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A joint Initiative of Ludwig-Maximilians-Universität and Ifo Institute for Economic Research
Labour Market Institutions and
Public Regulation
– A CESifo and ISPE Conference –
CESifo Conference Centre, Munich
26-27 October 2001
On the Political Economy of Dismissal Pay.
Laszlo Goerke
CESifo
Poschingerstr. 5, 81679 Munich, Germany
Phone: +49 (89) 9224-1410 - Fax: +49 (89) 9224-1409
E-mail: [email protected]
Internet: http://www.cesifo.de
On the Political Economy of Dismissal Pay*
by
Laszlo Goerke
University of Konstanz+, IZA (Bonn) and CESifo (Mu nchen)
+ Department of Economics - D 138
D - 78457 Konstanz
Germany
Phone: ++49(0)753188-2137
Fax: ++49(0)753188-3130
E-mail: [email protected]
Abstract:
The wage and employment effects of dismissal pay for individual job losses and collective
redundancies are investigated in a shirking model of efficiency wages. Payments for collective
dismissals reduce the incentives to shirk and can increase employment and profits while they
leave the workers' payoff unaffected. Thus, they can be agreed upon at the firm level. An
economy-wide introduction induces positive externalities, given the job creation effect. This
contrasts with the introduction of payments for individual dismissals which decreases the
combined payoff of firms, workers, and the government.
Keywords: collective and individual dismissal, dismissal pay, efficiency wages, political
economy
JEL-code: D 78, E 24, J 32, J 41, J 65
* I am grateful for helpful comments by Carsten Hefeker, Bernhard Boockmann, Guilio
Piccirilli, as well as by participants of the annual meetings of the European Public Choice
Society in Paris and the European Association of Labour Economists in Jyvaskyla, and the 10th
Silvaplana Workshop on Political Economy.
1
1. Introduction
Employment protection legislation (EPL) results in transfers to workers, for example, due to
dismissal payments or notification periods, and in regulations which solely raise labour costs and
effectively represent a tax, such as administrative or firing costs. The employment and welfare
consequences of these taxes and transfers can be radically different since only the latter have a
direct impact on the workers' behaviour. In the literature on the political economy of EPL, the
focus has mainly been on firing costs (cf. Saint-Paul 1996, 1999). However, recent evidence
indicates that dismissal pay is a decisive component of EPL and that differential rules apply for
individual and collective dismissals (Garibaldi and Violante 1999, OECD 1999).
This paper investigates the incentives for the introduction of dismissal payments. It is shown that
the wage and employment effects of variations in payments for individual dismissals differ from
those for collective dismissals. Since payments in the case of individual dismissals - due either
to an exogenous shock or to having been caught providing insufficient effort - make shirking
more attractive, the efficiency wage has to rise. Higher wages and dismissal costs reduce profits,
but can raise the payoff of employed workers. Thus, such transfers can only be introduced in the
political process if workers have substantial political power. In contrast, mass redundancies can
clearly be distinguished from job losses owing to insufficient effort. Only those workers will
benefit from higher redundancy pay for mass dismissals who have not been caught shirking.
These payments mitigate the incentives to shirk and allow for a reduction in wages. Overall
labour cost fall and profits rise. Moreover, at least those workers who experience a mass redundancy benefit from higher payments. Accordingly, there are incentives for an introduction of
these payments at the firm level. If redundancy pay raises employment, there is a positive externality due to a higher re-employment probability and there are additional incentives to establish
such payments at an aggregate level.
The paper is related to two strands of literature: first, analyses of firing costs and, in particular
dismissal payments in efficiency wage models and, second, the political economy of labour
market reforms. Severance pay for individual dismissals has, implicitly, been looked at by
Shapiro and Stiglitz (1984), since firms pay unemployment benefits in their efficiency wage
model. Thus, the negative employment and welfare consequences of unemployment benefits to
which workers are entitled who are dismissed for disciplinary or exogenous reasons also apply
for severance payments for individual dismissals. However, Fella (2000), based on Saint-Paul
(1995), assumes that workers who are dismissed for disciplinary reasons do not receive
severance payments. Accordingly, such payments reduce the incentives to shirk and raise employment (cf. Bull (1985) or Goerke (2000), as well). Turning to the political economy of EPL,
Saint-Paul (1999) investigates firing costs in a growing economy with technological progress
and creative destruction in which wages are determined by a rent-sharing rule. He shows that
employed workers generally favour firing costs while unemployed oppose them. The higher the
rents from employment are, the more likely are firing costs (see also Saint-Paul 2000, pp. 111).
2
This brief overview shows that the distinction between payments for individual and collective
dismissals has neither played a role in the literature on the labour market effects of dismissal pay
nor in the analysis of why according legislation is enacted. This paper aims to fill the gap. Section 2 contains the shirking model of efficiency wages, based on the set-up by Shapiro and
Stiglitz (1984). The model includes payments in the case of individual dismissals - labelled
severance pay - and also for collective dismissals - referred to as redundancy pay. Section 3
analyses the changes in the payoffs due to variations in these payments and derives the requirements for an introduction of severance and redundancy pay to be feasible. Section 4 summarises.
2. Model
Workers can lose their job for three distinct reasons. They might shirk and will be caught doing
so with probability q per unit of time. There might be a 'small' exogenous shock which induces
the firm to dismiss individual workers. In this case, severance payments have to be made. The
probability that a worker is dismissed owing to such a 'small' shock is given by b. Finally, there
might be a 'large' exogenous shock which requires the firm to fire a substantial fraction of its
workforce and to make redundancy payments. The probability that a worker loses the job owing
to such a mass redundancy is given by h. The probabilities b, h, and q are sufficiently small, implying that the time periods under consideration are very short, such that bq ≈ bh ≈ 0.1
2.1 Workers
Workers are infinitely lived, discount future payments with the rate r, r > 0, cannot borrow or
save and are characterised by an instantaneous utility w - e, where w is the wage and e their
effort, or the disutility from exerting effort. Effort can either be high (e = e ) and conform to the
level required by the company or it can be low (e = 0). Unemployment benefits w are paid to
every worker who loses the job. The discounted utility stream rVE,N from being employed and
not shirking consists of the wage less the disutility from effort and the utility loss in the case of
being fired. Denoting the utility in the case of being unemployed due to an individual dismissal
by VU,D and due to a mass redundancy by VU,M, an employed non-shirker can be described
by:2
rV E , N = w − e + b ( V U , D − V E , N ) + h ( V U , M − V E , N )
(1)
Simplification then yields:
1
Fixed dismissal probabilities imply that a change in the firm's employment level does not alter the individual's
probability of losing a job. This contrasts with Fella's (2000) hypothesis that a greater firm-specific employment
level raises the probability of a job loss. One consequence of the differential assumptions is that hysteresis effects
are feasible in Fella's (2000) model (cf. Saint-Paul 1995), which are of no relevance for the pre sent analysis.
2 Dismissal payments can either be incorporated into the utility stream from employment VE,N or from unemployment VU,D, respectively VU,M. Since the focus is on the impact of these payments on the utility from
unemployment, they are included into VU,D and VU,M. This approach obviously does not affect the results.
3
U
,
D
w − e + bV
+ hV U , M
V E,N =
r+b+h
(2)
The expected life time utility of an employed shirker VE,S is:
V E ,S =
w + ( b + q ) V U , D + hV U , M
r+b+q+h
(3)
The discounted utility stream rVU,D of a worker who has been dismissed individually is defined
by unemployment benefits w and severance payments σ per period, plus the expected utility
gain owing to a new job. The presumption that workers cannot save requires the definition of
dismissal pay as a transfer per unit of time. Moreover, and in line with Shapiro and Stiglitz
(1984), equations (2) and (3) are based on the assumption that shirkers and non-shirkers who
lose the job due to a small shock are both entitled to severance payments σ. This reflects the
predominant feature in Europe that dismissals imply severance payments even if a worker has
shirked since otherwise the employer could circumvent any according obligation by simply
claiming to have observed shirking. An unemployed worker finds a new job with probability a
per period, the job acquisition rate. Since all workers provide the required amount of effort in
equilibrium, re-employment yields a utility gain (VE,N - VU,D), plus the current value of severance payments σ/r.
rV U , D = w + σ + a ( V E , N − V U , D + σ / r )
(4)
If the worker finds a new job, s/he might again become entitled to severance pay if another dismissal occurs. Hence, the utility gain from finding a new job VE,N - VU,D is unaffected by the
level of severance pay from the initial dismissal since payments are not terminated, in contrast to
those of unemployment benefits. A worker who loses the job due to a mass dismissal is characterised by a utility stream VU,M and obtains redundancy pay S per period. The value of these
payments might differ from those for individual dismissals. This yields:
VU , D =
w + aVE , N σ
S−σ
+ = VU , M −
r+a
r
r
(5)
Using equations (2) and (5), the expected lifetime utility VU,D of a worker who has lost the job
owing to an individual dismissal is found to be:
V U,D =
w ( r + b + h ) + a ( w − e ) + ah ( S / r ) + ( σ / r ) r ( r + b + h + a ) + ba
r(r + b + h + a)
(6)
A worker will not shirk if VE,N ≥ VE,S holds. Substituting in accordance with (5) and (6) and
assuming that the constraint binds, allows for the derivation of the efficiency wage we:
we −
e
S σ
(r + b + h + a) − e − w + h − (r + h + a) = 0
q
r r
(7)
Higher payments for workers who have lost their job for other reasons than shirking increase the
utility from selecting the required amount of effort e . Effectively, payments for collective
dismissals enable a partial distinction between job losses for exogenous reasons and due to
4
insufficient effort. This distinction is not perfect as also workers who have lost their jobs owing
to small shocks have not shirked. But raising S makes only those workers better off who have
not been caught shirking. Hence, higher redundancy pay lowers the wage which induces the
effort level e = e . However, payments to individually dismissed workers are made irrespective
of the cause of the job loss. Shirking becomes attractive and the efficiency wage rises.
2.2 Firms
The economy consists of a fixed number τ of ex-ante identical firms. Consistency with the specification of the workers' maximisation problem requires that firms choose a level of employment
prior to the revelation of the exogenous shock which will be too high if the shock is negative and
too low if positive. Such a situation arises, for example, if firms can vary employment at no
costs before the type of shock is revealed, while they incur adjustment costs subsequent to its
disclosure. Below a kind of reduced-form approach is pursued. Before the beginning of a period,
each of the τ firms sets an efficiency wage and chooses optimally the employment level n. Thus,
the wage is not contingent on the economic situation (cf. equation (7)). It will employ Tn > n
people if there is a positive shock, and Cn (Pn), 0 < P < C < 1, people if a small (large) adverse
shock occurs. T, C, and P are fixed and, thus, do not vary with dismissal payments. This is true,
for example, if each firm consist of a given number of departments, of which a fraction 1 - C (1 P) has to be closed down completely in the case of a small (large) shock, since demand for their
output has vanished entirely. This assumption guarantees that dismissal payments have negative
employment effects in the absence of wage adjustments and does not affect the relative merits or
disadvantages of severance and redundancy pay. Shocks last only one period and are not correlated over time. That is, the next period it is again optimal to employ n people. For simplicity
and because the impact of dismissal pay is not affected by this presumption, the costless adjustment of employment prior to a period takes place by reallocating workers from firms with
excessive employment to those with an insufficient number of workers. Hence, the dismissal
probabilities b and h and the job acquisition rate a are unaffected by these adjustments.
Given the above assumptions, expected profits are invariant over time. Let the probability that a
firm experiences a positive shock and that the output price or demand rises from unity to T , T >
1, and that the firm employs Tn > n workers, be given by β, 0 < β < 1. Alternatively, β can be
interpreted as the fraction of firms experiencing a positive shock. In case of a small shock, the
output price will fall to C, C < 1 and employment be given by Cn. This state occurs with probability (1 - β)c. A mass redundancy is due to an output price P, P < 1, takes place with probability (1 - β)p, and leaves employment at Pn. Severance pay for individual dismissals is
5
obtained by (1 - C)n workers with probability (1 - β)c, as no one shirks in equilibrium. Redundancy pay for collective dismissals is received by (1 - P)n workers with probability (1 - β)p.3
Dismissals can involve costs in addition to transfer payments, such as for legal proceedings or
the adherence to procedural regulations (Bentolila and Bertola 1990, Burda 1992). These costs
are represented by a mark-up ξ, ξ ≥ 0, on dismissal payments. The firms' production function f is
strictly concave in effective employment (f '(en) > 0, f '' < 0), while the capital stock is fixed and
its costs are normalised to zero. Firms pay taxes ˆ, ˆ ≥ 0, on their payroll. These taxes include
all wage-related costs of employment, in addition to wages themselves. The gross efficiency
% e ≡ we(1 + ˆ). Given these assumptions, expected profits are:
wage is denoted by w
~ e nT  + (1 − β)(1 − c − p)(f (n e ) − w
~ e n)
E(Π ) = β  T f (Tn e ) − w


{
}
~ e n − [c(1 − C)σ + p(1 − P)S]n (1 + ξ) / r (8)
+ (1 − β) c C f (Cn e ) + pPf (Pn e ) − (cC + pP) w
In a steady-state, the flows into and out of unemployment are equal. Denoting aggregate employment by N and normalising labour supply to unity, a steady-state implies (b + h)N = a(1 - N),
since no worker shirks in equilibrium. The inflows into unemployment owing to dismissals are
given by (1 - β)τnc(1 - C). These inflows have to equal the inflows as defined on the aggregate
scale, i.e. b = (1 − β ) c (1 − C ) . Similarly, the inflows into unemployment due to mass redundancies and outflows owing to higher firm-specific employment levels have to equal their aggregate counterparts. This implies N = τn and β(T - 1) + 1 - (1 - β)[c(1 - C) + p(1 - P)] = 1. Substitution and maximisation of expected profits with respect to employment yields:
d(E(Π ))
σ
 S
≡ π n = f '− w e (1 + µ) −  h + b (1 + ξ) = 0 , where
dn
r
 r
[
(9)
]
f ' ≡ e{β T f ' (Tn e )T + (1 − β) (1 − c − p)f ' (n e ) + cC (f ' (Cn e )C + pP (f ' (Pn e )P } > 0
The second-order condition πnn < 0 will be warranted if f is strictly concave as assumed above.
2.3 Employment Effects
Taking into account that the efficiency wage changes with dismissal payments, the variation in
the firm-specific level of employment owing to an increase either of payments in the case of
individual or of collective dismissals in a particular firm can be derived as:
∂we
b
(1 + µ ) + ( 1 + ξ )
(1 + µ )( r + h + a ) + (1 + ξ ) b
dn
r
= ∂σ
=
<0
π nn
dσ
rπ nn
(10)
Since dismissal payments S and σ are defined per period, whereas firms have to take into account their present
value, some independent agency can be imagined which collects payments from firms at a point in time and hands
out the transfers to dismissed workers over their infinite lifetime.
3
6
e
h
∂w
(1 + µ ) + (1 + ξ )
dn
h(ξ − µ)
r
= ∂S
=
dS
rπ nn
π nn
(11)
If not only one but all τ firms raise dismissal payments, the impact of changes in aggregate employment on the job acquisition rate a will have to be taken into account. However, the direction
of the employment change is the same in aggregate as it is for a single firm (see appendix).
Higher severance payments σ raise unemployment since wages increase and because labour
demand shrinks for a given level of wages. Redundancy payments S for collective dismissals are
only obtained by workers who have not been caught shirking. Hence, wages can fall. Employment will be unaffected by a variation in redundancy pay if the payroll tax rate and the firing
cost mark-up are the same (ˆ = ξ). This is because the fall in wages has to compensate exactly
the rise in expected redundancy pay in order to induce workers to bring forward the same effort.
If the fall in wages is amplified by payroll taxes to the same extent as the increase in redundancy
pay is raised by the firing-cost mark-up, marginal employment costs and, hence, employment
will remain constant. This prediction can also be obtained for a competitive setting (Lazear
1990, Booth 1997) or in a matching model (Burda 1992) with respect to severance payments.
However, Garibaldi and Violante (1999) calculate that the non-transfer component of firing
costs in Italy and the UK is less than 15%. Given non-wage labour costs which might easily
exceed 20% of wages (OECD 1986), a payroll tax rate which exceeds the firing cost mark-up (ˆ
> ξ) is a plausible assumption. The decrease in marginal employment costs due to higher redundancy pay is amplified for ˆ > ξ since firms save not only on wages but also on tax payments.
Employment becomes cheaper at the margin and the number of jobs rises.4
3. Changes in Payoffs due to Dismissal Payments
This section investigates the incentives for introducing dismissal pay either at the firm level or
for the entire economy. While variations in these payments in a single firm have no impact on
the re-employment probability a, an encompassing change can affect a.
3.1. Individual Incentives
First, the impact of dismissal pay on profits is looked at. Second, the alterations in the utility of
workers are analysed. The changes in expected profits E(Π) due to dismissal payments, taking
into account the variation in wages, but holding constant the job acquisition rate a, are given by:
dE ( Π )
n
= − r + h + a + b + ( r + h + a ) µ + bξ < 0
dσ da = 0
r
4
(12)
The result that redundancy pay may raise employment in a shirking economy does not imply that it can be
increased without limits. All derivations have been based on the restriction that VE,N > VU,M, which will hold for
a value of S such that S < e r/q + σ (see also Saint-Paul (1995) or Fella (2000) for a similar restriction).
7
dE ( Π )
nh
=
µ−ξ
dS da = 0
r
(13)
Higher dismissal payments always decrease profits for a given level of wages. In the case of
mass dismissals, however, the wage falls and this wage reduction will be sufficient to raise
profits if the payroll tax rate ˆexceeds the firing cost mark-up ζ. Severance pay σ for individual
dismissals not only drives up labour costs directly but also wages. Thus, profits decline.
To answer the question whether a worker and a firm can agree on the introduction of dismissal
pay, furthermore, the change in the expected utility stream VE,N of an employed worker has to
be analysed. According to equation (2) this analysis requires the computation of the impact on
the utility of dismissed workers. For a given job acquisition rate a, one obtains from (6):
dVU , D
=
dσ da = 0
a
∂we
ba
+r+b+h+a+
U,D
∂σ
r = r + a > 0 = dV
r(r + b + h + a)
dS da = 0
r2
(14)
Higher severance payments σ make workers who lose their job owing to a small shock better off
since the wage and the payoff in the case of being dismissed increase. Higher redundancy payments S will only alter the payoff of a worker who loses the job owing to a small shock if s/he
finds another job and loses the job again due to a large shock. However, the reduction in wages
and the increase in the expected redundancy payment cancel out.
Turning to workers who lose their job owing to a mass redundancy, equations (5) to (7) imply
that such workers benefit from higher dismissal pay irrespective of the nature of these transfers.
dVU , M
a
a dVU , M
=
=
>0
dσ da = 0 r 2 r
dS da = 0
(15)
The positive impact of redundancy pay S can be explained as follows: from equation (14) it is
known that redundancy payments leave the utility stream VU,D of a worker who loses the job
due to an individual dismissal unaffected. The utility stream VU,M of a worker who experiences
a mass redundancy consists of the utility of a worker dismissed individually plus the
(discounted) difference in dismissal payments. Since this difference rises with higher
redundancy payments by 1/r (cf. equation (5)), VU,M increases by exactly this magnitude.
Higher severance pay σ directly reduces the utility stream of a worker who experiences a mass
redundancy by 1/r. However, the utility of a worker who experiences an individual dismissal
rises with severance payments by a multiple of 1/r. Accordingly, severance payments also make
a worker better off who loses the job owing to a mass redundancy.
Using equations (2), (5), (14), and (15), the change in the payoff of an employed worker due to
higher dismissal payments, holding constant the outflow rate from unemployment, is found to
be:
8
e
U
,
D
∂w
dV
dVU , M
+b
+h
∂σ
dσ da = 0
dσ da = 0 r + a
dVE , N
dVE , N
=
=
>0=
(16)
r+b+h
dσ da = 0
dS da = 0
r2
Redundancy pay S leaves the utility of employed workers unaffected because the direct, negative
wage effect exactly balances the increase in expected redundancy pay. Moreover, the utility if
fired on an individual basis is constant. However, severance pay σ increases the payoff of employed workers since, first, the wage and, second, the utility from becoming unemployed rises.
Severance pay σ reduces profits, while it raises the payoff of employed workers (cf. equations
(12) and (16)). Assuming a common discount rate r, the combination of both effects yields:
h + b + ( r + h + a ) µ + bξ
1 dE ( Π )
dVE , N
+r
=−
<0
r
dσ da = 0
n dσ da = 0
(17)
Since the combined payoff of a worker and firm declines, it is impossible to introduce severance
payments σ voluntarily at the firm level. In contrast, changes in redundancy pay S leave the utility of employed workers constant while expected profits will increase if the payroll tax exceeds
the firing cost mark-up. These results can be summarised in:
Proposition 1:
A firm and a worker will not agree on the introduction of severance payments for individual
dismissals if shirkers are entitled to these payments. If employment rises with redundancy payments for collectively dismissed workers, an individual firm and worker can negotiate a positive
level.
Proposition 1 demonstrates that individual labour contracts in the efficiency wage economy will
not contain agreements on severance pay for individual dismissals in excess of the level which is
mandated by law or collective agreements. This result is due to the following reasons: first,
while employees - and also unemployed workers - benefit from the wage rise, only the interests
of employed workers affect the payoffs which influence the feasibility of an agreement. Second,
the firing cost mark-up solely represents a loss to the firm but not a gain to workers. Third,
higher wages raise total labour costs owing to the existence of the payroll tax. In contrast to
severance payments, redundancy pay for collective dismissals can increase the combined payoff
of employed workers and the firm. This is because the wage reduction exactly balances the employed workers' gain due to higher redundancy payments S and a payroll tax rate in excess of the
firing cost mark-up in conjunction with a fall in wages implies that expected profits rise.
3.2 Collective Incentives
In contrast to a situation in which firms and workers agree individually on dismissal payments,
they can also be the outcome of the political process. This outcome is determined by the changes
in the payoffs which firms, workers, and the government experience. Since the introduction of
9
dismissal pay is analysed, the expected utility of a currently unemployed worker VU consists of
unemployment benefits w and the utility gain if becoming employed again and is given by VU =
(w + aVE,N)/ (r + a). The government's payoff is represented by its payroll tax receipts. While
the political process is not specified in detail, any form of dismissal pay which makes all groups
better off is likely to be agreed upon. Subsequently, it is analysed how the stakes of the involved
parties change if they take into account the variations in the job acquisition rate a. To do so, it is
assumed that the inflow rate into unemployment (b + h) remains unaffected, while the outflow
rate a adjusts in order to accommodate the variation in employment, where aggregate employment N potentially varies with changes in dismissal payments. For x = S, σ and Nx as the
change in aggregate employment one obtains ∂a/∂x = (b + h)Nx/(1 - N)2 (see appendix).
The actors are looked at in turn. Firms are exposed to random shocks, that is, at the beginning of
each period the same ex-ante level of employment is optimal. Thus, it was possible to relate the
probability of firm-specific shocks to the probability that workers will be dismissed. This
implies that the impact of changes in the outflow rate is internalised at the firm level and that
profits are unaffected by general equilibrium repercussions, for a given wage. However, from
equation (7) it can be noted that the efficiency wage rises with the job acquisition rate, ∂we/∂a >
0. Accordingly, expected profits E(Π) will fall less with severance payments (x = σ) and rise less
with redundancy pay (x = S) for ˆ > ξ if general equilibrium repercussions are taken into
account, in comparison to a situation with a given job acquisition rate.
∂we
dE ( Π ) dE ( Π )
=
− (1 + µ ) n
a x (< 0 for x = σ and Nw < 0)
dx
dx da = 0
∂a
(18)
If aggregate labour demand decreases with the wage (Nw < 0), the wage change due to a variation in the job acquisition rate will not reverse the direct effect and severance pay (x = σ) will
unambiguously reduce profits. Because wages decline with redundancy pay (x = S), the impact
of higher payments in the case of collective dismissals on profits is uncertain.
The impact of a change in severance payments σ on the utility stream VU,D of a worker who is
dismissed on an individual basis is given by (cf. equation (6)):
dVU , D dVU , D
∂VU , D
∂VU , D ∂we
=
+
aσ +
aσ
dσ
dσ da = 0
∂a
∂we ∂a
=
 (r + b + h )[w − e − w + (hS + bσ) / r ] a (e / q + σ / r ) 
r+a

+ aσ 
+
2
2
+
+
+
r
(
r
b
a
h
)


r
r (r + b + a + h )

(19)
The direct impact of higher severance pay σ for individual dismissals on VU,D is positive. However, the re-employment probability falls since employment per firm and in aggregate shrinks (a
σ < 0). This effect tends to reduce expected utility VU,D because there is a direct impact of a
lower job acquisition rate a and an indirect effect via the wage reduction. The overall impact is
uncertain, in contrast to a situation in which the worker looks at the impact of severance payments on his/her payoff in isolation.
10
For redundancy payments S the respective change in the utility stream is given by:
 ∂V U, D ∂V U, D ∂w e 
dV U, D dV U, D

=
+ aS
+
 ∂a

e
dS
dS da = 0
∂
a
∂w


 (r + b + h )[w − e − w + (hS + bσ) / r ] a (e / q + σ / r ) 
 > 0 , for ˆ> ξ (20)
= aS 
+
r (r + b + a + h ) 

r (r + b + a + h ) 2

The payoff of a worker who has lost the job due to an individual dismissal rises with redundancy
pay for ˆ> ξ, since higher employment make it more likely that s/he finds a new job. This raises
the expected utility VU,D directly and also via the induced increase in wages.
The changes in the payoff VE,N of an employed worker owing to a rise in dismissal payments x,
x = S, σ, can be derived from equations (2), (5), (14) and (15):
 ∂w e
 ∂V U, D ∂V U, D ∂w e 
ax
dV E, N dV E, N

=
+
+ (b + h )
+

e
dx
dx da = 0 r + b + h  ∂a
a
∂
∂
a


∂w

(21)
Since the efficiency wage increases with the job acquisition rate a and because VU,D also rises
with a and the wage, higher redundancy payments (x = S) will increase the payoff of an employed worker for ˆ > ξ if aggregate labour market effects are taken into account. This is
because VE,N is unaffected by changes in S for a given job acquisition rate and since the rise in
the job acquisition rate (aS > 0) reduces the utility loss from unemployment. As this positive
externality can be internalised by raising redundancy pay in all firms, the incentives to accept
such payments become larger in contrast to a situation with a given job acquisition rate. Higher
severance payments (x = σ) have a positive impact on the payoff of an employed worker for a
given job acquisition rate (cf. equation (16)). If, however, it is taken into account that severance
pay raises unemployment and, thus, reduces the probability of finding a new job, the impact
becomes ambiguous, the second term in equation (21) being negative for x = σ and aσ < 0.
Turning to an unemployed worker, the change in the payoff due to higher dismissal pay is:
dVU
VE , N r − w
a dVE , N
= ax
+
dx
r + a dx
( r + a )2
(22)
Since the participation constraint requires VE,Nr > w , redundancy pay (x = S) will make unemployed workers better off if the payroll tax rate exceeds the firing costs mark-up. The increase in
the job acquisition rate also raises the discounted utility stream of employed workers. Hence,
workers on the whole and irrespective of whether they currently have a job or not will benefit
from the introduction of redundancy payments S. If severance pay (x = σ) is introduced for all
workers, the unemployed workers' utility changes in an ambiguous manner since the direct positive effect if becoming employed conflicts with the reduction in the re-employment probability.
The incentives to introduce severance pay σ at an aggregate level are always greater for employed than for unemployed workers. This is the case because, first, unemployed workers can
11
only benefit from severance pay if they become employed, the probability of such an event being
less than unity. Second, the probability that an unemployed worker finds a new job declines.
Because employed workers will only favour severance pay when equilibrium repercussions are
taken into account if dVE,N/dσ > 0 holds, from equations (21) and (22) one obtains:
dVE , N dVU dVE , N r
( b + h )( VE , N r − w )
−
=
− Nσ
>0
dσ
dσ
dσ r + a
(1 − N ) 2 ( r + a )2
(23)
The incentives for employed and unemployed workers to introduce redundancy payments S cannot be ranked. On the one hand, unemployed workers benefit from redundancy pay with a lower
probability than their employed counterparts since they have to become employed again before
being entitled to such transfers. On the other hand, redundancy pay raises the probability of
finding a new job. While the finding for severance payments - employed workers are more likely
to support them than their unemployed counterparts - concurs with the results by Saint-Paul
(1999, 2000), the potentially different impact for redundancy pay provides a further argument for
distinguishing between different forms of dismissal pay.
The combined payoff Θ of firms, workers and the government consists of profits of τ firms, the
utility stream of N employed and (1 - N) unemployed workers and payroll tax receipts, each suitably discounted with the common rate r.
τ
Nw e
,
E
N
U
Θ ≡ NV
+ (1 − N ) V + E ( Π ) + µ
r
r
(24)
Combining the information from equations (18), (21), (22), and using the steady-state condition
(b + h)N = a(1 - N), the change in Θ due to higher severance payments σ is:

dΘ
dV E, N
dV U τ dE(Π ) Nµ  ∂w e ∂w e

aσ 
=N
+ (1 − N)
+
+
+
dσ
dσ
dσ
r dσ
r  ∂σ
∂a


+ N σ  V E, N − V U + w e µ / r 


dV U
τ dE(Π )
dV E, N
+ (1 − N)
+
+ N σ  V E, N − V U + w e µ / r 
=N


dσ da = 0
dσ da = 0 r dσ da = 0
+
 ∂V U, D ∂V U, D ∂w e 
Nr + a a σ  ∂w e
+ (b + h )
+

e
∂a
∂
r + a r + b + h  ∂a
a


∂w



V E, N r − w
N ∂w e
Nµ  ∂w e ∂w e

aσ +
aσ 
+ (1 − N)a σ
− (1 + µ)
+
r ∂a
r  ∂σ
∂a

(r + a ) 2

(25)
In equation (25), the wage changes due to the alteration of the job acquisition rate, that is all
terms involving ∂we/∂a, sum to zero. This is because a higher wage raises the payoff of all
workers by exactly the amount by which profits fall. Moreover, the change in the firms' payroll
12
tax payments is exactly balanced by the variation in the government's tax receipts. Thus, the
profit and tax revenue impact sum to zero. Using (7), (12) and (16), equation (25) can be simplified:

dΘ
r+a
a
N h + r + b + a + (r + h + a )µ + bξ
w e µ 
=N
+ (1 − N)
−
+ N σ V E , N − V U +

dσ
r
r 

r2
r2 r

+
Nr + a ( b + h ) aσ dVU , D
VE , N r − w
r+h+a
+ (1 − N ) a σ
+ Nµ
r+a r+b+h
da
r
( r + a )2
 Nr + a b + h dV U, D

V E, N r − w  Nbξ
w e µ 
−
= aσ 
+ (1 − N)
+ N σ V E , N − V U +

r 
 r + a r + b + h da

(r + a ) 2  r 2

(26)
The second and the third term in the last line of equation (26) depict the change in the combined
payoff of workers, firms, and government for a given job acquisition rate. The second term is
negative, since the increase in the employeds' payoff and in tax revenues for a given level of employment is more than compensated for by the decrease in profits, given a positive firing-cost
mark-up. The third term captures the direct effect of a fall in employment. Because the expected
utility of an employed worker must exceed the utility of an unemployed for anyone being willing
to work, this effect is also negative. Finally, the reduction in the job acquisition rate (aσ < 0)
reduces the expected payoff of those workers who lose their job owing to a dismissal and of
those who are unemployed. This effect is captured by the term in square brackets. The results
can be summarised in:
Proposition 2:
If the aggregate labour demand schedule is downward sloping, profits will decline with encompassing severance pay for individual dismissals. The combined change in payoffs for firms,
workers, and the government due to an economy-wide introduction of severance payments is
negative. If employees favour the comprehensive introduction of severance pay their gain will be
greater than that of unemployed workers.
Following the same methodology as above, the impact of an increase in redundancy payments S
on the combined payoff Θ of all firms, workers, and the government can be calculated as:
 Nr + a b + h ∂V U, D

dΘ
V E, N r − w  Nbξ
w e µ 
−
= aS 
+ (1 − N)
+ N S V E , N − V U +

dS
r 
 r + a r + b + h ∂a

(r + a ) 2  r 2

(27)
Since the job acquisition rate and employment rise with redundancy pay S, all but the second
term in (27) are positive. Unless the increase in employment lowers profits strongly, because
higher employment implies more dismissals an average and higher firing costs other than dis-
13
missal pay, the combined payoff of firms, workers, and the government rises. This positive
effect will be strengthened if the government's savings on expenditure for unemployment compensation are taken into account. This yields:
Proposition 3:
If employment rises with redundancy pay for collective dismissals, its economy-wide introduction has ambiguous effects on profits, while workers benefit. In the absence of additional firing
costs (ξ = 0), the combined change in payoffs for firms, workers, and government is positive.
4. On the Political Viability of Dismissal Payments
Using a shirking model of efficiency wages it has been shown that the incentives to introduce
payments for collective redundancies differ from those for individual dismissals. Moreover, the
changes in payoffs due to dismissal pay are influenced by their coverage. In particular, if redundancy payments for collective dismissals cover the entire economy, repercussions via the
increase in aggregate employment raise their attractiveness relative to an introduction at the firm
level unambiguously in the absence of a firing-cost mark-up. Severance pay for individual
dismissals reduces the combined payoff of firms, workers, and the government and will not be
agreed upon at the firm level. Table 1 sums up the results.
Table 1: Changes in Payoffs - Summary of Comparative Static Effects for ˆ> ξ
Severance Pay σ
Firm-level
Increase
F
E
U
G
+
+
?
Combined Payoff Change
-
Economy-wide
Increase
xxxxxx xxxxxx
-a)
?
?
?
Combined Payoff Change
-
Redundancy Pay S
F
E
U
G
+
0
0
?
Combined Payoff Change
+
xxxxx xxxxx
x
x
?
+
+
?
Combined Payoff Change
+b)
F - Firm; E - Employed, U - Unemployed, G - Government. Combined payoff at firm level incorporates profits and employed workers' utility, while economy-wide effects include unemployed
workers' utility and variations in tax receipts, in addition.
a) Unambiguously negative impact requires downward sloping aggregate labour demand schedule.
b) Unambiguously positive effect requires sufficiently low firing cost mark-up.
The theoretical predictions are broadly supported by OECD evidence (cf. OECD 1999). With the
exception of countries from southern Europe and Oceania, severance payments are generally
close to zero unless workers have been employed in the same company for 20 years. Entitlements to redundancy payments seem to be more widespread. The analysis of this paper can be
interpreted as a rationalisation of these features. However, severance payments for individual
dismissals can be observed in many countries for workers with high tenure. In addition, allowing
14
for positive employment effects of severance pay in the absence of wage adjustments, by
endogenising the extent of employment adjustments in the case of shocks, can enhance the
incentives for their introduction. Moreover, there are a number of countries in which redundancy
payments for collective dismissals do not seem to be higher than for individual dismissals.
Dismissal pay may, therefore, not only be used to mitigate the consequences of exogenous
shocks but, for example, as - conditional - pension. In addition, legal considerations might
restrict the divergence between severance and redundancy payments.
15
Appendix:
Aggregate employment effects are determined using the steady-state condition h + b = (1 - N)a/N.
Differentiation yields the expression in the main text. Substituting in (7) one obtains:
Z ≡ we −
e
b+h
S σ
bN + h 
=0
r +
 − e − w + h − r +
q  1− N 
r r
1− N 
(I)
Aggregating labour demand over all τ firms one obtains from (9):
σ
 S
Y = f ' ( N) − w e (1 + µ) −  h + b (1 + ξ) = 0
r
 r
(II)
The derivatives of Z and Y are given by Zw = 1, YN = f$ '' e < 0, Yw = - 1 - ˆ< 0, ZS = h/r > 0,
YS = - (1 + ξ)h/r < 0, Yσ = - (1 + ξ)b/r < 0,
ZN = −
e σ
 +  < 0 and
(1 − N) 2  q r 
b+h
ZS = −1 −
bN + h
<0
r (1 − N )
(III)
The changes in aggregate employment N due to higher dismissal pay are:
dN
h(ξ − µ ) / r
=
> 0 for ˆ> ξ
dS YN Zw − ZNYw
dN b (1 + ξ ) / r + (1 + µ ) 1 + ( h + bN ) / ( r (1 − N ))
=
<0
dσ
YN Zw − ZNYw
(IV)
(V)
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