Returns to Tenure or Seniority?
Sebastian Buhai, Miguel Portela, Coen Teulings and Aico van Vuureny

This version: 6 July 2009
Abstract
This study documents two empirical regularities, using data for Denmarkand Portugal. First, workers who are hired last are the …rst to leave the …rm(Last In, First Out; LIFO). Second, workers’ wages rise with seniority (= aworker’s tenure relative to the tenure of her colleagues). We seek to explainthese regularities by developing a dynamic model of the …rm with stochastic
product demand and irreversible speci…c investments. There is wage bargaining
between a worker and its …rm. Separations (quits or layo¤s) obey the LIFO ruleand bargaining is e¢ cient (a zero surplus at the moment of separation). The
LIFO rule provides a stronger bargaining position for senior workers, leading
to a return to seniority in wages.
Keywords: irreversible investment, options, seniority, LIFO, matched worker…rm data
JEL-codes: J31, J41, J63

We are grateful for insightful comments and suggestions to Jaap Abbring, Joe Altonji, Marianne
Bertrand, Paul Bingley, Moshe Buchinsky, Eric French, Pieter Gautier, Larry Katz, Espen Moen,
Dale Mortensen, Kevin Murphy, Derek Neal, Jean Marc Robin, Robert Shimer, Robert Topel, Till
von Wachter, and participants in seminars and conferences at ELE in Bergen, University of Alicante,
Harvard, UC Merced, University of Minho, IFS London, SED in Boston, LMDG in Sandbjerg, EALE
in Oslo, ESEM in Budapest, University of Mannheim, Aarhus School of Business, ESPE in Verona,
SOLE in Boston and CAFE in Nuremberg.
yBuhai (corresponding author): Aarhus School of Business, Aarhus University, sebu@asb.dk;
Portela: NIPE–University of Minho and IZA, mangelo@eeg.uminho.pt; Teulings: CPB Netherlands Bureau for Economic Analysis, University of Amsterdam and Tinbergen Institute,
C.N.Teulings@cpb.nl; Van Vuuren: Free University Amsterdam, avuuren@feweb.vu.nl

1

Introduction

Why does Lars earn a lower wage than Jens, while they have the same human capitaland work at the same …rm? And why is Pedro …red and his colleague Miguel allowed
to stay at the …rm, when their employer has to scale down employment? Some might
think that the answer to these questions is obvious: it is simply because Jens andMiguel have higher seniority at the …rm than Lars and Pedro, respectively. Seniority
is di¤erent from tenure in that it measures the worker’s tenure relative to the tenureof her colleagues. A worker’s seniority is her tenure compared to the tenure of all her
co-workers at the …rm. This paper provides empirical evidence and o¤ers a theoreticalexplanation for these phenomena. Using matched worker-…rm data for Denmark andPortugal, we show that a worker who is hired last, is likely to be …red …rst (Last In,
First Out; LIFO henceforth), that is, workers are …red according to their seniority.
When we claim that seniority a¤ects your separation risk, we mean that on top of thenegative e¤ect of the elapsed tenure on the hazard rate, being a senior worker withmany more junior colleagues has a further negative e¤ect. Furthermore, we show that
there is a return to seniority in wages, even when controlling for tenure. To the bestof our knowledge, this paper is the …rst to document the existence of this return toseniority.
We set up an economic theory for why …rms and workers would agree on applying
a LIFO layo¤ rule and why that leads to a return to seniority in wages. Our theory is based on a dynamic model of the …rm, with stochastic product demand andirreversible speci…c investments for each newly hired worker, similar to Bentolila and2Bertola (1990). Dixit (1989) considers the same model, but then for an individual
worker. Labor demand follows a geometric random walk in these models. The optimal hiring and …ring points can be calculated by considering the expected discounted
marginal revenue of hiring an additional worker while (i) accounting for the option
to …re that worker at a future point in time, (ii) taking as given all workers currently
employed by the …rm, and (iii) disregarding any workers that might be hired in the
future. In this way, the hiring and …ring of each worker can be considered separatelyfrom the hiring and …ring of all other workers, transforming a …rm level model intoa model of an individual worker, as in Dixit (1989). This turns out to be equivalent
to applying a LIFO separation rule. Whereas Bentolila and Bertola (1990) and Dixit(1989) take wages as given, we allow for wage bargaining over the quasi-rents generated by the speci…c investment. Here, we apply an idea developed by Kuhn (1988)
and Kuhn and Robert (1989). Consider the standard monopoly union model, where
the union bargains for wages above the market wage and the …rm reduces its labor demand below the e¢ cient level in response to this higher wage rate. This implies thatsome gains from trade between the union and the …rm remain unexploited. While
Kuhn and Robert elaborate these ideas in a static framework, we use the dynamic
model of Bentolila and Bertola. We take an eclectic approach on the functional form of
the return to seniority, by simply positing a log-linear sharing rule of the quasi-rents.
However, we impose e¢ cient bargaining: as long as there are positive quasi-rents,
the worker and the …rm will reach agreement on their distribution. Hence, …ring
decisions are e¢ cient. Hiring decisions are e¢ cient if and only if costs and revenues3

of the speci…c investment are shared in the same proportions. If not, hiring is below
the e¢ cient level due to a hold-up problem. We shall refer to this condition as the
Hosios (1990) condition, like in search theory. We elaborate our model under theassumption that the …rm must pay for the full cost of the speci…c investment, so thatany return to seniority implies sub-e¢ cient hiring because workers capture part of
the quasi-rents. As an extension, we consider the e¤ect of …ring costs, accounting
for its upward e¤ect on wages.1 By the e¢ cient bargaining assumption, …ring costs
do not a¤ect …ring, but further deteriorate hiring. Finally, we consider the role oftrade unions in this model. At …rst sight, the ideas in Kuhn (1988) and Kuhn andRobert (1989) seem to suggest the return to tenure to be higher in unionized …rms,
since unions are predicted to use the tenure pro…le as a rent extraction mechanism.
However, the sparse empirical evidence on the issue does not con…rm this hypothesis.
Following up on a further suggestion by Kuhn (1988), we observe that the state offacts might …t our theory. The LIFO layo¤ rule allows for a decentralisation of thebargaining process to the individual level –as required in the absence of a union–
leading to higher wages for senior workers. Instead, the political process within aunion would lead to a more egalitarian distribution of the rents among the workers,
that is, to higher wages but a lower wage return to seniority.
In the empirical part, we establish a number of features of our model. We needall-encompassing matched worker-…rm data to establish workers’ seniority because
1

In Bentolila and Bertola’s (1990) analysis of the e¤ect of …ring costs, wages are …xed. Accounting
for the e¤ect on wage setting turns out to be crucial for the conclusions.

4we need to know the tenure of all the workers in the …rm. We show that juniorworkers have ceteris paribus a higher separation probability than senior workers.
Second, we show that there is a wage return to seniority. Starting from the seminal
papers by Altonji and Shakotko (1987) and Topel (1991), there is a large and still‡ourishing literature on the estimation of the wage return to tenure. The main
problem in this literature is that within a job spell, tenure is perfectly correlated withexperience. Hence, the …rst order term of this return can only be estimated using
variation between job spells, but that introduces all kinds of selectivity problems,
which this literature sets out to resolve. We show that this problem is absent in theestimation of the return to seniority, since seniority is not perfectly correlated withexperience. Furthermore, Neal (1995) and others have shown that the return to thetenure at the …rm, as measured by the previous studies, is partly a proxy for a return
to tenure in the industry or occupation. We show that this …nding does not a¤ecteither our estimation of the return to seniority. We …nd wage returns to seniority of
1 to 2 % in Portugal, and returns half that range in Denmark. We argue that our
results cannot be explained by tournament models such as Lazear and Rosen (1981)
and Malcomson (1984), learning models à la Jovanovic (1979), or job search models
like Postel-Vinay and Robin (2002) and Burdett and Coles (2003).
The paper is set up as follows. Section 2 presents our theoretical framework. In
Section 3, we describe the data for Denmark and Portugal, and present our empirical
speci…cations and estimation results. Section 4 concludes.

5

2

Theoretical framework

2.1

Assumptions

Consider a world where …rms produce a di¤erentiated product. Each …rm faces astochastic iso-elastic demand curve for its output:

nt = zt

where

(1)

pt ;

> 1 is the price elasticity of demand, Nt is demand, Pt is its price; lower

cases denote the log of the corresponding upper cases, so nt is log demand (= output).
The variable zt is a market index capturing the exogenous evolution of demand; zt
is assumed to follow a Brownian with drift, such that

z

N( ;

2

). Labor is the

only factor of production. The production function exhibits constant returns to scale.
Without loss of generality, labor productivity is normalized to unity, so that output
is equal to employment. The market index is non-veri…able, such that the worker
and the …rm cannot contract on it. The hiring order of workers is veri…able, suchthat the contract may be contingent on this. Both workers and …rms are risk neutral.
Workers live forever and maximize the discounted value of their expected income.
Firms maximize the discounted value of their expected pro…ts. The discount rate isdenoted by . Finite discounted values require this discount rate to be larger than

6the growth rate of expected demand:

>

+

1 2
:
2

(2)

At the start of an employment relation, the …rm has to make a speci…c investment
I.2 This investment is irreversible: once made, the cost cannot be recouped byending the employment relation. For simplicity, we assume that this investment canbe made instantaneously, so that no time elapses between the start and the end of
the investment process. The speci…c investment is also unveri…able. Hence, the …rmand the worker cannot write a contract in which future payments are contingent onwhether or not this investments is actually made. Workers have some bargaining
power; workers will capture some share of the quasi-rents generated by this speci…cinvestment. Hiring new workers and making the speci…c investment requires theconsent of the incumbent workers. The motivation for this assumption is that a mainpart of the speci…c investment is the transfer of the …rm’s tacit knowledge, which
is a monopoly of senior workers. An alternative motivation is that senior workers
can harass newcomers, as suggested by Lindbeck and Snower (1990). At the outside
market, workers can earn an outside wage, which is constant over time. It is mostconvenient to think of this outside wage as the return to self employment. Without
loss of generality, it is normalized to unity: wr = 0, where wr denotes the log-outsidewage.
2

In Bentolila and Bertola (1990), there is both hiring and …ring costs per worker. For the moment,
we set the …ring costs equal to zero. As an extension, we consider the implications of …ring costs.

7

2.2

A benchmark case: w = 0; I = 0

As a benchmark, we analyze the simple case in which …rms pay workers the outside
wage, w = wr = 0, where w denotes the log wage paid by the …rm, and where there
are no speci…c investments required for starting an employment relation, I = 0. In
that case, labor demand can be adjusted costlessly at each point in time. Hence, theoptimal strategy is to maximize instantaneous pro…ts

t = Nt P t

t:

Nt ;

subject to the demand curve (1). The …rst term is total revenue, the second term is
the wage bill. The …rst-order condition for pro…t maximization yields the standard
Amoroso-Robinson rule:(3)

pt = ;
nt = zt

;

ln

1

> 0:

The …rm’s price is constant over time, since the …rm applies a …xed markup overmarginal cost: log marginal cost is wr = 0; so that

> 0. The log of the …rm’s labordemand follows a random walk, a regularity known as Gibrat’s law, which holds
particularly for larger …rms, see for instance Jovanovic (1982).

8

2.3

The case with speci…c investment: w = 0; I > 0

When I > 0 labor demand cannot be adjusted costlessly. On the hiring side, anadditional worker requires a speci…c investment, which has to be recouped from future
pro…ts. Moreover this investment is irreversible, so that delaying hiring has an option
value. If demand falls after hiring the worker, the …rm cannot get rid of the worker
without losing the speci…c investment. Hence, the …rm does not hire additional
workers at the …rst moment that pt rises above . Instead, the …rm postpones hiring
till pt is substantially above . The reverse holds at the …ring side. Firing per se iscostless, but irreversible. If demand surges after having …red the worker, the …rm isunable to bene…t from that demand without incurring the cost of speci…c investment
again. Hence, retaining the worker has an option value. The …rm postpones …ring till
pt is substantially below . Analogous to Bentolila and Bertola (1990), we shall showthat the optimal policy of a …rm is to hire workers whenever pt reaches a constanthiring bound p+ and to …re workers whenever pt reaches a constant …ring bound p .
The hiring bound is above the price level for the case I = 0, while the …ring boundis below it: p+ >>p .

The situation is sketched in Figure 1. The downward sloping curves are inverse
labor demand curves, specifying log marginal revenue mr ( ) as a function of zt

lnd (Nt Pt )
1
= (zt
dNt

nt )

mr (ztnt ) :nt :(4)

Let the current level of the market index be z0 . In the case I = 0, the …rm sets log
9Figure 1: Firing-hiring boundaries with stochastic market index

employment n0 such that log marginal revenue mr (z0cost wr = 0; hence n0 = z0n0 ) is equal to log marginal, see equation (3). Any change in zt will immediatelya¤ect log employment nt , but will leave the log price constant at. In the caseI > 0, the …rm hires additional workers only when zt rises above zh , because at thatpoint the price level hits the hiring bound, pt = p+ . Similarly, the …rm …res workers
only when the market index falls below zf , since then the price hits the …ring bound,pt = p . Hence, pt follows a random walk between p and p+ , while nt is constant at
n0 in this interval. However, when pt drifts outside these boundaries, the …rm uses nt
as an instrument to keep pt in the interval [p ; p+ ]. Then, pt is held constant, and nt
starts drifting, either up (if pt = p+ ), or down (if pt = p ). We provide expressions
for p+ and p later on.

10

2.4

The case with a LIFO rule and rent sharing

Speci…c investment creates quasi-rents. Since workers have some bargaining power,
they will be able to capture part of these rents. Hence, workers have an interest in
the continuation of their relationship with the …rm. Since hiring requires the consent
of the incumbent workforce and since incumbents have an interest in the continuationof their relationship with the …rm, they want to make sure that new hires will not
be used as replacement for themselves when the …rm has to downsize at some future
time. Since the layo¤ order is contractible, they can refuse to train new workers
unless the …rm agrees not to …re any of the current incumbents before having …red all
workers that will be hired. The …rm has no incentive to oppose this demand of theincumbents; it is indi¤erent between …ring either the one or the other worker whennecessary, since after having …red either of them, the bargaining position vis-à-vis
the remaining workforce is identical. Because similar bargaining has taken place atall previous points in time when the …rm has hired additional workers, this outcome
generalizes to the …rm applying a LIFO (Last-In-First-Out) separation rule: …re thelatest hires …rst.

Claim 1 Consider a …rm that satis…es the previous assumptions. If this …rm wants
to …re some of its workers, it applies a LIFO separation rule, …ring …rst the workers
whom it has hired last.

When the …rm pays its workers their outside wage, see Sections 2.2 and 2.3, there
is no rationale for a LIFO layo¤ rule. Since the worker receives her outside wage, she
11is indi¤erent between working at the …rm and being laid o¤. Hence, there is no point
in …xing an order of layo¤. However, when the …rm pays its workers some share of
the quasi-rents of the speci…c investment, a layo¤ order carries practical relevance, as
it protects the ‘property rights’of senior workers on their part of the quasi-rents.
Under this LIFO layo¤ rule, the distribution of completed job tenures is characterized by the following proposition.

Proposition 1 Consider a …rm that satis…es the assumptions of Section 2.1, andthat hires workers when pt = p+ and …res workers when pt = p . The distribution of
the completed tenure of workers hired by this …rm is equal to the …rst passage time
distribution, that is, the distribution of the time it takes a random walk zt , with initialvalue z0 , to pass the barrier z0(p+p ) for the …rst time. This distribution is

identical for all workers hired by the …rm, irrespective of the number of workers hired
previously.

Proof: The LIFO layo¤ rule implies that a particular worker who is hired attime h, when log employment is nh , will be …red at the …rst moment f > h that log
employment is equal to nh and pf = p , since this worker can only be …red when
all workers hired after her, by implication at h < t < f , have been …red, due to the
LIFO rule, whereas all workers that have been hired before her, at t < h, cannot be…red before this worker, also due to the LIFO rule. Hence, zh

zf = (p+p ) andzh

zt > (p+p ) ; 8t 2 (f; h). The distribution of the …rst moment in time thatzhzf = (p+p ) is independent of the starting value zh of the random walk at
12

time h, due to the Markov property of a random walk.
Bentolila and Bertola’s (1990) model of …rm level employment supplemented witha LIFO layo¤ rule corresponds therefore one-to-one with a simple model of individual
job tenures. Buhai and Teulings (2006) analyse the characteristics of the distributionof completed tenures implied by this model: its hazard rate starts at zero, then rises
quickly to a peak, and then falls slowly, to zero for
number for> 0; and to some positive< 0. Buhai and Teulings estimate this model on tenure data for theUnited States, and show that if …ts the data well.
Having established that a …rm and its workers agree to apply a LIFO layo¤ rule,the next question is whether all workers receive the same wage or whether the amountof rents each worker can capture di¤ers by her degree of seniority. Kuhn (1988)
and Kuhn and Robert (1989) o¤er a neat further legitimation for applying a wageschedule that di¤erentiates wages between otherwise equal workers. Consider the
standard monopoly union model, where the union bargains for a wage rate above theworkers’reservation wage. The …rm reduces its labor demand below the e¢ cient levelin response to this higher wage rate. This leaves some gains from trade unexploited,since there are workers who would be willing to work at the …rm for the outside wage
and the …rm would be willing to hire them, but these trades do not occur because
the …rm is not allowed to pay wages below the union rate. Kuhn and Robert observethat there is an alternative way for workers to extract rents from the …rm withoutleaving gains from trade unexploited. The idea is to simultaneously set a layo¤ orderand bargain on a wage schedule that di¤erentiates wages according to the worker’s
13

position in the order of layo¤. Since Kuhn and Robert (1989) specify their theory
in a static framework, the layo¤ ordering can be based on anything: height, IQ,
experience, or what else springs to mind. In the dynamic framework that we apply
here, this order must necessarily be the LIFO rule, see Claim 1.
For the implementation of the LIFO layo¤ rule, de…ne the rank qt of a particular
worker to be the log number of workers in the …rm with tenure greater or equal than
this worker (hence including herself), at time t. Suppose this particular worker has
been hired at time h; h < t. Due to the assumption that workers live forever and dueto the LIFO rule, all workers who have been hired before her are still employed by
the …rm, because they can only be …red after she is …red. Hence, her rank qt is equal
to log employment at the moment when she was hired: qt = nh . Since nh is constant,so is qt , such that we can drop the su¢ x t. Hence, a worker hired at time h gets rank
q, q = nh = zhp+ .

Consider a wage schedule that is in between the reservation wage and the …rm’s
inverted labor demand curve mr (ztq); then the …rm will never …nd it attractive

to …re any worker, since it makes a pro…t on the marginal worker at each employment level. Thus, even though inframarginal workers earn wages above the marginal
revenue of the last worker hired, the …rm has no incentive to …re these workers since
it may only …re these expensive inframarginal workers after having …red the cheap
marginal workers. Hence, the employment is set at the e¢ cient level where marginal

14

revenue is equal to the reservation wage.3 The LIFO rule provides senior workers
protection against layo¤, which they use to demand a higher wage. Given the lackof a formal theory of multiplayer bargaining, we take an eclectic approach in wage
setting. We assume the relation between the log-marginal revenue mr (ztq) andthe log-reservation wage on the one hand, and log wages on the other hand, to belinear:w(ztwith 0q) =mr (ztq) +1. The parameter

p

+! =

(zt

q)

p + !;(5)can be interpreted as the bargaining power ofworkers.4 This wage setting scheme is a form of price discrimination on the side of
the union. The case

= 1 corresponds to …rst degree price discrimination, where

the union has full bargaining power. In the case

= 0, workers have no bargaining

power and they get just their reservation wage. The parameter = is increasing in
the bargaining power of the workers, , and in the monopoly power of the …rm,
Since 0

1 andof …ring f , zf

q = p , and hence, by equation (4), w(zf1.

> 1, this parameter is between zero and unity. At the momentq) = !. The parameter! can therefore be interpreted as the log reservation wage of an incumbent worker.
We present an expression for ! later on.
3

We ignore here the ine¢ ciency that is due to the monopoly power of the …rm at its productmarket, which causes its marginal revenue to be below the output price.
4
In the case of a single worker-…rm pair, where we could apply the theory of two player bargaining,as in Buhai and Teulings (2006), the log-linear sharing rule would be almost equivalent to Nashbargaining, which would yield a linear (instead of log-linear) sharing rule of the surplus between theasset values of the worker and the …rm (instead of the surplus between current productivity and thereservation wage).

15

The situation is depicted in Figure 2. The left panel sketches the situation for
Kuhn and Robert’s (1989) static framework. The two continuous lines in the graph
are the marginal revenue, mr (z0q), and respectively the wage schedule, w (z0q).

The shaded area between them is the surplus of marginal revenue above marginal
cost for that level of log employment, q. As long as the log wage schedule is between
the marginal revenue curve mr (z0q) and the log reservation wage !, neither the…rm nor the workers have an incentive to deviate from the …rst best level of log
employment, n0 , since the surface of the shaded area is maximized by setting n =n0 . In that sense, equation (5) implies e¢ cient bargaining: all gains from trade are
exploited. Although inframarginal workers earn a log wage w (z0marginal revenue mr (z0q) above the logn0 ), the …rm has no incentive to …re them, because it isobliged to …re the less expensive marginal workers …rst. In the dynamic framework à
la Bentolila and Bertola (1990) there are some complications, see the right panel of
Figure 2. Since investment I is irreversible, workers have an option value for the …rm.
Hence, the …rm retains workers when marginal revenue has fallen just slightly below
marginal cost, wr > mr (z0n0 ) > p, since by …ring the worker the …rm loses

the option of bene…ting from the market index rising above z0 at a later stage without
having to pay the speci…c investment I again. Similarly, the marginal worker, q = n0 ,prefers staying employed at the …rm even when her wage rate is just slightly below
the reservation wage, wr < w (z0n0 ) < !, since by quitting the worker loses theoption of bene…tting when the market index zt rising above z0 at a later stage, andhence log wages rising above wr . For some range of zt 2 [zf ; z0 ], marginal revenue
16Figure 2: Static vs. dynamic frameworkis therefore below marginal cost, mr (ztn0 ) < wr , and the wage for the marginal

worker is below the outside wage, w (ztn0 ) < wr . Only when w (ztn0 ) is below! the marginal worker quits, because the prospect of future wage increases no longer
outweighs the cost of the current wage being below the outside wage. In the next
sections we derive expressions for these option values, for the log-reservation wage !,and for the hiring and …ring threshold p+ and p .
De…ne now the seniority index 5 rt at time t as

rt

nt

q:

(6)

Hence, the most senior worker has rank q = 0, and her seniority index is rt = nt ,while the least senior worker at time t has q = nt , and her seniority index is rt = 0.
The seniority index of worker i is the log of the ratio of the total number of workers
5

Seniority index and seniority are used interchangeably throughout the text.

17

to the number of workers with greater or equal tenure than worker i; keeping total
employment …xed, a 1% increase in your seniority is equivalent to the number of peer
workers with greater or equal tenure decreasing by 1%. To see how wages are related
to the seniority index rt , equation (5) can be rearranged as

w(zt

q) =

rt +

pt

p

+!

(7)

Wages depend on the seniority index of the worker, rt , and on the price of the …rm’s
output, which varies between p

and p+ . Hence, the return to seniority,= , isbetween zero and unity. As long as pt is in between the upper and lower bounds p
and p+ , the …rm’s employment, and hence the worker’s seniority index, are constant.
In this interval for pt , variations in the market index zt translate into ‡uctuations in
pt , or equivalently, in pro…ts per worker.6 Hence, there is a positive relation between
wages and pro…ts per worker, as documented e.g. by Abowd and Lemieux (1993).
When pt = p , a further decline in zt induces the …rm to …re some of its workers, sothat nt , and hence the seniority index rt , go down. The lower rt translates in a fallin the wage rate for the workers who are not laid o¤. The other way around, whenpt = p+ , a further increase in zt induces the …rm to hire additional workers, so thatthe seniority index of the incumbents goes up, which translates in an increase in thewage of incumbents.
6

A 1 % increase in the price of output yields % increase in the wage per worker, 0 < < 1.
Since productivity is normalized to unity and since labor is the only factor of production, cost perunit of output increase also by %. Hence, total revenue goes up more than total cost.

18

The …rm size e¤ect on wages has been extensively documented, see e.g. Brown
and Medo¤ (1989). Can our model o¤er an explanation for the …rm size wage e¤ect?
When we look at the issue from the point of view of an individual worker, the evolutionof her seniority rt is driven by the evolution of the log …rmsize nt , since the value ofher rank q is …xed over the duration of the job spell. At …rst sight, this suggests that
our theory could explain the …rm size wage e¤ect. This turns out not to be true. The
average log wage of a …rm at the …ring bound p satis…es

E wjpt = p

Z nt
1
=
w(zt q)eq dq
Nt 1
Z nt
1
! + = zt q
=
Nt 1

p

eq dq = ! + = ;where in the …rst expression the factor eq comes in as the Jacobian dQ=dq = Q = eq ,and where in the …nal equality we use the fact that at the …ring bound nt = zt

p .

Hence, the average log wage does not depend on …rm size. The intuition is that thepositive e¤ect of an increase in the market index zt on the average log wage for theincumbents is exactly o¤set by the negative e¤ect of the below average log wage for
new hires. Thus, although the model predicts …rm size to be a driver of wage changes
for incumbents, it does not explain why wages for the …rm as a whole depend on …rm
size. The average log wage does depend on the parameter = . Other things equal,
the model predicts the return to seniority,= , to be increasing in the average log

wage. A similar argument establishes that the average log wage of a …rm at the hiring

19bound is also independent of …rm size

E wjpt = p+ = ! + = +

p+

p

.

This reasoning implies that on the hiring and …ring bounds both the average wage
and pro…ts per worker are …xed and ‡uctuations in the market index zt translate
into variation in the size of the workforce, while in between the two boundaries thereverse holds: employment is …xed, and ‡uctuations in zt translate into variationin the average wage and pro…ts per worker. Note that ‡uctuations in pt (driving
variation in pro…ts per worker) and in the seniority index rt are orthogonal, since
when the one changes the other is constant, and the other way around. Hence, in aregression context, omitting either one as an explanatory variable does not a¤ect theconsistency of the parameter estimate for the other.

2.5

The worker’s problem

The value of the parameter ! in equation (5) can be derived using the theory of
option values, see Dixit and Pindyck (1994, 136–140)7 . E¢ cient bargaining implies
that at the moment of separation both the worker and the …rm are indi¤erent between
continuation of the employment relation. In this section, we analyse the worker’s sideof the problem, which yields an expression for !. The next section looks at the …rm’s
7

Dixit and Pindyck (1994) consider an optimal investment problem instead of an optimal stopping
problem, but this is mutatis mutandis the same. Their notation is somewhat di¤erent in that theirz denotes a geometric Brownian instead of standard Brownian. The equations are exactly the same,
but we feel our notation to be simpler.

20

side of the problem, which yields expressions for the hiring and …ring thresholds, p
and p+ . Let V (ztV (ztq) be the asset value of holding a job at a …rm. By Ito’s lemmaq) satis…es the Bellman equation

V (ztq)] + V 0 (ztq) = exp [w (ztq) +1 2 00
V (zt
2

q) ;

The left-hand side is the return on the asset. The …rst term on the right hand side,
exp [w (ztq)], is the current wage income, the second and the third term are the(expected) wealth e¤ects of the drift and the volatility in the market index zt . The
solution to this second order di¤erential equation reads

V (zt

q) =

1
exp ! +r( = )++A+ exp
r (x)
+;

(zt

q

p

+ A exp

(zt

q)

(8)

q)

1
( x)2 ;
x
2
p
2+2
2
2

where we substitute w (ztzt:q) from equation (5) and where A

and A+ are con-stants of integration that remain to be determined. r (x) is a modi…ed discount rate,accounting for the drift and the variability of zt . We have:r (0) = ; r (1) =
< 0;

+

> 1:

21

1 2
> 0;
2

where the …rst inequality follows from equation (2). The …rst term on the right-handside of equation (8) is the net-discounted value of expected wage payments, disregarding the worker’s option to quit the …rm when wages fall too far below the reservation+;

wage. The …nal two terms, A+; exp
one of the roots+;

zt , are the option value of separation. Only

is relevant, due to a transversality condition. For large valuesof zt , the …rm is doing well and hence, keeping the job is attractive to the worker for
the foreseeable future. Hence, the option value of separation must converge to zero,
which is the case for the negative root

, since limz!1 A exp

z = 0. Hence,the constant of integration A+ must be equal to zero.
E¢ cient bargaining implies that it is optimal for a worker with rank q to separate
when zt = q + p . Two conditions need to hold for that value of zt to be optimal:

V (zt

q) =

V 0 (ztq) =1
e! + A er( = )r( = )

e! +

z

1
= ;

A e

z

= 0:

The …rst condition is the value matching condition, which states that the asset valueof holding the job should be equal to the asset value after separation, that is, the net
discounted value of the outside wage,

1. The second condition is the smooth pasting

condition, which states that for small variations in zt the worker remains indi¤erent
between holding the job and separation. Since separation is irreversible, the worker
should not regret separation after a small perturbation of zt . This requires the …rst

22

derivative of V (ztq) to be zero. Elimination of A yields an expression for !:! = ln r ( = )

ln

ln 1

:

(9)

0; (ii) @!
< 0; (iii) @!
< 0; (iv) @!
< 0.
@
@
@

Proposition 2 (i) !

Proof: The proof is straightforward calculus.
! is below the log outside wage wr = 0 since separation is an irreversible decision. If
the demand for the …rm’s product, zt , goes up after the separation decision, the worker
is no longer able to bene…t from the wage increase. Hence, workers are prepared toincur some loss before they decide to separate. The higher the worker’s bargaining
power , the lower is !, since expected future revenues are higher so that workers areprepared to accept greater losses before separation. Similarly, ! is declining in thedrift

since a higher drift raises expected future revenues, and ! is declining in thevariability of demand2, since a higher variability raises the option value of hoping

for a future increase in the surplus.

2.6

The …rm’s problem

We now turn to the …rm’s optimal strategy. We observe that hiring a worker withrank q a¤ects neither log marginal productivity8 mr (ztq), nor log wage w (ztq),

for workers with rank q < q (the workers who have been hired before worker q ).
8

Note that the function mr (zt q) measures the marginal revenue of adding the q-th worker,
or equivalently, it is the …rm’s marginal revenue as if employment were only q. When actual
employment is larger, nt > q, the actual marginal revenue of the …rm is smaller, see Figure 2, which
is drawn for t = 0.

23

Similarly, whether or not the …rm hires any workers q > q after hiring worker qa¤ects neither mr (ztq ), nor w (ztq ). Furthermore, the option of …ring worker

q at a future date is una¤ected by the hiring of workers q > q . Hence, in its costcalculation, the …rm can attribute each worker her log marginal revenue mr (ztand her log wage w (ztq)q), taking the employment of workers hired previously as

given, and then consider when it is optimal to hire and subsequently …re this worker.
In this way, we can consider the decision to hire and …re the Nt -th worker separatelyfrom the hiring and …ring of workers hired before this worker, and of workers hired
afterwards. Then, the model is a straightforward extension of Dixit and Pindyck(1994: 216), the only di¤erence being that wages are constant in Dixit and Pindyck,
while they vary with the state of demand zt in this model. Let F be the asset valueof the …rm for the Nt -th worker, that is, taking the optimal behavior of the …rm forhiring workers with higher seniority as given. The Bellman equation for F satis…es

F (ztnt ) = exp [mr (ztnt )]exp [w (ztnt )] + F 0 (ztnt ) +

1 2 00F (zt2nt ) :The …rst term is the marginal revenue of that worker, the second term is the wage
for that worker. The …nal two terms capture the option value of separation. The
relevant solution to this di¤erential equation reads

F (ztnt ) =

1
r(

exp
1)

+B exp

1

(zt

nt )

(zt

nt ) :

24

1
exp [w (ztr( = )

nt )]

(10)

The …nal term is the option value of separation, with B

being the constant ofintegration. As in the case of the worker, the positive root+is irrelevant, due toa transversality condition: the option value converges to zero for large values of zt .
Suppose the …rm employs less than Nt workers. Then, the option value of hiring theNt -th worker at some future date is

G (zt

+

nt ) = B + exp(ztnt ) ;(11)

where B + is the constant of integration. There are no current costs or revenues, hence
only the option value term matters. Since this option value converges to zero for low+

values of zt , only the positive root

applies here. The value matching and smooth

pasting conditions read

F

p

=G

F0

p

= G0 ( p );F

p+ = Gp+ + I;F0

p+ = G0

p+ :

p

;

(12)

The …rst pair refers to the …ring decision, the second to the hiring decision. The …rst
condition states that at the moment of …ring, when by de…nition zt

nt = p , theasset value of keeping the worker is equal to the option value of a vacancy. The second
equation is the smooth pasting condition, which states that this condition also applies

25

for slight variations of zt , so that the …rm would not regret a decision to …re after
a slight variation in zt . The third equation is the value matching condition for the
moment of hiring, when zt

nt = p+ : the asset value of hiring the worker should beequal to the cost of investment plus the option value of …lling the vacancy at a later
point in time. The …nal equation is the smooth pasting conditions for the momentof hiring. This system of four equations determines four unknowns, the constants ofintegration, B and B + , and the hiring and …ring boundaries, p and p+ .

Proposition 3 The system of equations (12) has a unique solution for p+ ; p ; B + ; B
for which (i) p+>0>!>p; B + > 0; B > 0; (ii) @B@++

0; (iii) @p> 0;@(iv) @p< 0.
@

Proof: see Appendix.
A unique, economically meaningful solution exists, see Proposition 3-(i). In the static
version of the model by Kuhn and Robert (1989), the distinction between hiring and…ring is meaningless, so that there is only a single issue of e¢ ciency, namely the levelof employment. In the dynamic version of the model, the e¢ ciency of hiring and…ring are two separate issues. Since the asset value for outside workers is equal to thenet discounted value of their outside wage,

1, the option value of a …rm to hire an

outside worker conditional on nt and zt , is the residual claim in this economy. Anyine¢ ciency shows up as negative e¤ect on this option value. This option value is
proportional to B + , see equation (11). Hence, Proposition 3-(ii) implies that=0

is most e¢ cient, since then B + is at its maximum. This result is due to a hold-up
26

problem. For e¢ ciency, the Hosios (1990) condition should apply: the quasi-rents
should be shared between players according to their share in the cost of the speci…cinvestment. Since here the …rm is assumed to bear the full cost, any share of thequasi-rents being assigned to workers leads to ine¢ ciency. Hence,e¢ cient. If= 0 is most

> 0, …rms will postpone hiring of new workers till the surplus of log

marginal productivity mr (ztq) above the log outside wage wr is such that, eventhough the …rm gets only part of the quasi-rents, its net discounted value is su¢ cient
to cover the cost of investment. This explains why p+ is positively related to , see
Proposition 3-(iii). We now turn to the …ring decision. The elimination of B fromthe …rst two equations of (12) yieldsp= ln r

1

ln

ln 1

1

+

+ln 1

B + exp+p: (13)The …ring bound p does not depend on , except for its e¤ect on B + . This is anapplication of the Coase theorem: under e¢ cient bargaining, the distribution of thesurplus of the employment relation does not matter for the actual level of employment.
The only exception is the option value of hiring another worker for this vacancy at alater stage. This option value comes in because at the same time that the …rm …resthe Nt -th worker, it acquires the option to rehire at a later stage, provided that it pays
the cost I again. This option makes …ring more attractive, so it raises p . The larger
is , the lower is this option value of future rehiring, and the less attractive it is to …rea worker, see Proposition 3-(iv). Propositions 3-(iii) and (iv) imply that the higher is27the workers’bargaining power , the less volatile is employment, since it is insulated
from shocks to the market index zt over a larger interval of p < zt

nt < p+ , andthe larger is therefore the expected tenure of a newly hired worker. These implications
square well with the …ndings in Bertrand and Mullainathan (2003), who show thatwhen …rms are insulated from takeovers, the wages of the incumbent employees arehigher, suggesting a higher value of . This goes hand in hand with lower rates ofcreation of new plants, which in the context of our model is similar to a higher hiring
bound, p+ . Bertrand and Mullainathan also report a lower rate of destruction of oldplants, or in the context of our model, a lower …ring bound, p .

2.7

Unemployment and the welfare cost of hold up

The model implies that new jobs are rationed. This can be seen most easily byconsidering the wage of a worker who is just hired. This wage is higher than that ofa worker who is at the borderline of being laid o¤, that isw

p+ > wp= !:Since the asset value of a worker who is on the borderline of being laid o¤ is equal
to the net present value of her outside wage, 1= , the asset value of a worker who isjust hired must be higher than 1= . To close the model, we therefore have to explain
who gets hired by a …rm and who does not. A convenient way to model this rationing
process is to introduce unemployment. A worker who is just laid o¤ has two options.

28Either she decides to collect her outside wage by becoming self employed, or she candecide to queue for a new job at a …rm. During this waiting period she must spend
all her time searching and hence, she cannot produce as self employed. For simplicity,
we assume that leisure has no value.9 New jobs at …rms arrive at a rate

per unitof the labor force and are distributed randomly among the unemployed. Hence, theasset value of unemployment, V U , satis…es

VU =

u

p+

V

VU ;

where u is the unemployment rate. =u is the arrival rate of a new job for unemployed.
The lower unemployment, the higher this arrival rate, since there are less people
among whom new jobs have to be distributed. V ( p+ )V U is the asset gain ofgetting a job o¤er. The level of unemployment follows from the no-arbitrage condition
between self employment and unemployment

u=

V

p+

1

;

(14)

where we use V U = 1= , the asset value of self employment10 . The higher the asset
gain of getting a job at a …rm, the higher is unemployment. Hence, there are two types
9
Allowing for a value of leisure would not change the predictions of model. It would makeunemployment less costly per unit of time, but this e¤ect would be exactly o¤set by the increase in
unemployment.
10
We assume: u < 1. If not, everybody would be self-employed, since even if everyone weresearching for a job, …rms would not open vacancies.

29

of ine¢ ciency.11 First, not all gains from trade between the worker and the …rm are
exploited. Firms would hire more workers if= 0, since p+ is an increasing functionof . Firms’perception of the marginal costs of hiring a worker in net present value
terms exceed the social costs by the same amount as the asset gain for an unemployedof getting a job o¤er, V ( p+ )1= . This gives rise to a Harberger triangle. Next

to this Harberger triangle, there are the costs of rationing that dissipate workers’
surplus. The no-arbitrage condition (14) implies that the workers as a group spoil
their whole share of the quasi-rents in wasteful unemployment.
As discussed before, the ine¢ ciency is due to a violation of the Hosios condition
that the costs and quasi-rents of speci…c investments should be shared in the same
proportion between workers and …rms. At a deeper level, the failure to satisfy the Hosios condition is due to the combination of the non-veri…ability of speci…c investment
and the inability of workers to commit on not using their bargaining power after the
speci…c investment has been made. If wages were contractible, workers could commit
on not demanding any return to seniority, such that the …rm bears the full costs
and gets the full revenues of the speci…c investment, thereby satisfying the Hosios
condition. Alternatively, if speci…c investments were veri…able, the ine¢ ciency would
be resolved by shifting some share of the burden of investment to the worker, suchthat workers bear an equal share of the costs of the speci…c investment as they getfrom its revenues, again satisfying the Hosios condition. It is useful to consider this11

Throughout the paper, we do not pay attention to a third type, the ine¢ ciency caused by themonopoly power of the …rm vis-à-vis consumers.

30

case more closely. The asset value of a worker at the moment of hiring, V ( p+ ), is
independent of the worker’s rank, q. Hence, although at a particular point in timesenior workers receive a higher return on their speci…c investment than juniors, eachworker has the same net present value of expected rents at the moment she is hired,independent of her rank q. Seniors getting higher rents than juniors at a particularpoint in time re‡ects the fact that they were able to realize the upside of the risky
returns on their share in the costs of speci…c investment, I. Hence, in that case,the LIFO separation rule can be interpreted as a protection of the property right ofsenior workers on their share in the quasi-rents, against the temptation of the …rm
to …re the expensive senior workers, thereby depriving them from the upside of theirrisky returns. A LIFO separation rule is then a device for implementing an e¢ cient
contract.
In the basic model of this paper, workers are overcompensated. However, when
workers bear the full costs of the speci…c investment the hold-up problem is reversed.
Then, the non-veri…ability of workers investment and the inability of …rms to commit
on not using their bargaining power 1

leads to ine¢ ciency. Workers are only willingto enter the …rm when the net present value of quasi-rents of their investment is so highthat their share in this present value su¢ ces to cover the costs of investment. Thesearguments imply that as long as we do not know what share of the costs of speci…cinvestment is born by workers, empirical evidence showing that there is a return toseniority in wages is inconclusive on whether employment is below its ine¢ cient levelor not. However, there is an alternative statistic enabling the observer to establish
31

which side, either the worker or the …rm, is overcompensated in the ex-post bargaining
over the quasi-rents: when workers queue for jobs, so that there is unemployment,…rms are held up, as in the basic model; when …rms chase after workers, so that there
are vacancies, workers are held up.

2.8

Extensions

What would be the e¤ect of …ring costs in this world? We model …ring costs as a
wealth transfer L from the …rm to the worker, at the moment of …ring. This wealthtransfer raises the value of the outside option of the worker. The value matchingcondition reads V ( p ) =1+ L. Hence, the expression for ! reads (cf. equation(9))! = ln r ( = )ln+ ln (1 + L) :

ln 1

(15)

Firing costs raise !. The wealth transfer has two counteracting e¤ects on the …ringbound p : the direct e¤ect of …ring costs makes layo¤s less attractive to the …rm,
while the indirect e¤ect via higher wages makes layo¤s more attractive, since workers
are more costly. The …rst-order condition for optimal …ring now reads (cf. equation
(12))
F

p

=G

p

+ L;

where we use the value of ! from equation (15) to account for the e¤ect of …ring cost on
wages. Some calculations, see the Appendix, show that the value for p remains thesame as in equation (13). The direct and the indirect e¤ect cancel therefore exactly,

32except for the indirect e¤ect via B + , the option value of rehiring. On the hiring side,…ring cost has two e¤ects with the same sign: …rst, it raises wages, second, there is
the prospect of having to pay …ring cost in case of future layo¤. To the extent thatworkers have excessive bargaining power, as in the basic model, this increase comesto the detriment of e¢ ciency. The paradox here is that …ring cost aggravates theunemployment problem that it is meant to resolve.
The trade unions are often viewed as a necessary condition to provide workers
bargaining power.12 However, the ability of workers to refuse to transfer their tacitknowledge to new hires is an alternative source of power. The interesting aspect ofKuhn (1988) and Kuhn and Robert (1989) is that their rank related compensation
scheme allows a decentralization of the bargaining process. As soon as the layo¤order has been set, each worker can negotiate for herself. When a marginal worker
negotiates a wage increase raising her wage above marginal cost, she endangers her
own employment, not that of the inframarginal workers.13 Hence, a LIFO scheme
enables workers to exploit their individual bargaining power without having to solve
their collective action problem. Whether the LIFO model is really a more appropriate
description of a non-unionized than of a unionized environment is an empirical issue.
For the United States, some scattered evidence is mixed. On the one hand, Medo¤(1979) or Abraham and Medo¤ (1984) show that explicit LIFO layo¤ rules are far
12This problem has been suggested to us by Kevin Murphy.
The reverse is not necessarily true. An inframarginal worker can bargain a wage above her
productivity, if workers with lower seniority capture less than their full productivity. In that case,the …rm has an incentive not to …re the inframarginal worker because it …rst has to …re the marginal
worker.
13

33

more common in unionized …rms, suggesting that the model discussed here applies tounionized rather than non-unionized …rms. On the other hand, Teulings and Hartog(1998: 225) show that tenure pro…les are ‡atter in unionized …rms. To the extent thattenure proxies seniority, this suggests the opposite. This paper will not bring muchclarity on this particular issue either, since our data refer to Denmark and Portugal,
both countries where more or less all …rms are unionized.

3

Empirical framework

The model discussed in the previous section has two testable implications:

1. The Last-in-First-Out separation rule: the workers hired last, leave the …rm…rst.
2. A return to seniority in wages: a worker’s wage depends on her seniority in the…rm, that is, her tenure relative to that of her colleagues.
We shall analyze these implications empirically.14 For that purpose, we need longitudinal matched employer-employee data. Only by knowing the tenure distribution of
the entire workforce of the …rm at all times, we can calculate the seniority of a worker.
Though using this type of data has become more fashionable in recent years, they arestill not widely available. We have been able to get access to such data on Denmarkand Portugal. Below we give a brief description of both data sets; an accompanying
14

In the companion web appendix of this paper, we also verify that Gibrat’s law for the evolutionof the …rm sizes holds in both countries, in particular for …rms with more than 20 employees. Thisimplication is not speci…c to our model; moreover, it has been tested many times before. We showthat it holds for the datasets at hand just for the sake of completeness.

34

online appendix has details on data cleaning and structuring, as well as informationon the relevant labour market institutions in the two countries. Subsequently, we
proceed with discussing the tests of the model’s two implications.

3.1

Data description

For Denmark, we use the Integrated Database for Labor Market Research (IDA) for
1980-2001, from the o¢ cial statistics bureau, Statistics Denmark, which has been
often used previously, e.g. by Mortensen (2003). IDA tracks every single individual
between 15 and 74 years old. The labor market status of each person is recorded
at November 30 each year. The dataset contains a plant identi…er, which allows theconstruction of the total workforce of a plant, and hence of the …rm as a whole.
We use information on hourly gross earnings, occupation, education, and age, andon the plant’s location, …rm size, and industry. Industry is de…ned as the industry
employing the largest share of the …rm’s workforce. Firm size is de…ned as the numberof individuals holding primary jobs in that …rm and earning a positive wage. The
tenure of workers hired since 1980 can be calculated straightforwardly from the IDA.
For workers hired between 1964-1980 the tenure can be calculated from a second
dataset on the contribution histories to ATP; a mandatory pension program. Tenurein job spells started before 1964 is left censored (less than 3% of the observations).
Potential experience is age-schooling-6.

35

36

20.25

7.93
(8.54)

1403686 1403686 184957 4.06
(2.75)(5.78)(11.42)

20.47(11.68)(9)(11.18)36.73(11.95)(3.83)

7.59(2.74)(11.08)37.14(11.75)12.69 38.98(3.65)

6.81(3.05)

12.05 37.79

(8)

(11)

(0.81)

0.42 0.75(0.73)

0.36 0.61(0.85)

0.40 0.87(0.72)

0.35 0.63(10)(2.18)

3.64(2.48)

4.86(2.14)

4.04(2.44)

4.68(12)

Columns’ labels: (1) Observations, (2) Workers, (3) Spells, (4) Firms, (5) Average Real Hourly Wage (base year=2000, measure unit:
Euro), (6) Average Tenure, (7) Average Potential Experience, (8) Average Education, (9) Average Age, (10) Proportion of Women, (11)Average Relative Log Rank, (12) Average Log Firm Size. (Standard deviations in parentheses.)1403686

PT 2000(9.02)

21.10

1087922

Cross-section year 2000
1087922 1087922 79188 23.53 5.26

20.26
(11.39)(12.19)(8.61)(5.58)

8.43(7.99)(7)(2.52)(3)

11420191 3211990 4268149 330270 3.68

DK 2000

PT 1991-2000

(2)

(4)
(5)
(6)
Pooled sample
DK 1980-2001 22364083 2771627 6870869 301015 21.90 5.41

(1)

Table 1: Descriptive Statistics Denmark and Portugal

For Portugal, we use Quadros de Pessoal for 1991-2000, provided by the Ministry of Labour and Social Solidarity, also often used before, e.g. by Cabral and Mata
(2003). It is based on a compulsory survey of …rms, establishments and all their workers; compulsory participation enhances the data quality. The information available
is similar to Denmark’s except that workers’tenure is directly reported; the industry
is that industry with the highest share of …rm’s sales or, when allocation by sales is
not possible, the industry with the highest employment share. We use all full-time
employees in their main job, aged 15-74, and working for a …rm located in Portugal’s
mainland.
For both countries we use data for all private sector jobs, except agriculture, …shingand mining. We eliminate outliers by deleting all wage observations lower than thelegal minimum wage and drop the top 1% of the wage distribution, for each year.
Summary statistics for both countries15 are presented in Table 1, both for the pooleddata and for 2000 separately. There are several obvious di¤erences between the twocountries. For instance in 2000, the mean level of education is more than 5 years
higher in Denmark than in Portugal, while the mean tenure is almost 3 years longer
in Portugal than in Denmark. The number of …rms is far higher in Portugal thanin Denmark, and the average …rm size in Portugal is only 30% of that in Denmark.
Finally, Danes earn on average almost six times more than Portuguese.
Table 2 reports some summary statistics and correlation patterns for the main
15

In the online appendix of the paper summary statistics for broad category industries are alsopresented.

37

variables of interest, tenure, log …rmsize, rank and seniority. For the purpose of ouranalysis, it is important to note that rank is not perfectly related to either tenure orlog …rmsize. We return to this issue in Section 3.3, when discussing the identi…cationof the return to seniority.

Table 2: Correlations tenure, logfsize, rank, seniority

tenureMean
Std dev
Corr rank
Corr seniority

5.41
5.58
-0.09
0.77

Std dev
Corr rank
Corr seniority

2.64
-0.75
0.76

Mean
Std dev
Corr rank
Corr seniority

1.00
0.00

Denmarklogfsize rank

Portugallogfsize rankseniority tenure
seniority
A: All observations
4.68
4.05 0.63
8.43
4.04
3.17 0.87
8.61
2.14
2.17 0.85
2.44
2.45 0.72
0.96
1.00 -0.16
0.48
0.92
1.00 -0.23
0.13-0.16 1.00
-0.46
0.16
-0.23 1.00
B: Deviations from individual means within job spells
0.22
0.33 0.37
1.94
0.19
0.35 0.30
0.02
0.63
1.00 -0.87
0.17
1.00 -0.80
0.46-0.80 1.00
-0.02
-0.16
-0.87 1.00
C: Individual …rst di¤erences within job spells
0.01-0.14 0.16
1.00
-0.04
0.10 -0.14
0.23
0.19 0.23
0.00
0.20
0.41 0.32
0.62
1.00 -0.87
0.43
1.00 -0.40
0.64-0.40 1.00
-0.15
-0.87 1.00

Labels: Corr=correlation; Std dev=standard deviation. For Denmark the pooled sample is 19802001, for Portugal 1991-2000. The correlation rows with the rank and seniority are computed
using all observations with common nonmissing values for all four variables.

3.2

The LIFO separation rule

Since we apply an e¢ cient bargaining model, the distinction between quits and layo¤s
is arbitrary, compare McLaughlin (1991). As long as there is a positive surplus of theworker’s marginal revenue to the …rm above the worker’s reservation wage, the worker

38and the …rm will strike a deal. As soon as this surplus has vanished, it is in theirmutual interest to separate. Whether the separation is initiated by the worker or by
the …rm is irrelevant. Hence, the model predicts the LIFO separation rule to apply
to separations as a whole, not just to layo¤s separately. We use duration analysis totest wether or not the LIFO rule applies. Analogous to Section 2.4, qijt is de…ned as
the log number of workers employed at …rm j at time t with a tenure greater or equal
than that of worker i; hence qijt includes worker i herself. The seniority index rijt isde…ned as in equation (6):
rijt

njt

qijt :(16)

Were the LIFO separation rule to apply literally, the seniority index rijt would be theonly determinant of separation. However, there are two reasons why this is not likely
to be the case. First, the workforce of the …rm is not completely homogeneous, so thata …rm may wish to diminish its workforce in one skill category but not necessarily forother skill categories. This may disrupt a strict application of the LIFO separation
rule. Second, workers separate not only due to shocks to the demand for the …rm’s
product, but also due to worker speci…c shocks, e.g. when a worker’s partner gets a
new job in another city, which might cause the worker to quit from his or her current
job. A particularly important worker speci…c factor that does not …t in the LIFO
model is retirement. When establishing that there is a return to seniority in Section
3.3, we bene…t from this independent source of variation by using qijt as an instrument
for rijt . In this section, we just have to account for the fact that the LIFO rule does39not perfectly explain the order of separation. We intend to show that rijt has an
impact on the job separation rate, over and above the impact of tenure. Therefore,
we model the transition process by a mixed proportional hazard model with discrete
time periods. The probability of leaving the …rm conditional on an elapsed incomplete
tenure of Tijt years (i.e. the hazard rate) can be written as:exp

0 rijt +(rijt ; Zijt ; Tijt ; vi ) =1 + exp

1 Zijt +0 rijt +1 Zijt +Tijt + vi(17)

Tijt + vi

where Zijt is a vector of observed characteristics of the worker and the job (education,
experience, occupation, region and industry indicators) and where vi represents theunobserved worker heterogeneity. We include a full set of dummies

T for every tenurecategory, which is equivalent to a fully ‡exible speci…cation of the baseline hazard.
Identi…cation of the parameterof the baseline hazard

T

0 of the seniority index rijt separate of the parameters

requires variation in rijt that is independent of the tenure

Tijt . Such independent variation is available since the seniority index also depends
on the hiring and …ring of other workers and thus is a non-deterministic function oftenure. A LIFO separation rule implies that0 should be negative. For our estimation

method we use a two mass-point distribution for the unobserved heterogeneity. We use
up to 10 spells of an individual, which helps to estimate the unobserved heterogeneity
distribution. We use a discrete time model, since workers are observed only once per
year. Hence, we cannot observe the exact moment at which the worker enters or40

leaves the …rm.16 In addition, short spells are underrepresented since a worker has tostay at least till the next period of observation for a spell to be recorded. With thedata at hand, we cannot correct for these problems.
At some point in time, older workers leave the …rm for retirement. This process
is independent of the LIFO separation rule. Therefore, we exclude workers above theage of 55 from the analysis. Spells started before the age of 55 and …nished afterwards
are therefore right censored. Women are also more likely to leave the …rm for nonparticipation. Hence, we run separate regressions for men and women. We delete
spells that are left censored since we cannot compute the seniority of an individual
for the periods before she enters our observation sample. Deleting the left-censoredspells implies that we have a maximum of 22 years of tenure in Denmark and 10 for
Portugal.
Table 3 lists the main results. We …nd a negative and signi…cant impact of seniority
for both women and men, with small di¤erences between these categories, in both
Denmark and Portugal, in accordance with the LIFO separation rule. Though theactual coe¢ cients are not reported here, we also …nd negative duration dependence
and evidence of unobserved heterogeneity.17 Apparently, seniority does not pick up
all the variation in separation rates over the course of a job spell. There are two
explanations for this phenomenon. First, as noted before, our seniority index might
not exactly correspond to the actual layo¤ order, since the …rm’s workforce is likely to
16

For Portugal, tenure is reported in months. We use this information in the estimation. For the
rest, the modelling is identical to that for Denmark.
17
The detailed estimation results are presented in the accompanying web appendix of this paper.

41

be heterogeneous, with separate LIFO ordering applying to subsets of the workforce.
This is equivalent to measurement error in our seniority index rijt , leading to an
attenuation bias in the estimate of0,

and unobserved variation in the seniority

index being picked up by correlated variables. Second, not all separations are driven
by the ‡uctuations in the demand for the …rm’s product, and hence, the log seniority
index. For example, some separations might be driven by the worker and the …rm
learning about the quality of the match, see e.g. Jovanovic (1979). These separations
do not …t the LIFO pattern.

Table 3: Main results LIFO test
Denmark
Portugal
Males
Females Males
Females
Seniority index-0.0577 -0.0357 -0.0549-0.0669
Education
Experience
N obs(0.0019)(0.0025)(0.0054)(0.0065)-0.1169-0.1267-0.1204-0.1446(0.0003)(0.0005)(0.0009)(0.0012)-0.0771-0.0732-0.0490-0.0656(0.0001)(0.0001)(0.0003)(0.0004)

10788368 5990891 2118405

1488687

The estimation also controls for occupation, region and industry indicators. (Standard errors in parantheses)

3.3

The return to seniority

3.3.1

General speci…cation

The return to seniority in wages can be tested by extending the standard speci…cationof the log earnings equation with the seniority index, rijt . Consider the following

42

speci…cation of log wages wijt

wijt =+ Xijt + Tijt + Qjt + rijt + njt + "ijt ;(18)

where Xijt is experience and where Qijt is the industry (or: occupation) speci…cexperience, cf. Neal (1995). We omit higher order terms in experience and tenure, andother controls (including time e¤ects) from equation (18) for the sake of convenience,but include them in the estimation. The unobservable term can be decomposed into
four orthogonal components, a match, a …rm, a worker, and an idiosyncratic e¤ect18"ijt = 'ij +The idiosyncratic e¤ectof reasons for

ij ;

j +

i+

ijt :

(19)

ijt can also include measurement error. There are all kinds

j ; andito be correlated to Tijt , see Topel (1991) or Altonji

and Williams (2005). Learning and search theories imply that good worker-…rm
relationships tend to survive as the worker and the …rm learn about the quality of
their match and bad matches are broken up, leading to positive correlation between
'ij +

j +

i and Tijt .

Search theories imply that workers sample new jobs from a

job o¤er distribution. The longer this selection process is going on, the higher the
expected value of 'ij +between 'ij +j since bad jobs do not survive, leading to positive correlation

j and Tijt .

There are two obvious solutions to this problem, either

18

This formulation is similar to Topel (1991: 150), except that we add a …rm e¤ect and that wedelete the subscript t from the match e¤ect ij , as Topel does in his application.

43

within-job …rst di¤erencing (FD) or adding …xed e¤ects for every job spell (FE),eliminating the observables Xijt and Qijt and the unobservablesij ;j ; andi fromthe speci…cation. First di¤erencing yields

wijt =+++

rijt +

njt +

ijt :

(20)

Adding …xed e¤ects per job spell is equivalent to estimating (18) by taking deviations
from the mean over time, within a job spell:w
eijt = ( ++ ) Teijt + reijt + n
ejt + eijt ;(21)

where the upper tilde denotes deviations from the mean per job spell, e.g. w
eijt =

eijt from (21) because
wijt wijt , with wijt the mean of wijt for a job spell. We exclude X

it is perfectly collinear with Teijt . In both speci…cations above, it is immediately clearthat the …rst-order e¤ects of tenure (either …rm, or industry, or occupation speci…c)and experience are not separately identi…ed. This problem has troubled all attempts
to estimate the return to tenure, see e.g. Altonji and Shakotko (1987) and the large
stream of subsequent papers. The perfect collinearity of experience and tenure withina job spell rules out estimating the return to tenure on within-spell variation. Hence,researchers had to revert to between job spell variation. However, since job mobility is
not exogenous, using this type of information introduces all kind of selectivity issues,
which the literature has tried to resolve. Happily, this problem does not a¤ect the44

estimation of , since rijt is not perfectly correlated to Tijt , as noted above in Table
2. This means that we can use only within job spell variation in wages to estimate ,and hence we do not have to bother about the selectivity problems that plague theestimation of the return to tenure.
There is a second identi…cation issue. In the theoretical model, workers live forever
and thus the log number of workers with tenure greater or equal than the tenure ofworker i, qijt ; does not depend on t, see equation (6). In that case, the only sourceof within job spell variation in the seniority index rijt is log …rm size njt . Hence,the coe¢ cients of these variables,and respectively , are not separately identi…ed

when using only within job spell variation. As discussed in Section 3.2 and Table 2,
qijt does depend on t empirically, mainly because more senior workers than worker iretire at some point. Hence, we can use qijt as an instrument for rijt . Substituting
the de…nition of rijt ; equation (16), in equation (20) yields

wijt =++

qijt + ( + ) njt +ijt :This equation makes clear that the e¤ect of the seniority index on wage growth isidenti…ed from variation in qijt . Mutatis mutandis; the same argument applies for the
FE method, see equation (21).
The choice between the FE and FD estimators above depends on the error structure of vijt . The closer is vijt to a unit root, the more e¢ cient is the FD method;
the closer vijt is to being serially uncorrelated, the more e¢ cient is the FE method.
45

Previous empirical studies have typically found a high degree of autocorrelation in
vijt , even close to a unit root, see for instance Abowd and Card (1979) and Topeland Ward (1992). From that perspective, equation (20) is likely to be most e¢ cient.
However, this equation assumes that the e¤ect of rijt and njt on wijt is immediate.
Any lagged impact will not be captured after …rst di¤erencing. From that perspective,
equation (21) is preferred, since there lagged e¤ects of rijt and njt will be captured.
Hence, one would expect higher estimates forandfrom using equation (21) thanfrom using (20).19
Table 4: Residual Autocovariances for Within-Job LogWage Innovations
Lag
0
1
2
3
4
5
6

Denmark
0.0231

Portugal
0.0273(0.00002)(0.00007)-0.0043-0.0082(0.00001)(0.00006)-0.0006-0.0008(8.7e-06)(0.00003)-0.0003-0.0004(9.0e-06)(0.00003)-0.00039.2e-06(9.5e-06)(0.00003)-0.00008-0.00008(0.00001)(0.00004)-0.0001-0.0006(0.00001)(0.00005)

N obs 14907897

5758655

The generating regressions are the
FD wage regressions with seniority
index included, see the FD2 columns
in the next table. (Robust standard
errors in parentheses)

19

We report robust standard errors, so that correlation between the residuals over time does nota¤ect the validity of the standard errors.

46

First, we check the characteristics of the dynamic process of vijt . Table 4 reports
the variance-covariance ofvijt . For both countries, the covariance of "ijt with its…rst lag is substantial, the covariance with higher lags is negligible. Hence, the process
is well approximated by an MA(1) process, made up of a mixture of permanent andtransitory shocks. Abowd and Card (1979) and Topel and Ward (1992) …nd similar
results for the United States. The standard deviation of the permanent shocks canbe calculated as 0.12 for Denmark and 0.10 for Portugal.20 These numbers are of thesame order of magnitude as found for the United States.
This evidence suggests that in terms of e¢ ciency we prefer FD, while in terms ofallowing for a lagged e¤ect ofrijt onwijt , we prefer FE. Hence, we report both

the FD and FE estimation results. Our regressions control for up to quartic terms
in tenure and experience, log …rmsize, and industry, occupation, and region dummies21 . In Table 5 we report the results. We present the estimation results for two
speci…cations, one excluding rijt and another including it. We can draw the following conclusions. First, all coe¢ cients for log seniority are positive and statisticallysigni…cant. Second, the coe¢ cients are larger for FE than for FD, as was expected,
because FE allows for a lagged e¤ect of rijt on wijt , while FD does not. Third, comparing the estimation results with and without seniority, including seniority reduces
20

Let qijt and uijt be the transitory and permanent shock respectively. Thenvijt = uijt + qijt

qij;t 1 :Hence, Var( vijt ) =Var(uijt ) + 2Var(qijt ) and Cov( vijt ; vij;t 1 ) =Var(qijt ), so that
Var(uijt ) =Var( vijt ) + 2Cov( vijt ; vij;t 1 ).
21
Time e¤ects are also accounted for in all subsequent wage analyses, by time-detrending wages
prior to the regressions.

47

the coe¢ cients for tenure and log …rmsize by 530%. The coe¢ cients for experience

are hardly a¤ected by including seniority22 . The e¤ect of tenure and log …rmsize on
wages is at least partly a proxy for the e¤ect of seniority. Seniority is expected tobe measured with greater measurement error than tenure and …rmsize. Apart fromstraightforward reporting errors, the main source of measurement error in tenure is
who exactly is the relevant employer. Some job changes might either be classi…ed as
between …rms, justifying the tenure clock being set back to zero, or as within the …rm,
which does not a¤ect the tenure clock. However, this source of measurement error
only a¤ects changes at the borderline of the de…nition of a …rm. This is likely to be
only a small fraction of the …rm’s workforce. Still, misclassi…cation of the tenure ofeven a single worker a¤ects the measurement of the seniority of all other workers in
the …rm. In general, any measurement error in tenure or …rm size feeds into seniority.
Furthermore, seniority is a¤ected by measurement errors due to the fact that separate
seniority statistics might apply for subgroups of the workforce. The actual e¤ect ofseniority on wages is therefore likely to be underestimated, and part of the e¤ect oftenure and log …rm size is still a proxy for measurement error in the seniority variable.
Finally, the e¤ect of seniority is twice as high in Portugal as in Denmark.

22

In the FD and FE speci…cations from above these e¤ects can be seen for tenure and experiencein the higher order polynomial terms. In the accompanying web appendix of this paper we alsopresent the OLS estimates, with and without including seniority index in the regressions, wheredi¤erences under the two speci…cations in the linear experience and tenure terms can be noticed.

48

49(.00007)14907897
21163073745050
221106-.003(.00007)(.0007).039(.002)-.223(.0002).002(.001)-.105(.002).199(.0003).045(.0003)

.011

-.003

(.0007).039(.002)-.224(.0002).002(.001)-.101(.002).191(.0003).047(.0002).013(.0003)(.001).027(.003)-.086(.0005).068(.0004).025

FD1(00003).004(.0002)-.039(.0006).100(.0002)(.0001)-.003(.001).043(.004)-.204(.0002)-.002(.001).021(.003)-.069(.0005).065(.0005).015(.0005)FD2.0165758655
1752000
1965560
206361(.0001)-.003(.001).043(.004)-.204(.0002)-.0002 -.003(9.88e-07).008(.002)-.036(.0002).007(.0003).021(.0003)FE2.008

22364083
2771627
6870869301015(.00003).004(.0002)-.039(.0006).099(.0002)-.0009(.099).014(.002)-.052(.0001).010(.0003).026

Denmark
FD2
FE1
.003

(.00007)-.002(.0007).029(.002)-.147(.00009)-.002(.0007).019(.002)-.067(.0003).055(.0004).028(.0005)FE2.022

10743244
30923294053649
322502(.00007)-.002(.0007).030(.002)-.149(.00009)-.003(.0007).024(.002)-.083(.0003).059(.0004).040

Portugal
FE1

The dependent variable is the ( ) time-detrended log real hourly wage for the (FD) FE columns; the covariates
havein front for FD columns. Columns 1 report results for the same regressions as corresponding columns
2, but without seniority index included as covariate. The higher order polynomials in tenure and experienceare divided by the corresponding powers of 10. All regressions also control for region, industry and occupation
indicators. Signi…cance levels:
: 10%
: 5%
: 1%. (Robust standard errors in parentheses).

N obs
Workers
SpellsFirms

exper4exper3exper

2tenure4tenure3

tenure2tenure+experlogfsizesen. index

FD1

Table 5: FE and FD Wage Regressions for the Entire Private Sector in Denmark and Portugal

Are there other theories that might explain our results? For the answer to thisquestion, it is important to realize that the e¤ect of the seniority index rijt is identi…edfrom variation in the log number of workers with tenure greater or equal than thetenure of worker i, qijt . Any alternative theory explaining our …ndings must therefore
be able to explain why the wage of a worker goes up when qijt goes down. This rulesout a host of theories able to explain why rijt shows up signi…cantly, but not able
to explain why qijt does so. For example, the e¤ect of qijt cannot be rationalized bylearning models such as Jovanovic’s (1979), or search models like Postel-Vinay andRobin (2002) and Burdett and Coles (2003), because these theories relate in no way
the wage of worker i to the number of more senior workers in the …rm.
One might attempt to explain our …ndings by tournament models like Lazear
and Rosen (1981) or Malcomson (1984). In Malcomson’s model, workers’output isnon-veri…able, so that the …rm’s promise to award a performance pay is non-credible.
This credibility problem can be resolved by the …rm promising e.g. to promote thebest one out of every four workers to a better paid senior position within two years.
Hence, running a tournament allows the …rm to implement a credible system of performance pay. In its original form, Malcomson’s model yields an association between
tenure and wages, but does not yield an association between qijt and wages. However,an amended version of the model might do. The …rm would state its promise somewhat di¤erently, namely, that it has some well-paid top positions in the hierarchy. It
promises that as soon as one of them becomes vacant (e.g. by retirement), it will be…lled by the best worker in the …rm at a lower position. On average, this compensa50

tion system yields a positive association between qijt and wages. From a theoreticalperspective, the problem with this version of the tournament model is that it is inferior to Malcomson’s original model, since the promotion-bonus is conditional on theretirement of a senior worker, which is a more risky bonus than the unconditional
bonus, and hence this conditional bonus is a less e¢ cient incentive when juniors arerisk averse. One explanation is that the …rm seeks to combine both models, LIFO
layo¤ and the tournament: if the …rm has to pay its workers some rents, than it
can better use these payments to provide better incentives. Empirically, we do notsee an easy way to discriminate between this speci…c form of the tournament modeland the LIFO layo¤ model. A related explanation suggested to us argues that a …rmneeds “juniors” and “seniors” in …xed proportions, for example, because juniors do
the production work, while seniors do the planning and coordination. The …rm …lls
its vacancies for seniors by simply “promoting”some of its juniors to senior positions.
The problem with this explanation is that it does not explain why the …rm does nothire “seniors”on the outside market, and, even more problematic, why it would pay
higher wages to these “seniors”, apart from providing incentives for juniors, which,however, brings us back to Malcomson’s tournament model.
Commentators have suggested other, more informal, theories to us. Maybe the…rm has an “iron stock” of workers who are never …red, and a ‡uctuating stock of
temporary workers, receiving lower pay. Were this true, it would generate a positive
association between your seniority and your wage. However, this theory would not
generate a positive association between the change in the seniority of an individual51

worker and the change in her wage. Stating the same argument di¤erently, controlling for …xed worker e¤ects as we do in both the FD and FE regressions deals withthis alternative. Similarly, any theory that starts from the argument that …rms areheterogeneous, some …rms requiring more speci…c investments than others, fails to
explains our results. Firms are indeed heterogeneous, but …xed …rm e¤ects should
deal with these theories.
3.3.2

Returns to seniority for subgroups

The LIFO layo¤ rule is unlikely to apply unconditionally. One would expect the …rm
to apply separate layo¤ rules for di¤erent subgroups of its workforce. For example,
a construction …rm is unlikely to …re its secretaries if it has an excess supply ofbricklayers, whatever the seniority of both groups of workers. One can therefore
expect the theory to work better using separate seniority indices for broad groups ofworkers in our regression. One could calculate separate indices for each occupation.
Apart from the fact that we do not have a good classi…cation of occupations in ourdata, we hesitate to distinguish workers by their occupation, since that might change
endogenously. The wage increase due to a rise in the worker’s seniority might go handin hand with a relabelling of her occupation. However, we can distinguish workers
by typically time-invariant characteristics, unrelated to their actual job. Hence, we
repeat the analysis separately for males and females, and respectively for low- andhigh-educated workers. The results are reported in Table 6. The results for male andfemale categories do not di¤er much. The only apparent exception is for Denmark,52

when using the FE estimator, where the estimated coe¢ cient for males is twice ashigh as for females. However, the estimation results for education groups show thatthe e¤ect of seniority is much larger for higher educated workers than for low educatedworkers. The FE estimate is even signi…cantly negative for Denmark, though small
in absolute value. The impact of seniority for the highly educated workers is muchlarger, both in Denmark and in Portugal. These results are consistent with the factthat high educated workers have steeper wage-tenure pro…les than their low-educatedpeers. At the same time, they give support to the fact that the relevant seniority
hierarchy within the …rm is already more realistically captured when accounting for
education levels.

53

54

(0.0002)(.0002).006(.0004).016(.0007).031(.0005).014(.0004)8309095(.0002).006(.0005).024(.0004)

LowEduc
FD
FE
.002
-.002

9567345 14054988 5268672(.0004).040(.0004).007(0.0002).007(0.0004).025(0.0004)

FE
.010

Males

(0.0007).053(0.0007).015(0.0007)(0.0005).042(0.0006).028(0.0006)

Females
FD
FE
.015
.019

(0.0007).080(0.0006).019(0.0007)FD.014

259793(.002).116(.002).026(.002)

536920(.001).099(.002).026(.002)

HighEduc
FD
FE
.029
.032

6389436(0.0005).073(0.0006).031(0.0006)

FE
.019

Males

10206324(.0003).049(.0004).031(.0005)

LowEduc
FE.016

5492034(.0005).056(.0005).016(.0005)FD.013

9858509 14618407 2300767 4353808 3457888
Education Categories(0.0004).052(0.0004).014(0.0004)

FD.005

Gender Categories

Portugal

The dependent variable is the ( ) time-detrended log real hourly wage for the (FD) FE columns; the covariates havein front for FD columns. Seniority index has been computed separately for each category. "LowEduc" stands for
category of people with at most 12 years of education. All regressions include also up to 4th order polynomials intenure and experience and indicators for region, occupation and industry. Signi…cance levels:
: 10%
: 5%
: 1%. (Robust standard errors in parentheses).

N obs(ten+exp)

logfsizesen. index(.0004)

HighEduc
FD
FE
.010
.020
(.0003)50493887745676.009(0.0004)(0.0005)

.032

.014

(0.0005)(0.0005).002(0.0004)

Females
FE
.005

N obs

(ten+exp)

logfsizesen. index

FD
.005

Denmark

Table 6: FE and FD Regressions by Gender and Education Rank Groups

4

Summary and conclusions

We have shown beyond reasonable doubt that for both Denmark and Portugal there
exists a return to seniority in wages, with an elasticity in the order of magnitude of
0.01–0.02: a 1% increase reduction in the number of workers more senior than you
raises your wage by 0:01 to 0:02%. This return is higher for higher educated workers,
and it is twice as high in Portugal than it is in Denmark. Some 5 to 30% of what has
been know as the return to tenure and to …rmsize is in fact a return to seniority. A
number of familiar theories explaining the tenure pro…les in wages, like Jovanovic’s(1979) learning model or the search models by Postel-Vinay and Robin (2002) and
Burdett and Coles (2003), cannot explain this …nding. Our results are not at odds
with these theories, but these earlier theories cannot be the full story, because they
focus solely on the features of the worker herself (in case of learning, her ability; incase of search, her job o¤er history), while the return to seniority links the fate of theworker to that of the …rm as a whole. Our results might be explained by an amended
version of Malcomson’s (1984) tournament model, where the number of prizes in thetournament depends upon the number of seniors that leave the …rm. However, it ishard to explain why the …rm would use this type of conditioning on the number ofprizes, without referring to some sort of rent sharing, as in our LIFO layo¤ model.
A return to seniority implies that a worker is to some extent shareholder in her own…rm. Hence, the theory here links labor economics to …nance.
Our theoretical model provides a special interpretation of the return to seniority,
as being due to a hold-up problem, where …rms pay the full cost of the speci…c55

investment, while workers capture part of the return. This setup leads to ine¢ ciently
low hiring. This conclusion is conditional on the assumption that the …rm bears thefull cost of speci…c investment. This assumption has not been tested in this paper.
How to do that remains an open question. An indirect answer can be obtained byanalysing who is queueing for whom: when workers queue for jobs, so that there isunemployment, …rms are held up by their incumbent workforce; when it is the otherway around, and there are vacancies, workers are held up by their employer. E¢ ciency
requires the costs and the bene…ts of the speci…c investment to be born by the same
party, which is the Hosios condition. When workers are risk averse, e¢ ciency can only
be obtained when this is the …rm, since any other allocation assigns a risky return
to a risk averse player. Hence, our estimation results point to incompleteness in theinsurance market. Nevertheless, our analysis does not imply that LIFO layo¤ rules
are bad per se. They can o¤er a useful protection to the property rights of incumbent
workers on their share of the speci…c investment, thereby helping the …rm to solve a
commitment problem.
We have established the existence of a return to seniority for Denmark and Portugal. Whether such a return exists in other countries, in particular in the UnitedStates, remains an open question. On the one hand, returns to seniority might belargely due to legal institutions, and these institutions vary across countries. On theother hand, the economic mechanism for having a LIFO layo¤ rule exists everywhere
and the legal institutions might just be a formalization of rules of conduct and implicit
contracts that would have emerged anyway. There is only one way to investigate this,56

which is to repeat our empirical analysis for the United States.

5

References

Abowd, J.M. and D. Card (1989), “On the covariance of earnings and hours changes”,
Econometrica 57(2), 411–445.
Abowd, J.M. and T. Lemieux (1993), “The e¤ects of product market competition
on collective bargaining agreements: the case of foreign competition in Canada”,
Quarterly Journal of Economics, 108(4), 983–1014.
Abraham, K.G. and J.L. Medo¤ (1984), “Length of service and layo¤s in union andnonunion work groups”, Industrial and Labor Relations Review, 38(1), 87-97
Altonji, J.G. and R.A. Shakotko (1987), “Do wages rise with seniority?”, Review of
Economic Studies, 54(3), 437–459.
Altonji, J. G. and N. Williams (2005), “Do wages rise with job seniority? A reassessment”, Industrial and Labor Relations Review, 58(3), 370–397.
Bentolila, S. and G. Bertola (1990), “Firing costs and labour demands: how bad iseurosclerosis?”, Review of Economic Studies, 57(3), 381–402.
Bertrand, M. and S. Mullainathan (2003), “Enjoying the quiet life? Corporate governance and managerial preferences”, Journal of Political Economy, 111(5), 1043–
1075.
Brown, C. and J. Medo¤ (1989), “The employer size wage e¤ect”, Journal of Political
Economy, 97(5), 1027–1059.
Buhai, I.S. and C.N. Teulings (2006), “Tenure pro…les and e¢ cient separation in astochastic productivity model”, Tinbergen Institute DP 05–099/3.
Burdett, K. and M. Coles (2003), “Equilibrium wage-tenure contracts”, Econometrica, 71(5), 1377–1404.
Cabral, L.M.B. and J. Mata (2003), “On the evolution of the …rm size distribution:
facts and theory”, American Economic Review 93(4), 1075–1090.
Dixit, A.K. and R.S. Pindyck (1994), “Investment under uncertainty”, Princeton
University Press, New Jersey.
Dixit, A.K. (1989), “Entry and exit decisions under uncertainty”, Journal of Political
Economy, 97(3), 620–638.

57

Hosios, A.J. (1990), “On the e¢ ciency of matching and related models of search andunemployment”, Review of Economic Studies, 57(2), 279–298.
Jovanovic, B. (1979), “Job matching and the theory of turnover”, Journal of Political
Economy, 87(5), 972–990.
Jovanovic, B. (1982), “Selection and the evolution of industry”, Econometrica, 50(3),649–670.
Kuhn, P. (1988), “A nonuniform pricing model of union wages and employment”,
Journal of Political Economy, 96(7), 473–508.
Kuhn, P. and J. Robert (1989), “Seniority and distribution in a two-worker tradeunion”, Quarterly Journal of Economics, 104(3), 485–505.
Lazear, E. and S. Rosen (1981), “Rank order tournaments as optimal salary schemes”,
Journal of Political Economy, 89(5), 841-864.
Lindbeck, A. and D. Snower (1990), “Do cooperation and harassment explain involuntary unemployment?”, American Economic Review, June, 80(3), 167–188.
Malcomson, J.M. (1984), “Work incentives, hierarchy, and internal labor markets”,
Journal of Political Economy, 92(3), 486–507.
Medo¤, J.L. (1979), “Layo¤s and alternatives under trade unions in U.S. manufacturing”, American Economic Review, 69(3), 380-395
McLaughlin, K. J.(1991), “A theory of quits and layo¤s with e¢ cient turnover,”
Journal of Political Economy, 99(1), 1–29.
Mortensen, D.T. (2003), Wage dispersion: why are similar workers paid di¤erently?,
MIT Press, Cambridge.
Neal, D. (1995), “Industry-speci…c human capital: Evidence from displaced workers”,
Journal of Labor Economics, 14(4), 653-677
Postel-Vinay, F. and J.M. Robin (2002), “Equilibrium wage dispersion with worker
and employer heterogeneity”, Econometrica, 70(6), 2295–2350.
Sutton, J. (1997), “Gibrat’s legacy”, Journal of Economic Literature, 35(1), 40–59.
Teulings, C.N. and J. Hartog (1998), “Corporatism or competition? Labour contracts, institutions, and wage structures in international comparison”, Cambridge
University Press, New York.
Topel, R.H. (1991), “Speci…c capital, mobility and wages: wages rise with job seniority”, Journal of Political Economy, 99(1), 145–175.
Topel, R.H. and M.P. Ward (1992), “Job mobility and the careers of young men”,
Quarterly Journal of Economics, 107(2), 145–176.
58

A

Derivation

Substitution of equation (5), (9), (10), and (11) in equation (12) yields
2 3 2
32
3
0
1
1 1
1
R
607 6 1
7
+ 76
7
6 7 6
76
6 7=6
76
7;
4I 5 4E F G
H 5 4C 5
+
0
E
F G
H
C+
where

C

< 0;

+

B exp

p

1

1

R

r

E

exp [ ] ; F

+

> 1;

(
+
B exp

; C+

exp p
exp [

];G

p

p+

p ;

+

> 0;

> 0;

)
;

exp

;H

exp

+

:

Elimination of C from the …rst two equations of this system yields equation (13).
Matrix inversion yields
2

R

3

2

1
6
7 61
6
7 6
6
7=6
4C 5 4E
C+E

1> 0. The second equation of this system can(22)

S ( ; );+R( )S( ; )

3 12 3
0
607
+ 7
7 6 7
7 6 7;
H 5 4I 5
+
H
0
1

F G
F G

We are interested in a solution withbe written as
I R( )=

1

+

1

E+
1

+

1

(F G + EH) + (1+R (0) = 0; R (0) = 1
S (0; ) = 0; S (0; ) = 0; S

+

G+ 1
)

H;

+

(EF + GH)(F H + EG) ;+1+(0; ) > 0; S ( ; )59> 0; R ( )0:0;HenceS ( ; ) S (0; )=R( )2R (0)@ S( ; )
> 0;
@
R( )
S( ; )lim= 1:!1 R ( )
lim

!0

= 0;

where the second line follows from the evaluation of higher order derivatives. Hence,
there is a unique positive solution for . The other three equations can be written
as
( +

R=

( +

C =
C+ =

(

) F +( +
) G+(
) +H
;
R( )
) E + ( + 1) F + (1
) +H
;
R( )
) E (1) F + (1
) G
:
R( )

(23)

By a similar argument, one can prove that the numerators of these expression arealways positive. Hence, a positive solution for R; C ; and C + exists for every > 0.
This implies a positive solution for B and B + . Totally di¤erentiating equation(22) with respect to and yields an expression for d =d . Totally di¤erentiating
equation (23) with respect toand and using the expression for d =d proves
@p+
@p
@B +
< 0, @ > 0, and @ < 0.
@60