Full text of DOI:10.1111/1467-9914.00221

Severance Payments and Firm-specific
Human Capital
Jens Suedekum – Peter Ruehmann
Abstract. What effect does employment protection through severance payments
have on the behaviour of employed workers? We analyse this issue within a
stochastic two-period framework where workers decide on human capital
investments and find two competing effects: severance payments imply higher
job security that fosters human capital formation. At the same time, a lay-off is
perceived by the workers to be a weaker penalty if severance payments are
provided. This incentive lowers their optimal amount of firm-specific investments.
Which effect prevails on balance depends on the distribution of investment
returns among firm and workers. For strong positive reactions, employment
protection is also in the interests of the firm.
1. Introduction
There are probably few other issues that would produce such
broad agreement among economists and policy commentators, but
that European labour markets are highly inflexible and should
undergo substantial reforms. One device for ‘Eurosclerotic’
inflexibility that is frequently critiqued is the high degree of
employment protection legislation (EPL). The list of objections
against EPL is long. Ultimately, it is often seen, among other
Jens Suedekum (author for correspondence), Department of Economics,
University of Goettingen, Platz der Goettinger Sieben 3, 37073 Goettingen,
Germany. Tel: þ49 551=39-7633; Fax: þ49 551=39-4875; E-mail: jsuedek@gwdg.de.
Peter Ruehmann, Department of Economics, University of Goettingen, Platz der
Goettinger Sieben 3, 37073 Goettingen, Germany.
The authors are grateful to Andreas Haufler (University of Munich), Paulino
Teixeira (University of Coimbra), the participants of the research seminar at the
Department of Economics at the University of Goettingen and to an anonymous
referee for several very useful comments and discussions. The usual disclaimer
applies.
LABOUR 17 (1) 47–62 (2003) JEL J41, J65
2003 CEIS, Fondazione Giacomo Brodolini and Blackwell Publishing Ltd, 9600 Garsington Road, Oxford OX4
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48
Jens Suedekum – Peter Ruehmann
things, as being ‘at the root’ of high continental unemployment
(Siebert, 1997). Rigorous econometric testing only partly supports
this perception as significant negative impacts on overall un-
employment are difficult to identify in the data.1 At the same time,
one hardly ever hears convincing arguments that are in favour of
some EPL. Often it is defended on vague justice or equity grounds,
its existence seemingly due to mighty unions that manage to defend
the rents of well-organized insiders.
Recently, however, a literature on severance payments (SP)2 has
emerged, arguing that EPL can also have efficiency-enhancing
effects if the economy is subject to frictions and SP are suited to
solving certain market or coordination failures, e.g. in insurance
markets (Alvarez, Veracierto, 2001; Cahuc, Zylberberg, 1999;
Kuhn, 1992; Levine, 1991; Pissarides, 2001). In this paper, we want
to shed some light on the efficiency effects of employment
protection from a different perspective. We do not focus on
overall welfare or employment, as most authors do, but rather on
the behaviour of employed workers. This is a largely unexplored
issue. Still, at some points in the literature it is possible to find
controversial viewpoints on this matter.
It is sometimes argued that SP increase the incentive for
employed workers to invest in firm-specific human capital, or
respectively to provide more effort at the workplace3 (Buttler,
Walwei, 1990; Houseman, 1990; Schmid, 1995). The reason is
that workers perceive higher job security through EPL, they rely
more heavily on the long-term validity of their labour contracts
and are consequently willing to provide stronger commitment to a
specific employer.4 This enhancement of firm-specific skills is
generally thought to benefit both sides — employees and
employers. If this argument holds, which one might call the
incentive effect of employment protection, there might be some
neglected merits of continental European labour relations that
counteract the widely acknowledged problematic aspects. But
there are also different positions. Since a lay-off is cushioned by
redundancy transfers, workers might perceive firing not to be
such a strong penalty. Under this set of incentives, the motivation
of incumbent workers to invest in specific human capital is
reduced and a lower degree of ‘firm-specific commitment’ can
follow as the consequence of employment protection. Such
arguments, which one might label the lethargy effect of SP, are
presented by Ichino and Riphahn (2001) and Goerke (2003), for
example.
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Severance Payments and Firm-specific Human Capital
49
Which of the two scenarios is a better approximation of reality?
In this paper we argue that really both mechanisms are at work
in parallel and there is a trade-off between them. Our aim is
to provide a systematic theoretical analysis that is capable of
indicating under what circumstances either of the competing forces
is likely to dominate the other. Our main finding is that this
crucially depends on the conditions of the specific firm under
consideration, in particular on whether workers have strong
incentives to build up specific human capital to begin with.
However, even if the incentive effect of job security predomi-
nates, there might be no essential need for legislation if private
parties recognize the side-effects of job security.5 Some degree of
SP can also be in the interests of the firm if the induced human
capital formation is strong.
The remainder of the paper is organized as follows: Section 2
introduces the model structure, Section 3 presents the basic
decision problem of a representative worker, and Section 4
analyses the impacts of a marginal increase in SP on the optimal
human capital investment. Section 5 discusses the implications for
the firm’s profits and determines the optimal level of SP that the
firm would provide. Section 6 concludes.
2. The model structure
We present a simple two-period partial equilibrium model where
identical workers are employed at one particular firm and decide
on firm-specific human capital investments. In order to analyse the
impact of SP on optimal human capital formation, it is essential
that not only workers expect returns from the specific investment
in the form of higher earnings, but that the firm’s expected profits
are also an increasing function of the level of human capital
embodied by the firm’s employees. The second essential require-
ment is that the investment decisions are made in a stochastic
environment, where exogenous shocks might induce the employer
to lay off workers.
The firm in our model has a time horizon of two periods
t ¼ {1; 2} and produces a particular commodity Xt in an
imperfectly competitive market with some degree of market or
monopoly power. Labour is used as the only variable input, and we
assume that the marginal productivity of effective units of labour
employed by the firm (Lt) is constant and given by 1=ꢀ, i.e.
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50
Jens Suedekum – Peter Ruehmann
Lt ¼ ꢀXt. Furthermore, production in each period requires that the
firm pays a fixed sum Ft, which might be thought of as overhead
costs or a required licence fee. The level of fixed cost in the second
period, F2, is assumed to be a random variable and unknown to the
firm during t ¼ 1. With these assumptions, the firm’s profits at
time t are given by:
ꢁt ¼ ptXt ꢀ Ft ꢀ wtLt;
[1]
where pt is the sales price per output unit, and wt is the wage rate
for each effective labour unit employed by the firm. This (unit)
wage rate is determined by the market and has to be taken as given
by the firm. We suppose that this unit wage rate will not change
over time, i.e. w1 ¼ w2 ¼ w. But its market power allows the firm
to charge prices with a mark-up (1=ꢂ) over marginal costs. For
simplicity we assume that this mark-up 1=ꢂ is constant. The firm
thus charges output prices:
1
pt ¼ (ꢀw);
0 < ꢂ < 1:
[2]
ꢂ
Inserting the pricing rule and the production function Xt ¼ (1=ꢀ)Lt
into [1], it is clear that profits under this linear technology increase
proportionally with the variable input Lt:
0
1
1 ꢀ ꢂ
ꢂ
@
A
ꢁt ¼ ꢀFt þ
wLt:
[3]
Thus, for any given (unit) wage rate, and provided the firm is
active, it runs at some capacity level, which we impose to be given
K
exogenously by Xt. The firm’s labour demand at t ¼ 1 is given
L
K
simply by the output constraint as L1 ¼ ꢀX1, which refers to the
number of effective labour units employed by the firm. This
number of labour units is equal to the number of identically
employed people, which implies that in t ¼ 1 each of the employees
embodies exactly one effective labour unit. Let the level of fixed
costs at t ¼ 1 also be given at F1, which grants the firm some level
of profits ꢁ1 > 0.
During the first period, workers can invest in firm-specific
human capital and expand their embodied effective labour
units. More specifically, given that all workers are identical and
will reveal the same investment behaviour,6 the representative
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Severance Payments and Firm-specific Human Capital
51
employee will choose some optimal number of labour units h* ꢀ 1
that he=she will embody in t ¼ 2. We make the simplifying
assumption that the worker finances investments alone, i.e.
he=she bares the learning costs necessary to obtain the optimal
level of firm-specific human capital, h*.7 Through the firm-
K
specific investment of the worker, the output capacity limit Xt is
expanded for the second period t ¼ 2 by the factor h* > 1, i.e.
K
K
X2 ¼ h*X1. The firm will run at this capacity level provided it is
active during the second period, and hence benefits from the
output expansion because variable profits increase 1=ꢂ times
L
faster than payroll earnings wh*L1.
However, the firm has no power to directly influence the optimal
human capital choice of workers. Put differently, it is impossible
for the firm to raise output through pure increases in scale by
hiring more workers. But if incumbent workers invest in specific
human capital, then output and variable profits increase. This
might be so because an expansion of the technologically
K
determined capacity constraint X1 is conditional on quality
improvements which can be attained only by better training of
the incumbent workforce.
At the time when human capital investment decisions have to
be made, however, it is uncertain if the firm is actually going to be
active in the second period. This depends on the realization of
the random variable F2, which is observed by the firm at the
beginning of t ¼ 2. As noted above, the fixed costs do not
represent any sunk costs, but are required only if the firm remains
active during the second period. We consider a uniform
distribution of F2 over the range [F1 ꢀ c; F1 þ c], where c > 0 is
an exogenous parameter. Thus, the expected value of F2 is equal
to the known level F1.
In a world without employment protection, the firm would
choose to remain active in the market for good X if total profits
ꢁ2 are positive, given the information on F2. If fixed costs
K
outweigh variable profits at the capacity constraint X2, produc-
tion is ceased and the plant is shut down. The introduction of SP
alters the closure condition, since it makes exit costly for the
K
firm. Production is maintained whenever total profits ꢁ2(X2) are
greater than the sum of exit costs, which amount to sL1. The
L
variable s indicates the mandatory transfer, the SP, to each
L
8
of the single L1 employees in case of a lay-off. Given the
information on the distribution of F2, we can calculate the
probability ꢃ that the firm remains active during t ¼ 2. It is
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52
Jens Suedekum – Peter Ruehmann
given by
0
1
A
1 ꢀ ꢂ
ꢂ
@
L
L
ꢃ ¼ Pr F2 <
whL1 þ sL1
1 ꢀ ꢂ
ꢂ
L
L
ꢀ(F1 ꢀ c) þ
whL1 þ sL1
¼
;
[4]
2c
ꢃ is increasing in both s and h: it is less likely that the firm closes
the higher the level of exit costs s, and the higher the stock of
human capital.9 The intuition for the positive sign of ꢃh is
straightforward: the output level in t ¼ 2 and thus the level of
variable profits is exogenous to the firm, but (positively) depends
on the workers’ choice h*. For any given realization of F2 it is
less likely that total profits are negative the higher the stock of
specific capital.
The role of the firm in our model is admittedly quite passive.
Effectively, apart from setting marked-up prices, it only decides
whether to maintain production at the capacity level, or to cease
Figure 1. Profits ꢁt and the plant closure decision
π
t
π1
π2a
Aa
0
Xt
−sL1
−sL1
−F
π2b
1
Ab
−F2a
−F2b
X2 =hX1
X1
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Severance Payments and Firm-specific Human Capital
53
production completely and shut down the plant.10 The firm’s ‘all or
nothing’ decision is summarized in Figure 1. Profits are linearly
K
increasing in the output level up to the capacity constraint Xt,
which is higher in period t ¼ 2 the higher the level of specific
K
capital h*. Depending on the realization of F2, profits ꢁ2(X2) might
L
fall short of ꢀsL1, given by the thick horizontal line, in which case
(Fb2) the firm will decide to close.
3. The worker’s decision problem
L
Each of the L1 employed workers is identical, risk neutral,
embodies one effective labour unit in period t ¼ 1, and conse-
quently earns w. As argued above, we abstract from strategic
interactions in the human capital choice of single workers, and
consequently focus on a representative employee whose investment
decision will be replicated by all other workers. We assume that the
costs of ‘on the job’ learning are imposed exclusively on workers,
possibly through unpaid overtime devoted to training. Total
learning costs are given by ꢄ(h)h, where the cost function ꢄ(h) is
assumed to rise in h at an increasing rate, i.e. @ꢄ=@h > 0 and
@2ꢄ=@h2 > 0.
The investment payoff, however, is uncertain, since the firm only
keeps on operating with probability ꢃ. Note that the worker has no
incentive to quit him=herself, since he=she carries firm-specific
human capital and does not receive any better job offer from
another company. Thus, the worker would consider working for a
different employer only if the particular firm closed down at the
beginning of t ¼ 2. This event occurs with probability (1 ꢀ ꢃ), in
which case the worker will receive a redundancy compensation s,
loose his=her accumulated stock of specific human capital and
make earnings w at some other enterprise. The worker’s choice
problem is to maximize the following inter-temporal value function
with respect to the level of specific capital h:
Max ¼ {w ꢀ ꢄ(h)h þ ꢅ(ꢃhw þ (1 ꢀ ꢃ)(s þ w))};
[5]
{h}
where 0 < ꢅ < 1 is a time discount factor. The first-order condition
to this problem is given by:
dꢄ(h)
ꢀꢄ(h) ꢀ
h þ ꢅ(ꢃw þ ꢃhwh ꢀ ꢃh(s þ w)) ¼ 0:
[6]
dh
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Jens Suedekum – Peter Ruehmann
Keeping in mind that ꢃhh ¼ 0, we can write the second-order
conditions as:
dꢄ(h)
dh
|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
d2a(h)
dh2
!
ꢀ2
ꢀ h
þ 2ꢅꢃhw < 0 :
[7]
|fflfflfflfflfflffl{zfflfflfflfflfflffl}
ꢀ
þ
The sign of [7] is theoretically ambiguous and the existence of a
maximum hinges on functional forms. Yet if the existence of a
maximum is warranted,11 we can rewrite the first-order condition
in the following intuitive form:
ꢄ(h)
(1 þ ꢆꢄ; h) ¼ ꢃw þ ꢃh(hw ꢀ (s þ w)):
[8]
ꢅ
This expression consists of three terms. On the left-hand side are
the opportunity costs of human capital formation, where
dꢄ(h)
h
ꢆꢄ; h
¼
dh ꢄ(h)
is the elasticity of the function ꢄ(h) evaluated at the optimal level
h*. In equilibrium, this expression must equal the sum of two
effects that we label the direct wage effect ꢃw and the job security
effect ꢃh(hw ꢀ (s þ w)). The straightforward intuition for the direct
wage effect is that marginal investment costs must equal marginal
revenue for the worker. The job security effect stems from the
endogenous uncertainty. Since ꢃh is positive, any increase in h
makes the job ceteris paribus more secure. The overall sign of the
job security effect, however, depends on the difference between the
attainable earnings with this specific firm and the earnings in the
event of a lay-off.
The worker will choose some optimal h* such that [8] is satisfied.
The optimal choice h* depends on the properties of ꢄ(h), on the
exogenous variables w and ꢅ, and — most importantly for our
purposes — on s, the level of employment protection.
4. An increase in severance payments
We now ask what effect a marginal increase in s has on the
optimal choice h*. Total differentiation of [6] around the optimum
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Severance Payments and Firm-specific Human Capital
55
h*, with all variables except s held constant, yields:
0
1
dꢄ(h)
dh
d2a(h)
dh2
@
A
ꢀ2
ꢀ h
þ 2ꢅꢃhw dh* þ ꢅ(ꢃsw ꢀ ꢃh) ds ¼ 0: [9]
Substituting in ꢃh and ꢃs, we can rewrite [9] to give:
0
1
L
ꢅwL1
1 ꢀ ꢂ
ꢂ
@
A
1 ꢀ
2c
dh*
ds
¼ ꢀ
:
[10]
0
1
@2
@
A
(h*)
@h2
The denominator is equal to the second-order condition at h ¼ h*,
which is negative. Thus, at any maximum of , the marginal effect
dh*=ds is positive if and only if the following surprisingly simple
condition holds:
ꢂ > 12:
[11]
If the mark-up (1=ꢂ) of the firm is too large, i.e. if ꢂ < 12, an increase
in SP leads to a lower optimal value h*. An instructive way to
think about condition [11] is as follows: one can show that firm-
specific investments induce an increase in payroll earnings by
L
(h* ꢀ 1)wL1 units. The increase in variable profits makes up for
(1=ꢂ ꢀ 1) times this amount, and is thus smaller only if ꢂ is greater
1
than . In other words, when faced with higher SP, workers are
willin2g to invest more heavily in specific human capital only if the
L
expected increase in payroll (which is shared equally among the L1
workers) exceeds the expected increase of variable profits that the
firm takes out even though it had not contributed to the financing
of the investments.
More intuition for this result can be grasped in terms of the
direct wage and the job security effect. Upon an increase in s,
the worker perceives two changes: firstly, the probability ꢃ (and
thereby the direct wage effect) has increased. Secondly, the
attractiveness of maintaining the job relative to receiving s, i.e.
the job security effect, has decreased. Subsequently, the worker
re-optimizes over h such that the sum of the two matches the
(approximately) unchanged opportunity costs. It turns out that for
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56
Jens Suedekum – Peter Ruehmann
all cases with ꢂ > 12 the direct wage effect reacts more strongly in the
positive direction than the job security effect in the negative
direction. Consequently, the worker will increase h* in order for [8]
to match. The opposite occurs if ꢂ < 12. In this case, the return to
human capital investments for the worker is low, and an increase in
s induces the worker to invest less in human capital, since this
negatively affects the probability ꢃ that the firm stays in business
during t ¼ 2.
The result is summarized in Figure 2, which is a stylized, linear
representation of the optimal investments decision h* as a function
of s and ꢂ. The optimal h* is increasing in ꢂ, and the influence of s
is ambiguous. As long as ꢂ > 12, h* is higher with high SP than with
low SP. At ꢂ ¼ 12 the choice h* is independent of the level of s. With
ꢂ < 12, h*(slow) is higher than h*(shigh).
In the introduction we outlined competing arguments, citing
authors who attributed employment protection either with an
exclusively positive impact on the level of firm-specific human
capital, or with an exclusively negative one. Employment protec-
tion can work as an incentive to build up firm-specific skills,
because workers perceive a lower default risk of their investments
and rely on the long-term validity of their labour contracts. The
main idea of this incentive effect has been put forward by authors
such as Buttler and Walwei (1990), Schmid (1995) and Houseman
(1990), and is consistent with our analysis. Yet it is also possible
that more employment protection reduces the level of ‘firm-specific
commitment’ since a lay-off is perceived not to be such a strong
penalty. The transmission channel of this competing lethargy
effect, which has been described, for example, by Ichino and
Figure 2. Optimal human capital formation h*(s; ꢂ)
shigh
h*
slow
µ
0
½
1
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Severance Payments and Firm-specific Human Capital
57
Riphahn (2001) and Goerke (2003), is also part of our model. And
thus the basic message that follows from our analysis is that the
influence of SP on the optimal amount of human capital formation
is actually ambiguous, since there is a trade-off between two
competing forces. Which one dominates crucially depends on the
particular firm under consideration at which workers are
employed, specifically on the measure of its market power (1=ꢂ).
5. Implications for the firm’s profits
So far we have treated s as an exogenous parameter, imposed on
the firm by government policy. But since our analysis did not point
to an essential reason for government intervention, we now want to
analyse whether the firm would also provide some positive level of
s if it could foresee the investment behaviour of the workers.
Intuitively, there are three effects of SP for the firm. The first
two are negative: SP are exit costs that can force the firm to
operate under loss in t ¼ 2. And, in the event of a plant closure, the
firm actually needs to pay s and thus realizes negative profits. The
argument in favour of SP is that they can induce human capital
formation (provided that dh*=ds > 0) that also benefits the firm
through higher variable profits. If it turns out that this latter effect
is strong enough to compensate the two negative ones, we could
expect the firm to provide some SP as of free will, without being
obliged to do so as a result of public policy.
To demonstrate this, we need to derive a function of the firm’s
realized profits P2 that needs to be distinguished sharply from ꢁ2,
since the firm responds to some realizations of F2 with exit. Recall
that the firm keeps on operating if total profits ꢁ2 exceed the level
L
of exit costs ꢀsL1. This event occurs with probability ꢃ. If,
however, the realization of F2 is such that ꢁ2 is negative and below
the level of exit costs, an event occurring with probability (1 ꢀ ꢃ),
L
the firm exits and makes realized profits P2 ¼ ꢀsL1, regardless of
the value of ꢁ2. Thus, realized profits P2 are
(
L
ꢁ2
if ꢁ2 ꢀ ꢀsL
P2 ¼
:
[12]
L
L
ꢀsL1 if ꢁ2 < ꢀsL
Given that the firm remains active during t ¼ 2, the range of
L
L
possible profits goes from ꢀsL1 to ꢀ(F1 ꢀ c) þ (1 ꢀ ꢂ=ꢂ)wh*L1.
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Jens Suedekum – Peter Ruehmann
Since F2 is uniformly distributed, all cases between these two
extremes are equally likely. Expected realized profits E(P2) can
thus be written as:
0
1
1 ꢀ ꢂ
ꢂ
@
A
L
L
ꢀ(F1 ꢀ c) þ
wh*L1 ꢀ sL1
L
E(P2) ¼ ꢃ
ꢀ (1 ꢀ ꢃ)sL1: [13]
2
In [13], the two negative effects of SP for the firm can be seen
directly: s enters twice with a negative sign. The positive effect
operates through h*, which must be increasing in s (i.e. ꢂ > 12).
Rewriting [13] under the use of [4] yields:
2
L
E(P2) ¼ cꢃ ꢀ sL1;
[14]
with ꢃ ¼ ꢃ(h*(s); s). The firm aims to maximize expected realized
profits, and would thus choose the level of s so as to maximize
[14] for a given level of ꢂ, taking into account the effects of SP on
the optimal human capital formation h*(s). Suppose that initially,
i.e. at the beginning of t ¼ 1, a situation exists with s ¼ 0. The
question is then whether it is in the interests of the firm to set
some strictly positive level of s in order to induce human capital
investments, i.e. if there exists an interior maximum of E(P2)
associated with some optimal level s* > 0. In the Appendix we
show that such a maximum can exist if human capital investments
h* are highly responsive to changes in s. Provided a maximum of
E(P2) exists, the firm would set the following level of SP per
worker (s*):
L
2c=L1
F1 ꢀ c 1 ꢀ ꢂ
s* ¼
þ
ꢀ
wh*:
[15]
0
@
10
1
A
L
L1
ꢂ
1 ꢀ ꢂ
ꢂ
dh*
ds
A@
1 þ w
Hence, the firm can also have an interest in providing some
employment protection by means of SP if this has strong effects
on the human capital formation of the worker(s). We should
thus expect a profit-maximizing firm to provide s* in its own
interests, without being obliged to do so as a result of public
policy.
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Severance Payments and Firm-specific Human Capital
59
6. Conclusion
We have seen that the effect of SP on the behaviour of employed
workers, i.e. on the optimal human capital investment choice, is
ambiguous. Whereas other authors have pointed either to an
exclusively negative or positive impact, we have shown that there is
actually a trade-off between two competing forces (that we have
called the incentive effect and the lethargy effect). Which of the two
forces predominates is determined in our model by the mark-up
parameter ꢂ, which can be interpreted as a measure of the firm’s
market power.
The optimal amount of firm-specific human capital investments
for the representative worker is increasing in ꢂ, because the firm
extracts an ever smaller share of the additional output generated
through the workers’ learning effort.
If the mark-up of the firm is high (ꢂ < 12), human capital
formation is low, since any investment raises variable profits
stronger than payroll earnings. If in such an environment the level
of SP rises, it is optimal for workers to increase the chance of
actually receiving the redundancy compensation by lowering the
amount of firm-specific human capital investments.
If, however, the market power of the firm is low (ꢂ > 12),
investment returns induce stronger increases in payroll earnings
than in variable profits. Human capital formation is more
attractive to workers, because the additionally generated output
remains largely in their pockets. In such case, a rise in SP induces
an increase in the amount of optimal investment. The perception of
higher job security in environments like this is stimulating, because
the default risk is lowered, which effectively results in a more vital
investment behaviour.
Our model thus suggests that the overall effect of more job
security (through SP) depends on whether workers have high
incentives to invest in specific human capital to begin with. In
corporate environments where it is attractive for workers to
commit to their employer anyway, because human capital
investments are rewarded by sufficient payment increases, employ-
ment protection can act as a complementary motivation to invest.
Contrariwise, if workers have a low motivation for ‘firm-specific
commitment’, this may even decrease further if employment
protection is provided.
If the effects of SP on human capital formation are strongly
positive, firms can also have an interest in providing employment
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60
Jens Suedekum – Peter Ruehmann
protection. In this partial equilibrium model, a private provision of
some employment protection is possible if parties recognize the
positive side-effects of job security. But it would be precipitate to
conclude on the basis of our model that public policy is obsolete in
terms of providing employment protection legislation, given that
our analysis consists only of a partial equilibrium framework and
had to abstracted from several potentially important issues.
Probably the most restrictive part of our model is the very low
degree of adaptability of the firm, which effectively can produce
only at the capacity level or shut down the plant completely.
However, our main objective was to analyse how workers’ human
capital formation is affected by employment protection. The basic
insight that we have derived, the trade-off between job security and
the lethargy effect, does not critically depend on the low degree of
firm adaptability. Suppose the firm could adjust to adverse
exogenous shocks by realigning prices and output while maintain-
ing some production and employment. As long as any single
worker faces a non-zero probability of getting laid off, the
provision of more job security through SP would still imply two
things: (a) a lower default risk of specific investments, and (b) a
cushioning of lay-offs through redundancy compensations. There-
fore, the overall effect of SP on the optimal choice of firm-specific
human capital investments is ambiguous and presumably depen-
dent, at least qualitatively, on similar considerations as in our
simplified model.
Appendix: maximum condition @E(P2)=@s
The first-order condition of [14] with respect to s is:
0
1
@E(P2)
@s
dh*
ds
@
A
L
¼ 2cꢃ ꢃs þ ꢃh
ꢀ L1 ¼ 0
[A1]
[A2]
and the second-order condition is given by:
þ
ꢀ
d2h*
zfflfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflfflffl{
zfflfflfflfflffl}|fflfflfflfflffl{
0
1
@2E(P2)
@s2
dh*
ds
!
@
A
¼ 2c ꢃs ꢃs þ ꢃh
þ ꢃꢃh
< 0:
ds2
ð
Þ
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CEIS, Fondazione Giacomo Brodolini and Blackwell Publishing Ltd 2003.

Severance Payments and Firm-specific Human Capital
61
Since ꢃ, ꢃs, ꢃh and (dh*=ds) are positive, [A2] is negative only if
the term ꢃꢃh(d2h*=ds2) is strongly negative. Thus, the existence of
a maximum with respect to s requires that the optimal human
capital choice h* reacts very sensitively to a small change in s, and
that h* is increasing in s at a rapidly declining rate. In case a
maximum exists, the optimality condition [A1] can be rewritten as:
1
ꢃ ¼
:
[A3]
1 ꢀ ꢂ dh*
ꢂ
1 þ w
ds
Substituting in the definition of ꢃ and manipulating [A3] gives
equation [15].
Notes
1 Starting from Lazear (1990), who has argued both theoretically and
empirically that EPL substantially lowers employment, the subsequent literature
found little evidence for significant negative impacts of EPL (see Addison,
Teixeira, 2001; Bentilola, Bertola, 1990; OECD, 1999; Pissarides, 2001).
2 SP are government-mandated transfers from employers to workers in the
event of a lay-off, not a quit. It is a common form of EPL in many OECD
countries (see OECD, 1999), both de jure and de facto. Note that SP must not be
interpreted as a pure firing tax, and therefore must be distinguished from other
forms of EPL as discussed, for example, in Bentilola and Bertola (1990).
3 The terms ‘human capital investment’ and work effort are used synonymously
in the model.
4 Some related evidence for the positive impact of employment protection on
productivity is presented by Freeman and Medoff (1984). A result in the same
spirit comes from Acemoglu and Pischke (2001) for the case of minimum wages.
5 Pissarides (2001, p. 133) also makes this point: ‘it is difficult to see why firms
will need legislation to protect them from not wasting firm-specific skills’.
6 Each worker has a private investment incentive, but might spend too little
time on training and free ride on the job security externality induced by the
human capital investments of others. But we do not consider this strategic
interaction further, and pay attention only to cooperative behaviour among
workers, because this seems to be more relevant in the context of one particular
small firm with an intact system of social control.
7 Since the human capital is firm specific, we would normally expect the firm to at
least partially contribute to the financing. But including a firm’s share in learning
costs would only complicate the analysis, without affecting the central insights.
8 Note that the level of SP does not depend on the human capital decision h*,
i.e. employment protection is provided for employed people, not labour units.
9
L
L
From [4] we can compute that ꢃs ¼ (L1=2c) > 0 and ꢃh ¼ (1 ꢀ ꢂ=2cꢂ)wL1 > 0.
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62
Jens Suedekum – Peter Ruehmann
10 The construction of fixed mark-ups over linear marginal costs (which
effectively results in production at capacity level) is, however, used also in other
contexts, e.g. in the imperfect competition approach to macroeconomics (see
Carlin, Soskice, 1990, Ch. 18). We discuss some of its limitations in the
conclusion (Section 6).
11 Our numerical simulations show that it is almost impossible to find functions
ꢄ(h) that increase in h at an increasing rate for which a maximum of does not
exist.
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