a worker and a firm bargain in artificial time so that the worker and the firm discount payoffs
from the bargaining by a different interest rate ρ from that used for production, which is r. The
bargaining takes the following steps over an infinite horizon. I assume that a worker and a firm
accept an offer when they are indifferent.
(1) Nature determines the proposer at the beginning of each round. The worker makes an offerwith probability β, while the firm makes an offer with probability 1 − β.
(2) The respondent has the following three options.
• Accept the offer and start production.
• Reject the offer and look for other potential partners.
1

Strictly speaking, the value of a job is not measured by the productivity at the time when a worker and a firm meet.
But, as I will see below, the value of a job is strictly increasing in the initial productivity and the argument here stillworks.

JOB SEARCH, BARGAINING, AND WAGE DYNAMICS

8• Reject the offer, but wait for the next round after time ∆ elapses. The bargaining may
break down with the probability s∆ before they reach the next round (go back to step
1.)
The probability β that the worker makes an offer is the measure of the worker’s bargaining power.
The intuition is that agents with high bargaining power take the initiative during the bargaining
process. Thus, when a worker has high bargaining power, the offers are made more frequently
from the worker’s side.
Let Θ = {θ, θ } be the vector of match quality and idiosyncratic shock to the match. The
continuation values of employed workers and firms are denoted by U (h, Θ, w) and V (h, Θ, w),
respectively. Let U0 (h) be the continuation value for unemployed workers. I omit the innate
ability γ0 in the notation, because it is constant over time. The firms’ value of a vacancy is zero
because of the free entry condition. I find it convenient to define the joint value J(h, Θ),J(h, Θ) = U (h, Θ, w) + V (h, Θ, w).
Observe that w does not change the joint value J, although it certainly changes the allocation. This
will be clear when I see the condition for job turnover and the equilibrium payoffs in the case ofjob turnover, which are both independent of wages.
Lemma 3.1. The following outcome of the bilateral bargaining between an unemployed worker
and a firm is obtained when ∆ → 0 and ρ → 0.
1. J(h, Θ) < U0 (h): If the match is inefficient, they immediately separate to look for otherpotential partners. The resulting payoffs are {U0 (h), 0}.
2. J(h, Θ) ≥ U0 (h): If the match is efficient, they sign a contract immediately and the resulting
payoffs are{U (h, Θ, w), V (h, Θ, w)} = {βJ(h, Θ) + (1 − β)U0 (h), (1 − β)(J(h, Θ) − U0 (h))}.
Proof. See appendix A.

This is a fairly standard result in bargaining problems. From the viewpoint of axiomatic Nashbargaining solution, one interpretation is that the worker’s threat point is U0 and the firm’s threat
point is 0. They split the surplus J − U0 and the worker takes his fraction of β as well as U0 . The
contract is signed only when the match is efficient.
3.2.2. Multilateral bargaining between a worker and two firms. Employed workers are contacted
by firms other than the current employer at a rate λ. When a worker meets a firm, the worker
draws a match quality with the new firm and an idiosyncratic shock to the match. The outcome isprecisely observed by the worker, the new firm, and the incumbent firm. The bargaining procedureamong three players is the following:

JOB SEARCH, BARGAINING, AND WAGE DYNAMICS

9(1) The worker decides whether or not to initiate bargaining. If he decides not, the challenger
firm leaves and the current contract remains effective. If he decides to initiate bargaining,
the worker chooses which firm to start with first.
(2) The bargaining starts between the worker and the firm that is chosen by the worker in theprevious step.
(a) Nature determines the proposer at the beginning of each round. The worker makes anoffer with probability β, while the firm makes an offer with probability 1 − β.
(b) The respondent has the following three options.
• Accept the offer and start production.
• Reject the offer to look for other potential partners. If this is chosen, the firm
leaves and the worker starts bargaining with the remaining firm.
• Reject the offer, but wait for the next round (go back to step 2-a) after time ∆elapses. The bargaining may break down with probability s∆ before they reachthe next round. If this occurs, the firm leaves and the worker starts bargaining
with the other firm.
(3) If the worker does not reach an agreement with the firm initially chosen, the worker starts
bargaining with the remaining firm. The structure of the bargaining is exactly same as theone occurs between an unemployed worker and a firm.

The worker bargains with firms in order and the order is chosen by the worker. The intuition forthis assumption is that a worker and two firms do not meet at the same bargaining table in reality.
It is also plausible that the worker can schedule a job interview in a time convenient for him.
Let ΘC and ΘN be the vectors of match quality and idiosyncratic shocks to the match withthe current employer and the new potential employer, respectively. In the following, I assume
that the match with the current employer is efficient. This is actually true in equilibrium because
no inefficient matches exist. Also, the worker prefers the current employer to the new potential
employer and he prefers not bargaining when he is indifferent.

Lemma 3.2. The following equilibrium outcome of the three-player bargaining is obtained when
∆ → 0 and ρ → 0.
1. J(h, ΘC ) ≥ J(h, ΘN ) and U (h, ΘC , w) ≥ βJ(h, ΘC ) + (1 − β)[βJ(h, ΘN ) + (1 − β)U0 (h)]:the worker does not initiate bargaining. The worker stays with the current employer and the current
contract remains effective.
2. J(h, ΘC ) ≥ J(h, ΘN ) and βJ(h, ΘC ) + (1 − β)[βJ(h, ΘN ) + (1 − β)U0 (h)] > U (h, ΘC , w):
the worker first bargains with the current employer. The outcome is that the worker stays withthe current employer and he is promoted. The equilibrium payoffs of the worker and the current

JOB SEARCH, BARGAINING, AND WAGE DYNAMICS

10employer are{U (h, ΘC , w), V (h, ΘC , w)} = {βJ(h, ΘC ) + (1 − β)[βJ(h, ΘN ) + (1 − β)U0 (h)],(1 − β)[J(h, ΘC ) − βJ(h, ΘN ) − (1 − β)U0 (h)]}3. J(h, ΘN ) > J(h, ΘC ): the worker first bargains with the new potential employer. The
outcome is that the worker quits the current employer to take an offer from the new potential
employer. The equilibrium payoffs of the worker and the new potential employer are{U (h, ΘN , w), V (h, ΘN , w)} = {βJ(h, ΘN ) + (1 − β)[βJ(h, ΘC ) + (1 − β)U0 (h)],(1 − β)[J(h, ΘN ) − βJ(h, ΘC ) − (1 − β)U0 (h)]}Proof. See appendix A.



Dey and Flinn (2005) and Cahuc, Postel-Vinay, and Robin (2005) also consider a similar bargaining problem. Dey and Flinn (2005) impose an axiomatic Nash bargaining solution assumingthat the worker’s threat point is the match value with the losing firm. Cahuc, Postel-Vinay, andRobin (2005) consider this bargaining problem using a strategic model and find a particular bargaining procedure that can support the assumption used by Dey and Flinn (2005). My approachhere is to start with a relatively simple setup. I find that the worker’s threat point is the payoff thatthe worker could obtain in the bilateral bargaining with the losing firm.
There is a technical reason for the assumption that the current contract expires when the employee bargains with the new potential employer. Suppose to the contrary that the contract remains
effective even when the employee bargains with outside firms. Consider this worker’s bargaining
problem with new potential employers. If this bargaining breaks down, the worker ends up withthe current contract with the incumbent firm, i.e., the threat point of the worker is the value of thecurrent contract. Then the worker’s continuation value is increasing in wage for two reasons. First,
it gives him a higher flow payoff. Second, it gives him a better threat point when he bargains withoutside firms. For the second reason, the joint value J is increasing in wage, which implies that thebargaining set is non-convex. When the bargaining set is non-convex, neither an axiomatic Nashbargaining solution nor an alternating offer game is applicable.2 This assumption is necessary to
avoid such a technical problem.
3.2.3. Renegotiation in response to a productivity shock. An idiosyncratic productivity shock toa match θ occasionally changes at a rate δ. The new shock is drawn independently from theprevious shocks. Firms and workers may want to renegotiate the contract in response to the shock.
The bargaining takes the following steps.
2

Shimer (2005) addresses this issue in a Burdett and Mortensen (1998) model.

JOB SEARCH, BARGAINING, AND WAGE DYNAMICS

11(1) Nature determines the proposer at the beginning of each round. The worker makes an offerwith probability β, while the firm makes an offer with probability 1 − β.
(2) The respondent has three options.
• Accept the offer and continue the employment relationship under the new condition.
• Reject the offer to quit the employment relationship.
• Reject the offer and wait for the next round (go back to step 1) after time ∆ elapses.
The bargaining may break down before they reach the next round with probability ∆s.
When this actually occurs, they end up with the current contract. Separation does notoccur.
Notice that when an exogenous breakdown of bargaining occurs, they still keep the employment
relationship under the current contract. This comes from the assumption that the employment contract is not negotiable without mutual consent, which is widely observed in employment contract(see Malcomson, 1999 for a survey.) The intuition is the following. If they do not have a previous
employment relationship, it is natural to separate when a breakdown occurs. But, if they have aprevious relationship, it is also natural to end up with the original place when they fail to reach an
agreement. The breakdown caused by an exogenous factor implies that both agents come back to
the place before the bargaining is initiated. Separation is an outcome of decisions taken by agents,
not a direct consequence of an exogenous breakdown.
Lemma 3.3. The following outcome of renegotiation is obtained in response to a productivity
shock when ∆ → 0 and ρ → 0.
1. J(h, Θ) ≥ U0 (h) and V (h, Θ, w) ≥ 0: When the match remains efficient and the participation constraint of the firm is still satisfied, they keep the current contract.
2. J(h, Θ) ≥ U0 (h) and V (h, Θ, w) < 0: When the match remains efficient but the firm’s
participation constraint is not satisfied, wage is cut so that the firm’s participation constraint issatisfied with equality. The updated wage w∗ gives agents the following payoffs,{U (h, Θ, w∗ ), V (h, Θ, w∗ )} = {J(h, Θ), 0}.
3. J(h, Θ) ≥ U0 (h): When the match becomes inefficient, separation occurs. The resulting
payoffs are {U0 (h), 0}.
Notice that the participation constraint of the worker does not get violated due to productivity
shocks.
Proof. See appendix A.

Notice that a positive productivity shock does not cause a renegotiation because it does notmake a firm or a worker worse off and thus, the participation constraints do not get violated due tothe shock. Also, the participation constraint of the worker does not get violated due to the shock

JOB SEARCH, BARGAINING, AND WAGE DYNAMICS

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unless it is already violated before the bargaining is initiated. Of course, this does not happen in
equilibrium.
The wage dynamics presented here are different from those derived by an axiomatic Nash bargaining solution. In models with Nash bargaining, wages are continuously renegotiated so thatthe rent share is constant over time. On the contrary, wages are not renegotiated in my model
when both a worker and a firm receive positive rent shares under the existing contract. Whena small idiosyncratic shock reduces labor productivity, the firm wants to cut wages because theshock makes the firm worse off. However, the worker does not agree to such a modification of his
contract. The firm can fire the worker if it wishes, but it does not want to do so because the firm
still receives a positive profit under the existing contract. As a consequence, the existing contract
remains effective. Next suppose that the firm earns a negative profit due to a shock, i.e., the participation constraint of the firm is violated. The firm wants to cut the wage, or fire the worker toavoid a negative profit. The worker is willing to accept wage cut, because his value of employment
after wage cut is still better than the value of unemployment. The size of wage cut is made as small
as possible so that the firm is indifferent between firing the worker and retaining the employment
relationship.
Harris and Holmstrom (1982) find that this wage contract is optimal for risk-averse workers
who cannot commit to remaining in the job. The intuition is that these wage dynamics minimize
the fluctuation of wages given a lack of commitment, and thus they are preferred by risk-averse
agents. Another interpretation is that the proposed wage dynamics minimize the deviation from theex ante optimal wage dynamics in the case of full commitment. Although I assume that agents arerisk-neutral for analytical simplicity, this argument is still applicable if workers are even slightly
risk-averse.
The proposed wage dynamics are more plausible than a naive application of Nash bargaining. Inmodels of wage posting with counteroffers, wages grow on the job because the worker’s alternative
job opportunity improves. However, if a very small shock occurs and I naively apply a Nash bargaining solution to such a situation, the employee’s bargaining outcome is same as an unemployedworker. The employee easily loses his bargaining position due to a tiny shock. On the contrary,
wage cut does not occur in my strategic bargaining model, when the shock is small enough.
Endogenous separation is an important property from empirical viewpoint. In the model, matcheswith high-skilled or experienced workers are more likely to survive negative productivity shocks
than those with low-skilled or inexperienced workers. Matches are destroyed when they become
inefficient. Workers who have high labor productivity are unlikely to become unemployed. Thisprediction of the model is consistent with many empirical findings. These wage dynamics andworker mobility are useful for a quantitative analysis.

JOB SEARCH, BARGAINING, AND WAGE DYNAMICS

13

3.3. Value Function. I have not discussed how value functions are defined in terms of the primitives of the model. The next proposition provides the existence and the uniqueness of the valuefunctions.

Proposition 3.4. The value functions U, V, U0 , and J are uniquely determined by the following
contraction mappings. The value of unemployment U0 is given by(r + λ0 )U0 (h) = b + λ0 EX max[βJ(h, X) + (1 − β)U0 (h), U0 (h)]where X is a vector of the new match quality and idiosyncratic shock. The joint value of the match
J is given by(r + λ + δ0 + δ1 (θ) + δ)J(h, Θ)= y(h, Θ) + λ Pr(J(h, X) > J(h, Θ)) ·EX [βJ(h, X) + (1 − β){βJ(h, Θ) + (1 − β)U0 (h)}|J(h, X) > J(h, Θ)]˙ Θ).
+δ0 U0 (h) + δ1 (θ)J(h, Θ+ (θ)) + δEX max[J(h, X), U0 (h)] + J(h,The continuation value for the worker U and the continuation value for the firm V are given by(r + λ + δ0 + δ1 (θ) + δ)U (h, Θ, w)= w + λEX max[βJ(h, X) + (1 − β){βJ(h, Θ) + (1 − β)U0 (h)},βJ(h, Θ) + (1 − β){βJ(h, X) + (1 − β)U0 (h)}, U (h, Θ, w)] + δ0 U0 (h)+δ1 (θ)U (h, Θ+ (θ), w) + δEX max[min{U (h, X, w), J(h, X)}, U0 (h)] + U̇ (h, Θ, w)(r + λ + δ0 + δ1 (θ) + δ)V (h, Θ, w)= y(h, Θ) − w + λ Pr(J(h, X) ≤ J(h, Θ)) ·EX min[(1 − β){J(h, Θ) − βJ(h, X) − (1 − β)U0 (h)}, V (h, Θ, w)|J(h, X) ≤ J(h, Θ)]+δ1 (θ)V (h, Θ+ (θ), w) + δEX max[V (h, X, w), 0] + V̇ (h, Θ, w).

Proof. The value of unemployment U0 is determined by the following asset pricing equation,(r + λ0 )U0 (h) = b + λ0 EX max[βJ(h, X) + (1 − β)U0 (h), U0 (h)]where the first term on the right hand side is the flow of unemployment benefit and the second
term captures the value when the worker meets a firm. Notice that there is no human capital
accumulation while unemployed. Given J, the equation defines a contraction mapping for U0 .
The value of employment U is determined by the following asset pricing equation,

JOB SEARCH, BARGAINING, AND WAGE DYNAMICS

14(r + λ + δ0 + δ1 (θ) + δ)U (h, Θ, w)= w + λEX max[βJ(h, X) + (1 − β){βJ(h, Θ) + (1 − β)U0 (h)},βJ(h, Θ) + (1 − β){βJ(h, X) + (1 − β)U0 (h)}, U (h, Θ, w)] + δ0 U0 (h)+δ1 (θ)U (h, Θ+ (θ), w) + δEX max[min{U (h, X, w), J(h, X)}, U0 (h)] + U̇ (h, Θ, w)
where U̇ is a time-derivative term, which is given by U̇ = dU/dh · dh/dt. The second term on theright hand side captures the change of the continuation value when the worker is contacted by a firmother than the current employer. Specifically, the first element in the bracket is the value from job
turnover, the second element is the value from being promoted, and the third element is the valueof remaining in the current employment contract. The third term captures the value of exogenous
separation. The value of the growth of match quality is captured by the fourth term. The fifth term
captures the continuation value when an exogenous shock hits the match. The first element is thevalue of keeping the current contract, the second element is the value from renegotiation (wagecut), and the third element is the value from being fired (separation.) Given J and U0 , the recursive
equation above defines a contraction mapping for U .
Similarly, the firm’s value of filling a position is determined by the asset pricing equation,(r + λ + δ0 + δ1 (θ) + δ)V (h, Θ, w)= y(h, Θ) − w + λ Pr(J(h, X) ≤ J(h, Θ)) ·EX min[(1 − β){J(h, Θ) − βJ(h, X) − (1 − β)U0 (h)}, V (h, Θ, w)|J(h, X) ≤ J(h, Θ)]+δ1 (θ)V (h, Θ+ (θ), w) + δEX max[V (h, X, w), 0] + V̇ (h, Θ, w).
where V̇ is a time-derivative term. The first term on the right hand side is the income from output,
the second term is the labor cost, the third term captures the continuation value when the employee
receives outside offers. The value of match quality growth is captured by the fourth term. The fifthterm captures the continuation value when a productivity shock hits the match. In the third term,
the first element is the value of promoting the employee to retain him and the second element is thevalue from remaining in the current contract. In the fourth term, the first element is the value when
the contract remains the same and the second element is the value from firing (separation) or thevalue of employment when wage cut occurs. Given J, the Bellman equation defines a contraction
mapping for V .
Finally I solve the value function J. Combining the worker’s value function U and the firm’svalue function V , I find the joint value function J,(r + λ + δ0 + δ1 (θ) + δ)J(h, Θ)= y(h, Θ) + λ Pr(J(h, X) > J(h, Θ)) ·EX [βJ(h, X) + (1 − β){βJ(h, Θ) + (1 − β)U0 (h)}|J(h, X) > J(h, Θ)]˙ Θ).
+δ0 U0 (h) + δ1 (θ)J(h, Θ+ (θ)) + δEX max[J(h, X), U0 (h)] + J(h,JOB SEARCH, BARGAINING, AND WAGE DYNAMICS

15

F IGURE 3.1. Equilibrium Wage Determination

Notice that the joint value J is independent of wages as I mentioned at the beginning of the section,
because the wage only affects the allocation, not the size of the rent. This Bellman equation definesa contraction mapping for J given U0 .
The equilibrium wage is set so that the worker’s continuation value U (h, Θ, w) equals his payofffrom the bargaining. Suppose that the wage is determined through bargaining among three players,
and that the type-Θ firm wins and the type-Θ0 firm loses. The equilibrium wage w∗ satisfies
U (h, Θ, w∗ ) = βJ(h, Θ) + (1 − β)[βJ(h, Θ0 ) + (1 − β)U0 (h)].
This equilibrium wage determination process is illustrated in figure 3.1. The payoff in threeplayer bargaining is drawn as a horizontal line because it is not a function of the wage. The
continuation value for a worker U is strictly and monotonically increasing in wage w. This should
be clear from the Bellman equation shown above. The equilibrium wage is uniquely determined sothat the continuation value for the worker equals the payoff obtained from the bargaining, which
occurs at the intersection seen in figure 3.1. I find it intractable to derive an explicit solution to theequilibrium wage w∗ . The wage is numerically derived in the following empirical sections.
4. DATA
4.1. Sampling Criteria. The data are taken from the National Longitudinal Survey of Youth(NLSY) 1979 which includes information on the weekly work history of individuals from 1978
through 2002. The survey consists of individuals who were 14-21 years old as of January 1, 1979.
There are some advantages from using the NLSY to analyze career. First, the NLSY has a richwork history. In particular, more than one job is recorded in a survey year. Young workers frequently switch jobs and having more than one job in a year is not uncommon. To understand how
young workers build their careers, it is important to record job switching as accurately as possible.

JOB SEARCH, BARGAINING, AND WAGE DYNAMICS

16

Second, the survey period covers the initial transition to the labor market. I am particularly interested in the wages and labor mobility of young workers. The NLSY focuses on this part of the life
cycle.
I use a sample of white male high school graduates for the following reasons. First, I consider
the labor market to be heterogeneous across race, sex, and education. Second, this is the largest
demographic group if I take a subset of individuals in terms of the conditions given in the firstpoint. Third, this group is the most commonly used for wage and worker mobility analysis in theliterature and thus, my results can be compared to the previous contributions to some extent.
Following Farber and Gibbons (1996), I limit my sample to jobs that were held after an individual first made a primary commitment to become a full-time worker. I say that an individual
has made a long-term transition to the labor market if he works in full-time jobs for six or morequarters during three years after graduating. A full-time job is defined as a job that consists of 30
or more hours per week worked. I also omit self-employed jobs and jobs without pay. Details of
the construction of the data set are contained in appendix B. The final sample consists of 9,462
observations for 662 individuals and 3,882 full-time jobs.
4.2. Variable Definitions.
4.2.1. Wages. Hourly wages are computed by dividing weekly earnings by hours worked per
week. If earnings or hours per week worked are recorded on a monthly or an annual basis, I
convert them to weekly data. Wages are deflated by the monthly consumer price index of the yearof 2004.
4.2.2. Job-to-Job Transition Indicator. I say that an individual makes a job-to-job transition if (1)he stays unemployed or has a part-time job for three weeks or less before he starts working for
a new job and (2) he leaves the job voluntarily. Otherwise, I say that an individual changes jobs
via non full-time employment. For example, if a worker is unemployed for four weeks between
jobs, I say that he changes jobs via non full-time employment. Bowlus, Kiefer, and Neumann(2001) define job-to-job transition as the condition (1) only. But condition (2) is also relevant
for my analysis because between-firm competition must occur in the model whenever job-to-job
transition occurs.
5. E STIMATION
5.1. Solution and Simulation Method.
5.1.1. Empirical Specification. I allow for worker heterogeneity in terms of productivity. The
productivity of a type i worker who has h years of experience, match quality θ, and an idiosyncratic
productivity shock θ is given by(5.1)

yi (h, θ, θ ) = exp(γ0,i + γ1 h + γ2 h2 + γ3 h3 + γ4 h4 ) · θ · θ .

JOB SEARCH, BARGAINING, AND WAGE DYNAMICS

17

The distribution of individual types is assumed to have two support points: low-skilled and highskilled. I normalize the low-skilled type as γ0,LOW = 0. The parameters to be estimated are thesupport point for high-skilled type γ0,HIGH and its weight pHIGH . The distribution of match quality
is assumed to be lognormal, ln θ ∼ N (µ, σθ2 ). I discretize match quality into M support points sothat each point is equally distant. Let θm be the match quality at the m-th level (1 ≤ m ≤ M ).
When the match quality with the current employer is θm , match quality grows θm+1 at the Poisson
rate δ1 (θm ),δ1 (θm ) = δ1a + δ1b m if 1 ≤ m < M
0 otherwise.
The distribution of productivity shocks is assumed to have two support points: bad state and goodstate. Because it is imposed that Eθ = 1 for normalization, I only have to estimate the support
point of bad state θ,BAD and its weight pBAD . I also assume wages are measured with error but
this error is unbiased relative to the true log wage ln w∗ ,ln w = ln w∗ +  ∼ N (0, σ2 )where ln w is the observed wage. The interest rate r is set to 0.075. The parameter for bargaining
power β is fixed at 0.5 for identification purpose, which will be discussed in the section 5.4.
5.1.2. Model Implementation. The model is numerically solved using a contraction mapping in
discretized state space. Match quality is discretized to 20 levels. They are equally distant and theirweights are given by the method proposed by Kennan (2004). The lowest match quality is at 2.5%
quantile and the highest is at 97.5% quantile. Wages are discretized to 35 levels. The lowest hourly
wages on the grid is $1.0 and the highest is $45.0. This grid turns out not to be restrictive because
any simulated wage is on either of these boundaries in the estimation. The length of a decisionperiod is assumed to be a quarter (13 weeks.) This relatively fine grid is especially relevant while
agents are young, because they change jobs frequently and have multiple jobs during a year. If I
use a year as a decision period, I would lose more information about the early careers of young
workers. All events described by Poisson process with the rate a in the continuous time model
are approximated by a Bernoulli process with the rate a∆h where ∆h (= 0.25) is the length ofthe period in the discretized model. Each individual is simulated for K (= 10) times from his firsttransition to the labor market until his first exits from the labor market or the survey ends.
It is important to match the length of survey and the length of simulation so that I can re-generate
the actual sampling process. Suppose I am interested in the conditional mean wage given ten yearsof experience. If the agents are simulated for ten years, more productive workers are likely to be
included in the simulated sample of workers with ten years of experience, because high-skilledworkers tend to be more experienced. On the contrary, if the simulation length is as long as one

JOB SEARCH, BARGAINING, AND WAGE DYNAMICS

18

hundred years, probably all types of workers will be included in the simulated sample of workers
with ten years of experience. Due to the sampling mechanism, the conditional mean wage will
be higher in the former simulated sample. The simulation length can affect the auxiliary model
parameter estimates and thus, matching it with the survey length is important in the estimation.

5.2. Model Estimator. The parameters of the model are estimated by a simulated minimum distance estimator, which is closely related to the simulated method of moments, the efficient methodof moments, and indirect inference (see Carrasco and Florens, 2002, for a survey.) The model issimulated to generate an artificial data set of employment history and wage path. This simulated
data is summarized by descriptive statistics such as hazard rate of job and unemployment, wage
growth rate, and wage variance. These summary statistics of simulated data are compared with thecorresponding statistics of actual data. The objective of estimation is to look for structural parameters that give the best fit. Summary statistics used in a simulated minimum distance estimator
are called auxiliary parameters. Auxiliary parameters are often moments of data, but they can beparameters of a reduced form model. For example, coefficients of a wage regression are used as
auxiliary parameters.
There are a few reasons to use simulated minimum distance estimator to estimate the model.
First, implementation is straightforward. For example, maximum likelihood is computationally
too demanding for my model because it requires me to integrate out serially correlated unobserved
state variables. In particular, the match quality in one job is correlated with those in other jobs.
The match quality with an alternative job opportunity is also correlated over time, even when theworker does not change jobs. In addition, idiosyncratic shocks also need to be integrated out,
because they change only occasionally. Second, I directly match the important features of the data.
By looking at the gap between auxiliary parameter of the data (i.e., summary statistics of the data)
and their simulated counterparts, I can tell which features of the data the model fails to fit.
The simulated minimum distance estimator minimizes the criterion function that is defined as
the weighted average of the squared distance between the sample auxiliary parameters and thecorresponding simulated auxiliary parameters. Let φ be the vector of structural parameters. The
vector of sample auxiliary parameter estimated from the NLSY is denoted by ρ̂. The vector ofsimulated auxiliary parameter computed from a simulated data set with K simulations is denotedby ρK . The simulated minimum distance estimator φ̂ is defined asφ̂ = arg min[ρK (φ) − ρ̂]0 W [ρK (φ) − ρ̂]φwhere W is a positive definite matrix. The variance of the estimated structural parameters is
minimized when the weighting matrix W is the inverse of the covariance matrix of the auxiliary
parameters. Notice that an auxiliary parameter is a function of structural parameters. The choiceof auxiliary parameters affects efficiency and they should be good descriptions of the data. One

JOB SEARCH, BARGAINING, AND WAGE DYNAMICS

19

interpretation is that I see the data through the “lens” of a descriptive statistical model. The optimal weighting matrix W ∗ for a simulated minimum distance estimator is given by the inverseof the variance-covariance matrix of the sample auxiliary parameter V ar(ρ̂). When the optimal
weighting matrix W ∗ is used, the covariance matrix for the structural parameters is given by 0
−1∂g (φ) ∗ ∂g(φ)
V ar(φ̂) = (1 + 1/K)
W
∂φ∂φ
where W ∗ = V ar(ρ̂)−1 , g(φ) = ρ(φ) − ρ̂, and K is the number of simulation.
5.3. Auxiliary Models. The auxiliary parameters that describe employment history data are haz40
ard rates of full-time job spells {pJ,t }40
t=1 , full-time employment spells {pF,t }t=1 , and non full-time
employment spells {pN,t }5t=1 . Non full-time employment includes part-time employment and unemployment. A spell of non full-time employment ends if a worker finds a new full-time job. The
hazard rate of non full-time employment captures the transition from unemployment or part-time
employment to full-time employment. A spell of full-time employment ends if a worker loses
a full-time job and gets unemployed or switches to a new part-time job. Thus, the hazard rateof full-time employment captures the transition from full-time employment to unemployment or
part-time employment. Lastly, a spell of full-time job ends if a worker loses full-time employment
status or he switches to another full-time employment. The hazard rate of full-time job captures
the job-to-job transition as well as a transition to non full-time employment. Quarterly hazard rates
of full-time job spells (up to 40 quarters), full-time employment spells (up to 40 quarters), and non
full-time employment spells (up to 5 quarters) are nonparametrically estimated by a Kaplan-Meierestimator using both censored and non-censored spells. The length of the periods is chosen so thatroughly 90% of spells die during that time interval. For example, the hazard rate of a full-time job
at quarter t is given byNtCτ ≥t (Nτ + Nτ +1 )pJ,t = P

where Nt is the number of jobs that end at quarter t and NtC is the number job spells that are
censored at quarter t.
The auxiliary parameters that describe the wage data are the average log wage conditional on
general work experience, within-job wage growth rate, and within-individual wage growth rate.
Let wijt , GXijt and T Nijt be log wage, experience, and tenure of individual i when he works for
employer j in period t. Following Murphy and Welch (1990), the average log wage conditional on
general work experience is estimated by OLS with quartic term,
wijt = β0,OLS + β1,OLS GXijt + β2,OLS GX 2 + β3,OLS GX 3 + β4,OLS GX 4 + ijt
2where ijt is a statistical error. The coefficients βOLS and the residual variance σOLS
are used as
the auxiliary parameters. This auxiliary model provides a parametrically estimated conditional

JOB SEARCH, BARGAINING, AND WAGE DYNAMICS

20

mean and variance of log wage given experience. Notice that the estimated coefficients should
not be interpreted as returns to experience because of endogeneity. In particular, experience andunobserved innate ability are positively correlated. This motivates me to estimate within-individual
wage growth rate using a fixed effect model.
Denote the average log wage and experience of individual i by wi and GX i . Let w̃ijt = wijt − w̄ibe the deviation of log wage from the average over the entire job history of individual i. I also
define the averages and the deviations for GX and  in a similar way. The fixed effect model forwithin-individual wage growth is given by]2 ijt + β3,F E GX
]3 ijt + β4,F E GX
]4 ijt + ˜ijt .
g ijt + β2,F E GX
w̃ijt = β1,F E GX
Notice that I use wage variation within individual job histories to identify returns to experience.
The coefficients βF E and the residual variance σF2 E are used as the auxiliary parameters. The
residual variance of this fixed effect estimator σF2 E is expected to be smaller than the residual2, because the individual fixed effect is eliminated in this model. Thus,
variance of the OLS σOLS
the difference between two is useful to identify the dispersion of individual innate ability.
The estimated returns to experience include both within-job wage growth and the wage growththrough job switching. To understand the wage growth structure more deeply, I estimate within-job
wage growth using a fixed effect estimator. Denote the average log wage and tenure of individual
i at job j by wij and T N ij . Let w̃˜ijt = wijt − wij be the deviation of log wage from the averageover the duration of job j. I also define the averages and the deviations for other variables such as
T N and  in a similar way. The fixed effect model for within-job wage growth is given by
g2
g3
g4
g
w̃˜ijt = β1,OJF E Tg
N ijt + β2,OJF E Tg
N ijt + β3,OJF E Tg
N ijt + β4,OJF E Tg
N ijt + ˜˜ijt .
5.3.1. Estimates of Auxiliary Parameters. The estimated hazard rates are plotted in figure 6.1
through 6.3. Some selected numbers are also presented in table 1 for detailed information. The
quarterly hazard rate of non full-time employment at the first quarter is 0.51. It decreases to 0.46
in the fifth quarter. The estimates imply that the average time to find a full-time job is about 2
quarters. The quarterly hazard rate of full-time employment at the first quarter is 0.16. It quickly
decreases in the first few years and drops to 0.05 at the tenth quarter. The rates seem to be stablearound 0.03 after the fifteenth quarter. The hazard rate of full-time job at the first quarter is 0.20,
which is higher than the employment hazard rate because some jobs end with job-to-job switching.
Similar to the full-time employment hazard rate, the job hazard rate decreases quickly in a first few
years and it drops to 0.07 at the tenth quarter. The pattern found here is very similar to the one
reported by Farber (1999).
The estimated sample auxiliary parameters for wages are presented in table 2. The first twocolumns are the OLS estimates. The results imply that the average initial log wage is 2.1 (= $8.1)
and the average log wage with ten years experience is 2.6 (= $13.6.) The next two columns present

JOB SEARCH, BARGAINING, AND WAGE DYNAMICS

21

TABLE 1. Sample Hazard Rates

Note: The hazard rates are estimated by the Kaplan-Meier estimator. Non full-time employment includes part-time
employment and unemployment. The standard deviation of the estimated hazard rates is obtained by a nonparametricbootstrap with blocking for time dimension at the individual level. The number of replications in bootstrap is 10,000.
The survival rate of full-time jobs and full-time employment at 40th quarter is 0.07 and 0.14, respectively. The
survival rate of non full-time employment at 5th quarter is 0.04.

the regression estimates for within-individual wage growth. The results imply that the averageannual return to experience in the first ten years is 0.054. Also notice that the residual varianceis smaller than that of OLS, because individual effect is eliminated in this model. The last twocolumns show the regression estimates for within-job wage growth. The results imply that the
average annual wage growth rate on the job is 0.033. Again, the residual variance is smaller thanthose from OLS and within-individual wage regressions, because both individual and employer
fixed effects are eliminated.
The distance between the sample auxiliary parameters and the simulated counterparts is optimally weighted by the estimated variance-covariance matrix of the sample auxiliary parameters.
I estimate it by a nonparametric bootstrap with 10,000 replications. To preserve the dependent
structure of the data, I sample individuals with blocking over the time dimension. If a particular
individual i is selected, his entire wage and employment history are included in the sample. There
are some advantages using a bootstrap to estimate the optimal weighting matrix. First, I can avoid
small sample bias for second order moments as is pointed out by Altonji and Segal (1996). Second, analytical solutions to covariance between auxiliary parameters can be complex. But I canestimate it through simulation. The estimated standard deviations are presented in table 1 and 2.
Third, no update of the weighting matrix is necessary. This simplifies computation.
The number of auxiliary parameters is 101 (40 from the full-time job hazard rate, 40 from thefull-time employment hazard rate, 5 from the non full-time employment hazard rate, 6 from the
OLS wage regression, 5 from the fixed effect model for on-the-job wage growth, 5 from the fixed
effect model for overall wage growth.) The simulated minimum distance estimator φ̂ is formally

JOB SEARCH, BARGAINING, AND WAGE DYNAMICS

22

TABLE 2. Sample Auxiliary Parameters

Note: Log of hourly wages deflated by 2004 price are regressed on experience (Exp) or tenure (Ten.) Eighteen
observations of hourly wages are higher than $100 and they are excluded from regressions. The fixed effect estimatoris used to estimate within-individual wage growth and within-job wage growth. The standard deviation is obtained bya nonparametric bootstrap with blocking for time dimension at the individual level. The number of replications inbootstrap is 10,000.

given byφ̂ = arg min[ρk (φ) − ρ̂]0 W ∗ [ρK (φ) − ρ̂]φwhere
φ = {γ1 , γ2 , b, λ0 , λ, δ0 , δ, γ0,HIGH , pHIGH , θ,BAD , pBAD , α, θM IN , σ }

40
5
2
2
2
ρ = {pJ,t }40
t=1 , {pF,t }t=1 , {pN,t }t=1 , βOLS , σOLS , βF E , σF E , βOJF E , σOJF E
W ∗ = V ar(ρ̂)−1 .
Remember that ρ̂ is the sample auxiliary parameter estimated by the observed sample.
5.4. Identification. Flinn and Heckman (1982) show that search models are underidentified if
only unemployment duration and initial accepted wages are used. Because employment durationand the subsequent wages after the initial accepted wages are also used in the estimation, I might
be able to fully identify the model. However, identification through such information is not fully
studied.3 Thus, following Flinn and Heckman (1982), I impose three parametric assumptions tosatisfy the recoverability condition to assure the identification of the structural parameters. The
additional information such as employment duration and wages other than the initial ones improves
the efficiency of the estimator. First, I fix the annual discount rate r at 0.075. They show that it
is not separately identified from the value of unemployment benefit b. Second, the match quality
3

Barlevy (2005) finds nonparametric identification conditions for a search model without bargaining.

JOB SEARCH, BARGAINING, AND WAGE DYNAMICS

23

distribution is assumed to be lognormal. This shape restriction is necessary to identify the fractionof unaccepted match quality, and thus the rate at which an unemployed worker meets a firm.
In other words, the reason for unemployment cannot be decomposed into the reservation match
quality and job availability without this shape restriction. Third, the bargaining power of workers
β is set to 0.5, because it is weakly identified without additional structure.4 Intuitively, it is difficult
to distinguish the bargaining power from the size of the ‘pie.’ These parametric assumptions arecommonly used in the literature such as paper by Dey and Flinn (2005).
Although the model is identified using the parametric assumptions, it is probably worthwhile
to intuitively discuss the identification of the bargaining effect on wages. For simplicity, let us
suppose that the match-specific capital (e.g. tenure effect) does not grow on the job. More generalcase will be discussed below. Consider two groups of workers with same general work experience.
Workers in the first group have worked for years in the same employer, and thus their tenure islong. Workers in the second group were unemployed, but they have just found a new job. The
bargaining position and the match quality of workers in the former group are expected to be high,because they stay with the same employer for years for good match quality and because theyshould have received many job offers from outside on the job. Thus, the wage growth of theseworkers is solely driven by the accumulation of general human capital. On the other hand, on-thejob wage growth of workers with zero tenure is also driven by the change in bargaining position.
The difference in the average on-the-job wage growth between two groups identifies the wage
growth through bargaining. Notice that workers in both groups are highly experienced, because
long tenure implies high labor market experience. Nevertheless, the estimated effect of bargaining
can be applied to inexperienced workers, because the match quality distribution and the rate at
which a worker meets a firm are same across workers with different experience, which is also acommon identification assumption in the search literature.
When match-specific capital grows over time, its effect on wages must be taken into accountin order to identify the bargaining effect on wages. This effect may not be negligible for workers
with zero tenure, while it probably has little effect for workers with long tenure. The growth ofmatch-specific capital is included in the model so that match quality with the current employer
stochastically grows. This productivity component is identified using job-to-job transition rate.
When the growth of match quality is fast, job turnover rate is strongly decreasing in tenure (i.e.,the slope of job hazard rate will be steep.) The contribution of this component to wage growthis derived from the model, because it explicitly relates productivity to wages. Thus, the effect ofbargaining on wage growth is still identified by comparing the two groups.
6. E STIMATION R ESULTS AND A PPLICATION
4

Cahuc, Postel-Vinay and Robin (2005) address the identification of bargaining parameters using employer-employee
matched data.

JOB SEARCH, BARGAINING, AND WAGE DYNAMICS

24

6.1. Estimation Results. The estimation results are presented in table 3. The objective function
is minimized by simulated annealing.5 A worker’s productivity grows by 30% during the first ten
years of his career through accumulation of general human capital. Notice that this is not the entire
productivity growth of a typical worker with ten years work experience, because the productivity
also grow through match quality change. The value of unemployment benefit amounts to $5.2 perhour in 2004 dollar. This value is lower than the minimum wage during early 80s, which was
5Fortran software is provided by Goffe, Ferrier, and Rogers (1994) in netlib.org.

TABLE 3. Parameter Estimates
Parameter
Human Capital

Notation Estimates Std. Dev.
γ1
0.382
0.075
γ2
-0.198
0.087
γ3
0.097
0.032
γ4
-0.014
0.003
Unemp. Benefit
b
5.167
0.540
Poisson Rate
Unemp.
λ0
3.197
0.133
Emp.
λ
1.024
0.065
Separation
δ0
0.117
0.004
Match Q. Change
δ1a
0.474
0.052
δ1b
-0.016
0.003
Prod. Shock
δ
1.776
0.086
Type Dist.
High-skilled
γ0,HIGH
0.614
0.039
Weight
pHIGH
0.389
0.143
Shock Dist.
Badθ,BAD-2.6860.288
Weight
pBAD
0.385
0.020
Good
θ,GOOD
WeightpGOOD
Match Q. Dist.
Mean
µ
0.440
0.088
Std. Dev.
σθ
0.436
0.037
Measurement Error
σ
0.282
0.012
Interest Rate: r = 0.075
Bargaining Power: β = 0.5
No. of Moment Conditions: 101
Function Value at the Minimum: 224.649
Note: The coefficients of production function are denoted byγ. The hourly value of unemployment compensation
measured in 2004 dollar is b. The annual arrival rate of an offer for those who do not have a full-time job is λ0 . The
annual offer arrival rate on the full-time job is λ. The annual arrival rate of an exogenous separation is δ0 . The
parameters for the annual rate of match quality change are δ1a and δ1b . The annual arrival rate of productivity shockis δ. The support point for high-skilled individuals and its weight are denoted by γ0,HIGH and pHIGH . The support
point for low-skilled workers are normalized to zero. The support point for bad (negative) shock and its weight areθ,BAD and PBAD . Those for good (positive) shock are θ,GOOD and PGOOD . I impose a restriction that the meanof the shock be one for normalization. The location and the scale parameter of match quality distribution, which is
lognormal, are µ and σθ , respectively. The standard deviation of measurement error is σ .

JOB SEARCH, BARGAINING, AND WAGE DYNAMICS

25

between about $7.00 and $5.50. Those who do not have a full-time job meet 3.2 firms during
a year. Full-time job holders are contacted by 1 firm during a year. Notice that these numbers
are not same as the number of offers actually made by firms. In many cases, they immediately
separate because they realize they do not have a good match quality as soon as they meet. The
match quality distribution is assumed to be lognormal. The mean and the standard deviation of log
of match quality are 0.44 and 0.44, which implies that the mode of the distribution is 0.83. The
lowest possible match quality in the estimated model is 0.95, which is 5th out of 20 levels of thediscretized match quality. So only the right side of the mode affects the behavior of agents. The
medians of match quality of workers with zero, five, and ten years of experience are 1.95 (13th),
2.79 (17th), and 3.05 (18th), respectively. The means of match quality of workers with zero, five,and ten years of experience are 2.01, 2.86, and 2.94, respectively. Match quality grows once inevery five years if a five-year-experienced worker has the median match quality. When match
quality changes, it improves by 9% (calculated by taking log difference.) Given these estimates,
the average annual match quality growth rate is about 2%. A negative productivity shock occurs
once in every 1.5 years. This negative shock causes a significant productivity drop. When aworker-firm match is in a bad state, their output is almost zero. Also a match is destroyed due toan exogenous shock once in 8.6 years. The proportion of high-skilled workers is 39% and they are
61% more productive than low-skilled workers, which implies that the distribution of worker types
is skewed to the left. Lastly, the lowest wage and the highest wage in the simulation are $4.59
and $39.6, respectively. This implies that my wage grid is not restrictive, because the grid covers
wages between $1.00 and $45.00.
6.2. Model Fit.
6.2.1. Hazard Rates. The sample hazard rates and simulated hazard rates are plotted in figures
6.1, 6.2, and 6.3. The results indicate that the model captures the basic features of the hazard rates.
The apparent dependence of the non full-time employment hazard rate is driven by heterogeneity
in innate ability and human capital. High-skilled workers and experienced workers receive more
job offers. However, the model does not have duration dependence here, because human capitaldoes not depreciate while workers are unemployed.
The hazard rate of full-time employment is declining because of both duration dependence andheterogeneity. Workers accumulate human capital through learning-by-doing. This process makes
a worker-firm match more and more productive. As a consequence, the transition rate from fulltime employment to unemployment (or part-time employment) decreases over time. Matches areheterogeneous in terms of the innate ability and the experience of the worker and the match quality. Because less efficient matches are destroyed by negative productivity shocks, the selection
mechanism generates declining hazard rate over time.
The full-time job hazard rate decreases over time for a similar reason, but there is one importantdifference because this includes job-to-job transition. Observe that human capital and innate ability

JOB SEARCH, BARGAINING, AND WAGE DYNAMICS

26

TABLE 4. Sample and Simulated Auxiliary Parameters (Hazard Rate)

do not affect the job-to-job transition rate, because these are transferable across jobs. However, aworker is more likely to separate from the match and switch to a new job if the match quality islow. This is another source that generates a declining hazard rate.

JOB SEARCH, BARGAINING, AND WAGE DYNAMICSF IGURE 6.1. Non Full-time Employment Hazard Rate

F IGURE 6.2. Full-time Employment Hazard Rate

F IGURE 6.3. Full-time Job Hazard Rate

27

JOB SEARCH, BARGAINING, AND WAGE DYNAMICS

28

TABLE 5. Sample and Simulated Auxiliary Parameters (Wage Regression)

Note: Hourly log-wages are regressed on experience (EXP) or tenure (TEN). For the detailed information on the
results for sample auxiliary parameter estimation, see table 2.

6.2.2. Wages. The sample and simulated auxiliary parameters of wage regression are presented intable 5. The prediction of average low wage given experience is reasonably close to the data,
as is shown in figure 6.4. The difference between the simulation and the observation is 0.02
when experience is ten years. Notice that the slope quickly decreases around the point whereexperience is five years. This feature cannot be captured by wage regression if only linear andquadratic terms are used, which is also emphasized by Murphy and Welch (1990). The predictionof average within-individual wage growth rate also captures the basic features of the data (see figure6.5), although the simulated wage growth path is less concave than the observation. The model
generates a similar wage growth path to the simulation, partly because human capital accumulation
function includes a quartic term. The difference between the simulated path and the observationis largest at five years of experience and it is 0.03. Figure 6.6 presents within-job wage growthrate. The model captures the basic patterns of on-the-job wage growth. However, the simulated
on-the-job wage growth path is less concave than the observation: the simulated wage growth isslower than the observed wage growth when tenure is short, while it is too fast when tenure islong. A possible explanation for the gap between the model and the observation is that match
quality distribution and the rate at which a worker meets a firm are assumed to be the same acrossworkers with different experience and tenure. If inexperienced workers (or workers with shorttenure) meet firms more frequently than experienced workers (or workers with long tenure), thewages of inexperienced workers will grow more rapidly, which helps the model fitting the observed
on-the-job wage growth path.

JOB SEARCH, BARGAINING, AND WAGE DYNAMICSF IGURE 6.4. Average Log-wage by Experience

F IGURE 6.5. Within-Individual Wage Growth Rate

F IGURE 6.6. Within-Job Wage Growth Rate

29

JOB SEARCH, BARGAINING, AND WAGE DYNAMICS

30

6.3. Counterfactuals.
6.3.1. Reducing labor market frictions. The main empirical question of the paper is what the effectof the labor market frictions on wages is. Due to the labor market frictions, workers have to searchfor better jobs and outside options, and bargain wages. In the absence of frictions, workers are able
to immediately find the best match and an alternative job opportunity which is as good as the best
one. Thus, the wage growth is solely driven by the growth of human capital in this economy. By
comparing the actual wage profile with the counterfactual wage profile in the absence of frictions, I
can quantify the effect of the labor market frictions on wages. Since the simulation of the model iscarried out in a discrete time model, it is impossible to simulate an economy with absolutely zero
friction. But it is still worth simulating an economy with the feasibly lowest possible frictions.
To implement the idea, the model is parametrized in the following way. First, workers always
have the best match quality with all firms. This “best” match quality is at the 97.5% quantile in
the estimated underlying match quality distribution and the idiosyncratic productivity shock is ina good state. In the simulation of the estimated model, 18.6% of workers have this match quality
when they have ten years of work experience. Second, workers meet one firm in every quarter
regardless of their employment status. So the parameters are set so that λ0 = λ = 4. Rememberthat Poisson processes are approximated by the corresponding Bernoulli processes and that thedecision period is a quarter. This parametrization implies that the probability that a worker and afirm meet in a quarter is 1. Third, workers do not lose a job. In a labor market without frictions,workers are able to find a job immediately even if they lose one. To bring about this situation ina discrete time model, the parameters are set so that δ0 = δ = 0. All other parameters remain thesame as the estimated model.
The simulated wage profile is presented in figure 6.7. There are two interesting features. First,
the wage growth in the frictional labor market is more rapid than the wage growth without frictions. In the absence of frictions, wage growth is solely driven by the growth of human capital.
To the contrary, in a frictional labor market, workers are improving their match quality and thevalue of outside option, which also increases their wages. The wage gap between two wage profiles is quickly decreasing during the first six years by 20% (measured by log difference) and theremaining gap is not reduced after that. Because the observed wage growth rate during the firstten years is about 50%, labor market frictions account for about 40% of the observed wage growthduring this period. This estimate is greater than the number claimed by Topel and Ward (1992),
which is 30%, because they do not take into account the effect of the improved value of outside
option. The wage growth due to job search across different skill levels is also presented in figure
6.8. For both types, the wage growth due to search slows down after six years of work experience.
But high-skilled workers achieve a more rapid wage growth due to labor market frictions. Because
high-skilled workers generate larger rents from any matches, they have more room for renegotiation than low-skilled workers, which results in a higher wage growth rate. The second interestingJOB SEARCH, BARGAINING, AND WAGE DYNAMICS

31

F IGURE 6.7. Wage Profile in a Labor Market with Few Frictions.

F IGURE 6.8. The Effect of Labor Market Frictions on Wage Growthfeature of the comparison of two wage profiles in figure 6.7 is that the wage gap remains unfilledeven after ten years of job search. This is explained by the average productivity of worker-firm
matches. In a labor market without frictions, workers are always assigned to the best match. But,
in a frictional labor market, workers are occasionally taken away from a job due to productivity
shocks even if they once find the best match quality. Thus, the average match quality in a frictional
labor market is strictly lower than the best match quality even after several years of job search.
6.4. No Human Capital Growth. Another way to examine the effect of labor market frictions
on wages is to simulate a counterfactual economy where workers do not accumulate their humancapital. In an economy without human capital growth, the wage growth is driven by job search andbargaining. There are two objectives in this exercise. First, I will examine the robustness of theresult obtained above by looking from a different angle. Second, I will evaluate the effect of the

JOB SEARCH, BARGAINING, AND WAGE DYNAMICS

32

F IGURE 6.9. Wage Growth Rate without Productivity Growth.
improved value of outside option on on-the-job wage growth. One of the most interesting featureof the model is that wages grow due to the improved value of outside option without productivity
growth or job changes. In this counterfactual experiment, the on-the-job wage growth is solely
driven by this effect.
This counterfactual experiment is implemented by the following way. First, the growth of humancapital is shut off, i.e. γi = 0 for i = 1, · · · , 4 and δ1a = δ1b = 0. Second, innate ability of all
workers is increased by 30% so that the reservation match quality is not very different from theone in the estimated model. When productivity does not grow with experience and everything else
remains the same, the (joint) value of a match is reduced. As a result, the reservation match quality
is increased. When the reservation match quality is high, the wage growth due to job search isnecessarily decreased because there is not much room to be improved. To mitigate this problem,
innate ability of all workers is increased by 30%, which amounts to the productivity of the worker
with ten years of experience. The resulting labor mobility patterns are not quite different from theestimated model. All other parameters remain the same as the estimated model.
The simulated wage growth rate is presented in figure 6.9. Without productivity growth, wages
quickly grow early in a worker’s career, and the wage growth rate converges to around 20%. This
result is consistent with the result presented in the previous subsection. The simulated on-the-job
wage growth rate is also presented in figure 6.10. When productivity does not grow on the job,on-the-job wage growth is solely explained by the improved value of outside option. This effectraises wages by about 10% in the first ten years. Since the wage growth during the first ten years
is about 50%, this effect accounts for about 20% of the observed wage growth.
6.5. Wage Decomposition.
6.5.1. Wage Growth Rate. One of interesting applications is a decomposition of wage growth.
This is not straightforward because the equilibrium wage is defined implicitly (see figure 3.1.) MyJOB SEARCH, BARGAINING, AND WAGE DYNAMICS

33

F IGURE 6.10. The Effect of Labor Market Frictions on On-the-job Wage Growth.

approach is to approximate the wage function by a polynomial function of state variables. Supposethat the equilibrium wage is determined in a three-player bargaining. Imposing a separability
among general human capital, match-specific capital, and bargaining position, the approximatedwage function given a set of state variables S takes the following form:ln w(S) = w0 (γ0 ) + wGHC (h) + wM SC (θ, θ ) + wBGN (θ0 , 0θ ) + R
where w0 is a constant term, wGHC , wM SC , and wBGN are quadratic functions with interaction
terms, and R is a residual.
This wage equation can be also applied to the equilibrium wage in bilateral bargaining between
a unemployed worker and a firm. Notice that the equilibrium payoff of the worker in this bilateralbargaining coincides with the payoff in three-player bargaining when the joint value with losing
firm is same as the value of unemployment. So I can still apply the above wage equation if I
assign a match quality θ0 and an idiosyncratic shock 0θ such that J(h, θ0 , 0θ ) = U (h). Because acombination of a match quality and an idiosyncratic shock is not uniquely determined, I randomly
draw 0θ from its estimated distribution and solve for θ0 so that J(h, θ0 , 0θ ) = U (h). Unfortunately, I
cannot apply this wage equation for bilateral bargaining in response to productivity shocks, because
the corresponding bargaining position is not well defined. One possible solution is to assume
that the employer effect is fully responsible for a change of wage due to productivity shock, i.e.
∆ ln w = ∆wM SC regardless of other state variables.
Using the simulated data, I estimate the wage function for each skill level separately. In thesimulation, measurement error is not included to obtain precise estimates. The result shows that
the R2 of the regression is 0.99 for the low-skilled and 0.98 for the high-skilled, which implies
that the quality of the approximation is fairly good. The contribution of each component to wage
growth rate is now easily computed by taking the difference between two points in time. However,notice that wages are not updated in all periods even though state variables change and that the

JOB SEARCH, BARGAINING, AND WAGE DYNAMICS

34

TABLE 6. Decomposition of Wage Growth Rate (overall)above method can be applied only at the time when wages are updated. If a wage update does notoccur in a given period, the total wage and all components such as the general human capital effectremain the same as the previous period, although the worker’s general human capital certainly
increased.
I decompose the wage growth rate for five, ten, and fifteen years of experience for each skill
level. The results in table 6 indicate that not only the level, but also the wage growth rate isincreasing in unobserved individual skill. The wages of high-skilled workers grow by 55% in thefirst ten years, while those of low-skilled workers grow by 50%. Second, this difference mainly
comes from the match-specific capital and bargaining. For high-skilled workers, the general humancapital effect accounts for about 50% of the total wage growth. The match-specific capital effectand the bargaining position effect account for 30% and 20%, respectively. For low-skilled workers,
the general human capital effect accounts for about 55% of the total wage growth. The matchspecific capital effect and the bargaining position effect account for 25% and 20%, respectively.
As it will be shown below, the contribution of match-specific capital growth on-the-job is verysmall. Thus, the most of match-specific capital growth is due to job search, rather than on-the-job
skill learning.
Why are the wage growth rates different across unobserved skill groups? This can be explainedby differences in reservation match quality. Low-skilled workers have high reservation match
quality because they produce less output even if they get employed. They prefer remaining unemployed and receiving unemployment benefit. They would work only when match quality is high.
The average match quality of low-skilled workers at the first job is higher than that of high-skilledworkers. Because the match quality is high from the beginning of their careers, there is not muchroom to improve. On the other hand, high-skilled workers have a low reservation match quality.

JOB SEARCH, BARGAINING, AND WAGE DYNAMICS

35

TABLE 7. Decomposition of On-the-job Wage Growth Rate

Because they produce more, they prefer working to remaining unemployed. Thus, high-skilledworkers are willing to accept an offer from a low match quality firm. They first accept low match
quality, but improve match quality through job search. This is why high-skilled workers benefit
more from job search than low-skilled workers.
The most important feature of the model is on-the-job wage growth through bargaining. I decompose wage growth by path and evaluate the contribution of the bargaining position to on-thejob wage growth by the following way. In each simulation period (a quarter), I record the wage
growth from the previous period and the corresponding employment status, i.e., whether or not tochange jobs. Not only the wage growth itself, but also each component such as the general humancapital effect is recorded here. This calculation gives me the cumulative wage growth by path atany given point in time. The results are presented in table 7. The average cumulative on-the-job
wage growth for ten years experience is 33% for high-skilled workers. The change in bargaining
position accounts for about 40% of the on-the-job wage growth. In the standard literature on wage
growth, job search does not contribute to on-the-job wage growth. But I find that a substantial
part of on-the-job wage growth can be explained by bargaining caused by job search. It is also
found that the on-the-job growth of match-specific capital little raises the wage. This is consistent
with the estimation results discussed in section 6.1: the growth of match-specific capital on-the-job
is much smaller than the growth through job changes. It may seem counterintuitive that matchspecific capital decreases the wage at the beginning of the career. The reason is that the growth of
productivity is not reflected in wages until a worker receives a job offer from outside. The match
quality of some workers grow very early in the first job. But this does not directly translate into
wage growth. It contributes to wage growth when workers receive job offers. However, negative
productivity shocks may decrease wages as soon as they occur. Thus, wages decrease on the job
due to match-specific capital, i.e. negative productivity shocks at the very beginning of the career.
But this effect is gradually dominated by the growth of match-specific capital on the job as it isshown in table 7.

JOB SEARCH, BARGAINING, AND WAGE DYNAMICS

36

7. A LTERNATIVE M ODELIn this paper wages are assumed to be constant until renegotiation. However, this is not the only
possible assumption. Alternative assumption is that wage is a product of efficiency unit of laborand its price and that the price of efficiency unit of labor is constant until renegotiation. In thisalternative specification, wages grow over time without renegotiation as workers accumulate their
human capital. Let q be the price of efficiency unit of labor and y be the labor productivity. The
flow wage payment is then w = qy. In bargaining, the price is set so that the continuation valueof the worker coincides with the equilibrium payoff in the bargaining. Suppose that the wage isdetermined through bargaining among three players, and that the type-Θ firm wins and the type-Θ0
firm loses. The equilibrium price q ∗ satisfies
U (h, Θ, q ∗ ) = βJ(Θ, h) + (1 − β)[J(Θ0 , h) + (1 − β)U0 (h)].
Similar to the result presented in figure 3.1, this equilibrium price q ∗ is also determined uniquely.
One advantage of this specification is that wage decomposition is straightforward. Assuming
the production technology is given by equation (5.1), wages can be decomposed asln w = γ0,i + γ1 h + γ2 h2 + γ3 h3 + γ4 h4 + θ + θ + ln q(h, Θ, Θ0 )where q only captures the effect of change in outside option value. For normalization, the lowest
price q is set 0.01 and the highest price q̄ is set 1.00, because price and labor productivity are notseparately identified.
7.1. Estimation Results. The estimation results are presented in table 8. A worker’s productivity
grows by 30% during the first ten years of his career through accumulation of general humancapital. This estimated human capital accumulation process is similar to that in the original model.
The value of unemployment benefit amounts to $7.9 per hour in 2004 dollar. Those who do nothave a full-time job meet 3.95 firms during a year. Full-time job holders are contacted by 1.24
firms during a year. The match quality distribution is assumed to be lognormal. The mean and thestandard deviation of log of match quality are 1.44 and 0.36. The estimated mean of log match
quality is much larger than the original counterpart, but this is due to normalization. A productivity
shock occurs once in every 2 years. When a worker-firm match is in a bad state, their output isreduced by 66%. But this negative shock is smaller than that of the original model, which reduces
productivity by 93%. This difference is the most significant one between the original model and thealternative model. I will discuss its implication in the next subsection. Also a match is destroyed
due to an exogenous shock once in 6.32 years. The proportion of high-skilled workers is 39%
and they are 61% more productive than low-skilled workers, which implies that the distribution ofworker types is skewed to the left.
7.2. Model Fit.

JOB SEARCH, BARGAINING, AND WAGE DYNAMICS

37

7.2.1. Hazard Rate. The sample hazard rates and the simulated hazard rates are plotted in figures
7.1, 7.2, and 7.3. The simulated non full-time employment hazard rate presents the downward
trend. It is 0.46 at the first quarter and it declines to 0.43 in the fifth quarter. The level of thenon full-time employment hazard rate and the trend are similar to the observed patterns in the data.
However, the simulated employment hazard rate does not fit to the data quite well. In particular, thesimulated hazard rate does not have a downward trend: it is around 0.04 in all periods. Because theannual Poisson rate for the exogenous separation is about 0.16, no endogenous separations occur in
our simulation. This simulation result implies that the estimated model does not have sufficiently
TABLE 8. Parameter Estimates
Parameter
Human Capital

Notation Estimates Std. Dev.
γ1
0.483
0.049
γ2
-0.243
0.045
γ3
0.086
0.020
γ4
-0.011
0.004
Unemp. Benefit
b
7.894
0.863
Poisson Rate
Unemp.
λ0
3.950
0.502
Emp.
λ
1.236
0.091
Separation
δ0
0.158
0.004
Match Q. Change
δ1a
1.237
0.080
δ1b
-0.0270.004
Prod. Shock
δ
0.509
0.068
Type Dist.
High-skilled
γ0,HIGH
0.591
0.063
Weight
pHIGH
0.618
0.094
Shock Dist.
Badθ,BAD-1.0800.130
Weight
pBAD
0.148
0.020
Good
θ,GOOD
WeightpGOOD
Match Q. Dist. Mean
µ
1.439
0.117
Std. Dev.
σθ
0.361
0.029
Interest Rate: r = 0.05
Bargaining Power: β = 0.5
No. of Moment Conditions: 101
Function Value at the Minimum: 524.5206
Note: The coefficients of production function are denoted by γ. The hourly value of unemployment compensation
measured in 2004 dollar is b. The annual arrival rate of an offer for those who do not have a full-time job is λ0 . The
annual offer arrival rate on the full-time job is λ. The annual arrival rate of an exogenous separation is δ0 . The
parameters for the annual rate of match quality change are δ1a and δ1b . The annual arrival rate of productivity shockis δ. The support point for high-skilled individuals and its weight are denoted by γ0,HIGH and pHIGH . The support
point for low-skilled workers are normalized to zero. The support point for bad (negative) shock and its weight areθ,BAD and PBAD . Those for good (positive) shock are θ,GOOD and PGOOD . I impose a restriction that the meanof the shock be one for normalization. The location and the scale parameter of match quality distribution, which is
lognormal, are µ and σθ , respectively.

JOB SEARCH, BARGAINING, AND WAGE DYNAMICS

38

TABLE 9. Sample and Simulated Auxiliary Parameters (Hazard Rate)large negative productivity shock to generate endogenous separation. However, if the model had
a larger negative productivity shock, it would drive too much fluctuation in wages, because allchanges in productivity translate into wages in this alternative specification. More specifically, theresidual variance in wage regressions would be too high, if a larger negative productivity shock
existed. Unless exogenous separation rate is directly related to work experience, the model cannot
match both the employment hazard rate and the wage variance at the same time if I assume agentsnegotiate the price of efficiency unit of labor.
The simulated job hazard rate presents a downward trend. But the slope is less steep than theobserved counterpart. Because the workers with low match quality are more likely to make job
turnover, the simulated job-to-job transition rate is decreasing in job tenure, which results in a
downward job hazard rate. However, the slope is not steep enough because the model does not
generate transitions from employment to unemployment.
7.2.2. Wages. The sample and simulated auxiliary parameters of wage regression are presented
in table 10. The simulated variance of residual in each wage regression is close to the observedcounterpart. The prediction of average log wage given experience is reasonably close to the data,
as is shown in figure 7.4. The difference between the simulation and the observation is 0.03 whenexperience is ten years. The prediction of average within-individual wage growth rate also captures
the basic features of the data (see figure 7.5), although the simulated wage growth rate is faster thanthe observation. The difference between the simulated path and the observed path is largest at sevenyears of experience and it is 0.03. Figure 7.6 presents within-job wage growth rate. Similarly, thesimulated on-the-job wage growth rate is faster than the observation. The gap at five years of tenureis 0.04.
7.3. Wage Growth Decomposition. The estimated parameters are used for wage growth decomposition. Because wage is a product of efficiency unit of labor and its price, log wage at period t
can be written as
ln wt = γ0 + γ1 ht + γ2 h2t + γ3 h3t + γ4 h4t + θt + θ,t + ln q(ht , Θt , Θ0t )JOB SEARCH, BARGAINING, AND WAGE DYNAMICSF IGURE 7.1. Non full-time employment Hazard Rate

F IGURE 7.2. Full-time Employment Hazard Rate

F IGURE 7.3. Full-time Job Hazard Rate

39

JOB SEARCH, BARGAINING, AND WAGE DYNAMICSF IGURE 7.4. Average Log-wage by Experience

F IGURE 7.5. Within-Individual Wage Growth Rate

F IGURE 7.6. Within-Job Wage Growth Rate

40

JOB SEARCH, BARGAINING, AND WAGE DYNAMICS

41

TABLE 10. Sample and Simulated Auxiliary Parameters (Wage Regression)

Note: Hourly log-wages are regressed on experience (EXP) or tenure (TEN). For the detailed information on the
results for sample auxiliary parameter estimation, see table 2.

TABLE 11. Wage Growth Decomposition

where Θt = (θt , θ,t ) is a pair of match quality and productivity shock for the employer and Θ0 isthat for the potential employer. Let wh,t = γ1 ht + γ2 h2t + γ3 h3t + γ4 h4t be the contribution of generalhuman capital to log wage. Similarly, the contributions of match specific capital Θ and the price ofefficiency unit of labor q to log wage are denoted by wΘ,t = θt + θ,t and wq,t = ln qt , respectively.
The wage growth rate from period t to period t + 1 can be decomposed into the general humancapital effect, the match specific capital effect, and the price effect:ln wt+1 − ln wt = ∆wh,t + ∆wΘ,t + ∆wq,t .
The results of a wage growth decomposition are summarized in table 11. The average simulated
wage growth rate for the first ten years is 0.57, which is only 0.03 higher than the observation. The
growth of general human capital explains the largest part of the wage growth and it accounts forabout 55% of the observed wage growth. The second largest component of wage growth is match
specific human capital, which accounts for 43% of the observation. The price effect is quite small
and it accounts for 2% only.
7.4. Remark. I have examined alternative specification in which agents negotiate the price of efficiency unit of labor, rather than wage. Although this specification provides a straightforward wage
growth decomposition, the model does not fit the observed patterns in the data. More specifically,
the model does not match the employment hazard rate and the wage variance simultaneously. In

JOB SEARCH, BARGAINING, AND WAGE DYNAMICS

42

this specification, all variations in productivity are translated into variations in wages. If I allow for
endogenous separation and the model matches the observed employment hazard rate, the model
generates too large wage variance compared with the observed wage variance. In contrast, myoriginal specification in which agents negotiate wages fits both the employment hazard rate andthe wage variance simultaneously, because productivity is not directly translated into wages.
8. C ONCLUSION
The main contribution of this paper is to investigate wage dynamics using a model of wage
bargaining with on-the-job search. This is a departure from the conventional wage growth literaturein the sense that I consider a new component of wage growth: the improved value of outside
option. The model improves on previous work in two respects: it allows for productivity growth,and it deals with wage renegotiation following productivity shocks. These changes make the model
analytically complex and the equilibrium wage is numerically solved rather than using the explicit
wage solution used in previous work. However, the first change allows me to measure the effectof general human capital growth, which is the greatest contributor to the wage growth. The model
also generates a wage decrease on the job and endogenous separation due to productivity shocks.
Both of these are necessary to match the observed wage dynamics and worker mobility.
The model captures important features of wage dynamics and worker mobility in the NLSY
79. The empirical results show that only about 60% of the observed wage growth reflect theaccumulation of human capital. The effect of the improved value of outside option accounts forabout 20% of the observed wage growth in the first ten years of workers’ careers. I find that labormarket frictions explain a larger part of wage growth than previously considered in the literature.
This paper provides a detailed econometric model of bargaining with on-the-job search thatallows for rich forms of heterogeneity and time-varying productivity components. Nevertheless,there are important extensions that will be addressed in the future work. First the role of fellow workers in wage bargaining is ignored. Large firms can easily replace their employees fromtheir internal labor market. Thus, the bargaining position of the worker tends to be low in larger
firms. Second, parametric assumption for match quality distribution is strong. The assumption of
lognormality is common in the literature, but there are a number of possible alternative assumptions. Nonparametric identification might be possible using the idea of record statistics, which is
proposed by Barlevy (2005) for a job search model without bargaining.
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43[3] Abowd, John, Francis Kramarz, and David Margolis, “High Wage Workers and High Wage Firms,” Econometrica, vol. 67, no. 2, pp. 251-334.
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Theory and Evidence,” Universite de Paris 1.
[15] Carrasco, Marine and Jean-Pierre Florens (2002), “Simulation Based Method of Moments and Efficiency,” Journal of Business and Economic Statistics, vol. 20, no. 4., pp. 482-92[16] Dey, Matthew and Christopher Flinn (2005), “An Equilibrium Model of Health Insurance Provision and Wage
Determination,” Econometrica, vol. 73, no. 2. pp. 571-627[17] Farber, Henry (1999), “Mobility and Stability: The Dynamics of Job Change in Labor Markets,” in The Handbook of Labor Economics, vol. 3.
[18] Farber, Henry and Robert Gibbons (1996), “Learning and Wage Dynamics,” Quarterly Journal of Economics,
vol. 111, no. 4, pp. 1007-47.
[19] Flinn, Christopher and James Heckman (1982), “New Methods for Analyzing Structural Models of Labor Force
Dynamics,” Journal of Econometrics, vol. 18, pp. 115-168[20] Goffe, William, Gary Ferrier, and John Rogers (1994), “Global Optimization of Statistical Functions with Simulated Annealing,” Journal of Econometrics, vol. 60, no.1-2. pp.65-99[21] Gourieroux, C., A. Monfort, and E. Renault (1993), “Indirect Inference,” Journal of Applied Econometrics, vol.
8 (S). pp. 85-118.
[22] Hall, George and John Rust (2003), “Simulated Minimum Distance Estimation of a Model of Optimal Commodity Price Speculation with Endogenously Sampled Price,” Yale University.
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72, pp. 716-24.
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[25] Harris, Milton and Bengt Holmstrom (1982), “A Theory of Wage Dynamics,” Review of Economic Studies, vol.
49, no. 3, pp. 315-33.

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44[26] Heckman, James and Burton Singer (1984), “A Method for Minimizing the Impact of Distributional Assumptionsin Econometric Models for Duration Data,” Econometrica, vol.52, no. 2, pp. 271-320.
[27] Keane, Michael and Anthony A. Smith, Jr. (2003), “Generalized Indirect Inference for Discrete Choice Models,”
Yale University.
[28] Kennan, John (2004), “A Note on Approximating Distribution Functions,” University of Wisconsin-Madison.
[29] Kiyotaki, Nobuhiro and Ricardo Lagos (2005), “A Model of Job and Worker Flows,” Staff Report 358, Federal
Reserve Bank of Minneapolis.
[30] Mortensen, Dale T. and Christopher A. Pissarides (1994), “Job Creation and Job Destruction in the Theory of
Unemployment,” Review of Economic Studies, vol. 61, no. 3, pp. 397-415.
[31] Murphy, Kevin M. and Finis Welch (1990), “Empirical Age-Earnings Profiles,” Journal of Labor Economics,
vol. 8, no. 2, pp. 202-29.
[32] Neal, Derek (1999), “The Complexity of Job Mobility among Young Men,” Journal of Labor Economics, vol.
17, no. 2, pp. 237-61.
[33] Postel-Vinay, Fabien and Jean-Marc Robin (2002), “Equilibrium wage dispersion with worker and employer
heterogeneity,” Econometrica, vol. 70, no. 6, pp. 2295-2350.
[34] Rubinstein, Ariel (1982), “Perfect equilibrium in a bargaining model,” Econometrica, vol. 50, no. 1, pp. 97-109.
[35] Shimer, Robert (2005), “The Cyclical Behavior of Equilibrium Unemployment and Vacancies,” American Economic Review, vol. 95, no. 1., pp. 25-49.
[36] Shimer, Robert (forthcoming), “On-the-Job Search and Strategic Bargaining,” Structural Labour Market Models.
[37] Stole, Lars and Jeffrey Zwiebel (1996a), “Intra-firm bargaining under non-binding contracts,” Review of Economic Studies, vol. 63, no. 3, pp. 375-410.
[38] Stole, Lars and Jeffrey Zwiebel (1996b), “Organizational design and technology choice under intrafirm bargaining,” American Economic Review, vol. 86, no. 1, pp. 195-222.
[39] Topel, Robert (1991), “Specific Capital, Mobility, and Wages: Wage Rise with Job Seniority,” Journal of Political
Economy, vol. 99, pp. 145-76.
[40] Topel, Robert, Michael Ward (1992), “Job mobility and the careers of young men,” Quarterly Journal of Economics, vol. 107, no. 2, pp. 439-79.

A PPENDIX A. P ROOFS
A.1. Proof of Lemma 3.1.
Proof. First notice that a worker and a firm care only about the present value of income and thatthe timing of the payment does not actually matter because they are risk-neutral, have a common
discount rate, and have access to capital markets. For analytical simplicity, I consider a lump-sum
payment W to the worker that gives him the same value as the contract based on the constant flow
payment w. In each bargaining round, the following recursive equations for reservation values
hold,


1
[s∆U0 + (1 − s∆){βW2 + (1 − β)W1 }] , U0
W1 = max
1 + ρ∆
1J − W2 = max[(1 − s∆){β(J − W2 ) + (1 − β)(J − W1 )}] , 0
1 + ρ∆JOB SEARCH, BARGAINING, AND WAGE DYNAMICS

45

where I omit the arguments of the value functions U0 and J for notational simplicity. The firstequation says that the worker is indifferent between accepting the payment W1 and the maximumof the following: waiting for the next round after the time ∆ elapsed and quitting the bargaining tolook for other potential partners. The second equation says that the firm’s reservation payment is
W2 .
(1) J ≥ U0 : In this case, the match is efficient and there is surplus to be split. Solving the systemof linear equations and letting ∆ go to zero, I finds
W1 = W2 = βJ +(1 − β)U0 .
s+ρ
I can interpret the worker’s threat point s/(s + ρ) · U0 as the worker’s payoff when the worker andthe firm perpetually disagree. When agents are patient during the bargaining, i.e. ρ → 0, I findthat W1 = W2 = βJ + (1 − β)U0 . In equilibrium, the proposer makes an offer βJ + (1 − β)U0
and it is accepted immediately. The payoffs of the worker and the firm are {U, V } = {βJ + (1 −β)U0 , (1 − β)(J − U0 )}.
(2) J < U0 : The match is inefficient in this case. When the worker is the proposer, he asks for
U0 or more and the firm rejects this to look for other workers. When the firm is the proposer, it
asks 0 or more for the profit and the worker rejects this to look for other firms. In any case, they
immediately separate. The payoffs are {U0 , 0}.

A.2. Proof of Lemma 3.2.
Proof. I solve the problem by backward induction. Without loss of generality, I assume the match
quality with firm A is at least as good as the match quality with firm B, i.e., J(h, ΘA ) ≥ J(h, ΘB ).
Suppose that the worker bargains with firm A first. Then the worker bargains with firm B in stage
3. Because this bargaining is exactly same as the bilateral bargaining between an unemployedworker and a firm, the equilibrium payoff of the worker is given by
U3 (ΘB ) = max[βJ(ΘB ) + (1 − β)U0 , U0 ]where U3 is the equilibrium payoff the worker earns in this subgame.
Next consider the subgame in stage 2. The following recursive equations for reservation values
are satisfied1[s∆U3 (ΘB ) + (1 − s∆){βW2 + (1 − β)W1 }] , U3 (ΘB ), U0
W1 = max
1 + ρ∆
1J − W2 = max[(1 − s∆){β(J − W2 ) + (1 − β)(J − W1 )}] , 0 .
1 + ρ∆
Remember that the worker will bargain with firm B if this bargaining fails. If βJ(ΘA ) + (1 −β)[βJ(ΘB ) + (1 − β)U0 ] ≥ U3 (ΘB ), the worker and the firm reach an agreement immediately as∆, ρ → 0. The worker receives βJ(ΘA ) + (1 − β)[βJ(ΘB ) + (1 − β)U0 ] and the firm receives(1 − β)[J(ΘA ) − {βJ(ΘB ) + (1 − β)U0 }] in this subgame. If βJ(ΘA ) + (1 − β)[βJ(ΘB ) + (1 −JOB SEARCH, BARGAINING, AND WAGE DYNAMICS

46β)U0 ] < U3 (ΘB ), the respondent rejects the offer and the worker starts bargaining with the otherfirm and receives U3 (ΘB ).
Next suppose that the worker chooses to bargain with firm B first. By a similar argument to thatin the previous paragraph, the worker’s payoff in the subgame is max[βJ(ΘB )+(1−β)[βJ(ΘA )+(1 − β)U0 ], βJ(ΘA ) + (1 − β)U0 , U0 ].
Because J(ΘA ) > J(ΘB ) by assumption, the worker chooses to bargain with firm A first. If theequilibrium payoff in this subgame exceeds the value of the current contract, the worker starts thebargaining. Otherwise, he lets the challenger firm go.

A.3. Proof of Lemma 3.3.
Proof. The proof is basically same as the one for the lemma 3.1. The only difference is the payoff when bargaining breaks down. The following recursive equations for reservation values are
satisfied
1
W1 = max[s∆U + (1 − s∆){βW2 + (1 − β)W1 }] , U0
1 + ρ∆
1[s∆V + (1 − s∆){β(J − W2 ) + (1 − β)(J − W1 )}] , 0
J − W2 = max
1 + ρ∆
where U and V are the values under the current contract for the worker and the firm, respectively.
(1) J ≥ U0 and V ≥ 0: The match is efficient and both agents’ participation constraints are notbinding. Solving the system of linear equations, I find W1 = W2 = U · s/(s + ρ) as ∆ → 0. As
a firm and a worker become more patient, i.e. ρ → 0, the worker’s equilibrium payoff is U , while
the firm’s payoff is V . They eventually end up with the current contract.
(2) J ≥ U0 and V < 0: The match remains efficient, but the firm’s participation constraint is
not satisfied. Then I have J − W2 = 0. Thus, the worker accepts a wage cut so that the firm’s
participation constraint is just binding.
(3) J < U0 : The match becomes inefficient after the negative shock. They immediately separate
to look for other potential partners.

A PPENDIX B. D ETAILS OF DATA S ET C ONSTRUCTION
B.1. Weekly Job Information. First I collect information about each job. In particular, I am
interested in (1) the start week of the job, (2) the end week of the job, (3) wages, and (4) hours
worked per week. To determine the start and the end week of a job, I collect information fromthe most recent survey. I use white male high school graduates in this analysis. High school
graduates are defined as individuals who have high school diploma but did not pursue further
formal education until the most recent survey year. There are 950 white male high school graduatesin my sample and they had 10,128 jobs in total. Because an individual may have a job for morethan one survey year, I have multiple observations for each job. I have 24,565 observations in
my sample. To reduce the initial condition problems, I need information about the transition from

JOB SEARCH, BARGAINING, AND WAGE DYNAMICS

47

school to work. I omit individuals who graduated high school before January 1978, which is earlier
than the first survey year. This condition leaves me 18,114 observations for 685 individuals and7,780 jobs. Because I am interested in jobs after the transition to labor market is made, I omit
jobs that ended before graduating. I have 16,364 observations for 684 individuals and 6,555 jobs
after imposing this condition. Next I omit self-employment jobs and jobs without pay. Then I have
15,695 observations for 684 individuals and 6,417 jobs.
I determine whether a job is full-time or not by taking the average hours over all observations
for each job. A full-time job is defined to be a job that individuals work at for 30 hours per weekor more. The number of hours per week worked is topcoded so that it does not exceed 96 hours
before the average is calculated. My model precludes a transition between part-time and full-timewithout changing employer. I expect that this does not cause a serious bias, because more than
90% of jobs (5,914 jobs) did not have such switching. Omitting all part-time jobs, I have 13,686
observations for 678 individuals and 5,388 full-time jobs in the sample.

B.1.1. Dual Jobs. Several individuals have more than one job at the same time. In particular, there
are some short term full-time jobs that are started and ended while an individual holds a primary
full-time job. I omit these short term jobs for two reasons. First, these jobs may be misclassified as
full-time because individuals are unlikely to have two or more full-time jobs. Second, even if they
are correctly classified, those secondary jobs are temporary and less important for an individual’s
career. There are 601 secondary jobs and the median duration of a job is 17 weeks (the mean
duration is 34 weeks.) On the other hand, there are 4,787 primary jobs and the median duration ofa job is 51 weeks (the mean duration is 126 weeks.)
Some jobs are started before old jobs are ended. To reconcile the gap between the data and themodel, I move the start week of a job, while the end week of a job is not edited. If there are twojobs that have overlapping periods, I assume that the second job started right after the first job isended. There are 250 jobs (about 5% of all jobs) of which start weeks have to move. The medianchange is 15 weeks (mean is 34 weeks.)After all the operations described above, I have 12,846 observations for 678 individuals and4,787 jobs. The information is used to construct a quarterly job array in the followings.

B.1.2. Job-to-Job Transition Indicator. As is mentioned in the main text, I say that an individual
makes a job-to-job transition if (1) he spends three weeks or less before he starts working for a
new job and (2) he leaves the job voluntarily. Otherwise, I say that an individual changes jobs via
non full-time employment. Under this definition, I find that 1,612 jobs are started as job-to-job
transitions, while 2,480 jobs are not. If I change the search duration from three weeks to two
weeks, 1,461 jobs are started as job-to-job transition. If I change the search duration from three
weeks to four weeks, 1,694 jobs are started as job-to-job transition.

JOB SEARCH, BARGAINING, AND WAGE DYNAMICS

48

TABLE 12. The number of observations.

B.2. Quarterly Work History Array. Using the information constructed in the previous subsection, I construct a quarterly work history array for each individual. A quarter consists of 13 weeks.
The quarterly labor force status of an individual is determined by the labor force status of the firstweek in a given quarter. This implicitly assumes that the labor force status does not change during
a quarter, although it may for some short term jobs. It is true that I could avoid this discretization
bias by making the decision period shorter, but that may cause another problem. Weekly work history data would contain more noise. As Neal (1999) points out, NLSY work history file includes
measurement errors. As I make the decision period shorter, I may pick up every noise contained in
the data. Aggregating the weekly information to quarter may moderate the bias. In addition, using
shorter decision period can be computationally expensive and make my estimation intractable.
B.2.1. Entry and Exit from the Full-time Labor Market. I trace each individual from his initiallong-term transition to the full-time labor market until he exits from the full-time labor market or
the survey ends. The definition of an initial long-term transition to the full-time labor market issimilar to that of Farber and Gibbons (1996). I consider an individual has made this transition if
he works for six or more quarters during three years.
Exit from the full-time labor market occurs when an individual does not work at a full-time job
for three years or more. If this is observed in the data, I record his separation from a job and drop
the information after that. Re-entry to the full-time labor market is not included in my sample,
because I do not have any information about when individuals re-entered the labor market, i.e., thetime job search is re-started.
B.2.2. Wages. Hourly wages are computed by dividing weekly earnings by hours worked per
week. If those are not recorded on a weekly basis, such as monthly or annual, I convert themto weekly data. Wages are deflated by monthly CPI (the average in 2004 is set to 100.) If an
individual had a job that ended before the interview week, I use the wage is observed in the last
week of the job. Otherwise, I use the wage observed in the interview week. In both cases, I assume
that the wage is constant during the quarter that includes the week when wage is observed. When I
need to move the starting date of the job as I explained above, the wage observation is also moved.
I keep the link between employment record and corresponding wage observations.

JOB SEARCH, BARGAINING, AND WAGE DYNAMICS

49

B.3. Variables for Auxiliary Models. My auxiliary parameters are hazard rates and conditionalmean and variance of wage given experience and tenure. To compute the auxiliary parameters, I
need full-time job spells, full-time employment spells, non full-time employment spells, wages,
and the corresponding experience and tenure.
B.3.1. Job spells, Full-time Employment spells, and Non Full-time Employment spells. Using thequarterly work history array made above, I construct full-time job spells, full-time employment
spells, and non full-time employment spells. A full-time job spell ends when an individual switches
to a new job or loses full-time employment status (his new status is non full-time employment.)
On the other hand, a full-time employment spell ends only when an individual does not have afull-time job any more. Thus, the difference between job spells and employment spells is whether
they include job-to-job transitions. A non full-time employment spell ends if an individual who
does not have a full-time job finds a new full-time job.
B.3.2. Work Experience. All individuals start their career with zero experience and zero tenure,regardless of their actual experience recorded in original NLSY work history file. I constructthese variables using only my quarterly work history array. It is important to make my variablesconsistent with my model. Otherwise I would be unable to interpret the data in terms of my model.
As it is assumed in my theoretical model, experience does not depreciate. So, experience is the
cumulative number of quarters that an individual had a full-time job in the past.
B.4. Sensitivity Checks. One major concern is a potential bias introduced by ignoring all parttime job experience. I constructed another quarterly work history array that includes part-time jobs.
The differences from the original array are the following. First, if individuals have both a full-time
job and a part-time job in a given week, only the full-time job is recorded in weekly work history
array. Then I convert it to a quarterly array. Second, I assume part-time experience accounts for ahalf of full-time experience.
Using this quarterly work history array I construct two different measures of work experience:
one includes both full-time and part-time job experience, and another includes full-time job experience only. The paths of the two different measures are reported in figure B.1. If I include part-timejobs, the average work experience is 7.4 years ten years after graduating, while it is 6.9 years if I
do not include part-time jobs. Even 20 years after graduating, the difference is small and it is 0.8
years. This result suggests that the bias from ignoring part-time jobs is negligibly small.
I also present the proportion of all jobs that are part-time in figure B.2. Part-time jobs arequite common among the young. About a half of job holders worked in part-time jobs right after
graduating. After a year, the proportion of all jobs that are part-time quickly drops to 23% andit continues to decrease. This pattern is consistent with the result found by Klerman and Karoly(1994.) This result implies that part-time jobs are common only within a couple of years after
graduating.

JOB SEARCH, BARGAINING, AND WAGE DYNAMICS

50

F IGURE B.1. The difference in work experience when part-time jobs are not counted.

F IGURE B.2. Ratio of Part-time Jobs

A PPENDIX C. N UMERICAL I SSUES
C.1. Optimal Weighting Matrix. The optimal weighting matrix used in a simulated minimum
distance estimator is given by the covariance matrix of the sample auxiliary parameters. I firstiintroduce some notations. Let Wi = {wi,t }Tt=1
be the wage history of individual i from the initialperiod (t = 1) to the last period included in my sample (t = Ti .) Although subscripts for a job areiomitted, this wage history includes wages in different jobs. Let dJi = {dJi,j }Jj=1
be the vector ofjob spells that individual i have worked at. The number of jobs that individual i had in my sample
iis denoted by Ji . Let dFi = {dFi,k }Fk=1
be the vector of full-time employment spells for individual
N Ni
i where Fi is the number of full-time employment spells of individual i. Let dN
i = {di,l }l=1 be

JOB SEARCH, BARGAINING, AND WAGE DYNAMICS

51

the vector of non full-time employment spells for individual i where Ni is the number of non fulltime employment spells of individual i. Finally, let Di = {Wi , dJi , dFi , dNi } be the work history ofindividual i and let D = {Di }N
i=1 be the whole sample.
The covariance matrix of the sample auxiliary parameters is estimated using nonparametric bootstrap with blocking at the individual level. Specifically, I draw Di for N times with replacement.
This is important to preserve the dependent structure of the data. For example, I assume that wages
are serially correlated due to the individual fixed effect and the employer fixed effect. Another example is that full-time job spells and full-time employment spells are positively correlated, because
a long job spell necessarily implies a long employment spell. Also, the model predicts that wages
and job spells are positively correlated, because workers with high match quality earn high wages
and they are likely to remain in the job longer.
The B-th bootstrapped data set DB is used to compute the auxiliary parameters ρ̂B . I replicate
the bootstrap for 1,000 times and compute the covariance matrix of the auxiliary parameters. Although this computation takes about an hour for a 2-GHz CPU machine, it is worth doing because
the estimated covariance matrix can be used for many different specifications of the structuralmodel. This is very useful because I have to estimate models with different prefixed parameterssuch as bargaining power parameter β for sensitivity checks.
There are a few reasons that a nonparametric bootstrap should be used to estimate the optimal
weighting matrix. First, this matrix can be computed even when the analytical form is very complex. One such example is the covariance between the coefficients of wage regression (e.g., βOLS )and the hazard rates (e.g., pJ,t .) However I can still compute it through simulation in a straightforward way. Second, the weighting matrix does not have to be updated over during the iteration in
the estimation of structural parameters. This reduces the computational burden.
C.2. Minimizing the Objective Function Value. The objective function is not smooth in the
structural parameters, because actions of simulated agents are discrete such as whether or not tochange jobs. The equilibrium wages of agents are also chosen from the discretized wage grid.
Suppose a simulated agent does not change his action if I change the structural parameter values
from φ to φ + , but he changes the action if I further change the parameter to φ + 2. This discrete
response makes the objective function non-smooth through the auxiliary parameters. It is true that
this non-smoothness vanishes as the number of simulations is increased up to infinity, but there arelimitations for computational time and for computer memory to store actions of simulated agents.
I could not make the objective function smooth enough to use a quasi-Newton method.
For the minimization of the objective function, I use a simulated annealing.6 The method isrobust to a non-smooth objective function and it works well for my model. Alternative algorithm
that can be used for a non-smooth function is the Nelder-Mead simplex method. But, it converges
to one of local minima, presumably because the surface of the objective function is too noisy. This
6

Goffe, Ferrier, and Rogers (1994) implemented a Fortran software that is downloadable from http://www.netlib.org.

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problem still happens when the number of simulation is 100, but I could not increase it given mycomputational resources. The additional advantage of simulated annealing is that it searches for the
global minimum. The global optimum can be found as the number of iteration goes to infinity. The
main disadvantage is that simulated annealing often requires several ten thousands of iterations toachieve convergence. In particular, about 50,000 iterations are needed for my model, which takesme three days.
C.3. Standard Deviation of the Structural Parameters. Non-smoothness of the objective function is also problematic when I estimate asymptotic standard deviations of the structural parameters, because Jacobian of the objective function has to be computed. Remember that the objectivefunction is not differentiable due to discontinuous responses of simulated agents. The most formal
method for this problem is to use a nonparametric bootstrap. However, it would take me a year
for about 100 replications, which is not tractable. A practical solution here is to compute the Jacobian using a finite difference method with assuming smoothness. This should work well when
the number of simulations is large enough, because the discontinuity vanishes as the number ofsimulations is increased to infinity. If this is not the case, the estimated standard deviations can be
extremely small particularly when the step size for derivative is small. The reason is that the finite
difference method captures a noise on the surface of the objective function and that the absolutevalue of the computed derivative is very large.
Different step sizes are tested to see how the estimated standard deviations change. As a reference point, the final step size of simulated annealing is used because it reflects the surface ofthe objective function around the minimum. I will also check the validity of the method in a little
informal way. I will estimate the structural parameters using nonparametric bootstrap with a small
number of replications, say, ten times. This should not be used to make a formal inference for theestimates. But it is worth doing to compare the results obtained by a finite difference method andthose obtained by a bootstrap. If these two sets of results are very different, a different step size
should be used.