expression for the optimal level of period-three profits, conditional on

period-three demand and period=two employment, as follows:

(a/2)D2 *c?/2a -c(BL, “Ds “c/a) if Ds < BLz ~c/a

*
8) 13 = (a/2)D3 = (a/2)(BL2 + D3)? if BL,~c/a< D, < BL2

(x/2)D3 if D,; > 8L,

In this expression, the first term, (a/2)D?, is what profits
would be in the absence of severance costs. The second terms, (c?/a) and
(a/2)(BL2°D;)? for the low=demand and highedemand cases respectively, are
the costs to the firm of the overemployment induced by the severance
costs. This cost is borne by the firm in both the low= and medium demand
cases, The final term, c($L,°D,;7c/a), is the cost of actual
severance payments by the firm. These arise only in the low-demand case,
when optimal employment is D,+c/a; to reach this level of employment
requires that (8L,°D,;*c/a) workers be fired.

In period two, the firm will set employment to maximize the
discounted sum of period-two profits and expected period=three profits
where, because the firm knows that it will behave optimally in period
three, the period=three profit function is given by (8). Denoting F,(D3)
as the cumulative probability function for D, conditional on D, and D.,

expected period-three profits are:

BL27Cc/a
2

E.(ms3L2) = (a/2)E(Ds) = ¢ S {(Ly “Ds -c/a)dF3(D3) ~
BLa*c/a BLa
- 2 - -) 2
« (e?/a) _f dF3(D3) (0/2), J (hha D,)?dF,(D;)

9)


39

The intuitive reason for this inverse relation between trend
demend growth and employment is obvious. If a firm expects to want a
much higher labor force in future periods, then the probability that
demand will be low enough to make the firm want to fire workers from a
labor force of a given size declines, reducing the expected costliness of
the severance payments policy.

In Table Five I investigate the impact of changes in the
variability of labor demand. As one would expect, an increase in the
var:.ability of labor demand increases the expected cost of severance
payments, because ~ for a given trend growth in demand - an increase in
the variance of labor demand raises the probability that demand will fall
below the level of employment left over from the previous period. An
increase in labor demand variability also makes the cost more sensitive
to e. The reason for this is that the more variable is demand, the more
likely it is that demand will be low enough to make the firm start
actually firing workers, This means that more of the expected cost is
due to expected severance payments, rather than expected overemployment
costs, and the value of expected severance payments are more closely
related to c than is the expected overemployment cost.

In Table Six I examine the impact of different assumptions
about the firm's labor force attrition rate. Again, the results are
perfectly intuitive; an increase in the rate of attrition (decrease in B)
decreases the expected cost of the severance payments significantly.
This makes sense because the faster the natural reduction in the firm's
workforce, the less firing it is going to have to do to get down to a

given next-period level of employment.


35

TABLE TWO
PERCENT EMPLOYMENT DECREASE (ED) AND QUIT RATES (Q)
IN SELECTED INDUSTRIES

Italy (1981)* Sweden (1984) ** United States (1980)
Industry ED Q Industry ED Q Industry ED Q
Pulp~based 19.6 5.6 Shipyards 11.8 11.8 Wood 6.9 27.6
textiles Printing 9.1 20.6 Primary 6.8 7.2

Mining 10.6 5.2 Instruments 3.4 17.4 metals
Wood 10.1 10.7 Stone, clay 6.0 15.6
Textile 8.0 7.3 Metal 5.8 16.8
Primary 7.2 5.7 products
metals Rubber 5.5 22.8
Wood 7.0 9.7 Transport. 5.3 9.6
products equipment.
Apparel 6.9 6.8 Furniture 4.6 25.2
Chemicals 6.4 4.7 Textile 3.6 26.4
Mechanics 6.0 6.7
Shoes 5.7 9.5
Rubber 5.2 4.5
Transport 5.1 6.2
equipment.

* Manual workers in establishments with fifty or more employees
** Manual workers
Source: OECD (1985) p. 13

In the United States and Sweden, quits are generally
substantially higher than declines in employment, which implies that
firms are generally able to bring their employment into line with the
desired level without recourse to firing. In Italy, on the other hand,
there are many cases in which the quit rate is below or approximately
equal to the employment decline. For these industries, employment could
not be reduced more quickly without resorting to firing.

An intriguing aspect of the Italian data is the number of cases
in which the employment decline is approximately equal to the quit rate.

This is consistent with the theoretical model offered above, in which


43

period. A second conclusion is that for plausible parameter values, the
incidence of firing decreases as the firing cost, C, increases. Thus,
empirical work which uses a measure related to the ineidence of firing
(for example, Nickell (1982)) as a proxy for the costliness of severance
restrictions may run into problems, Third, and within the context of the
analytical framework advanced in this paper, it appears that the
costliness of severance payments is much more sensitive to estimates of
the workforce retention rate (8) and the variability of labor demand (0)
than the other structural parameters identified above. Thus, a sensible
empirical strategy would probably focus on obtaining information abcut
these parameters.

One should be reluctant to draw firm policy conclusions until a
more thorough empirical investigation is completed, but if the
conclusions discussed above are supported by such an investigation, then
there would be some policy conclusions to be drawn, First, while the
impact of severance costs on employment is non-negligible, it is unlikely
to account for more than a fairly minor fraction of the unemployment
currently being experienced in the European economies. Further, it may
well be that at current levels of demand abolition of severance costs
would reduce employment, so that the long-run benefits of the policy
would be accompanied by a short-run reduction in employment. (This was
the conclusion of the study by INSEE (1985), although that study. did not
attempt to estimate the impact of severance restrictions on n firms’
desired labor demand. ) An additional implication of the above estimates
is that marginal reductions of the firing cost, c, froma level above two

or three months' wages would have a negligible impact on the expected


12

the period-n labor force, which is (with no hiring and firing between
period one and period n) p"L,. For plausible workforce departure rates,
the probability that this combination of events will occur becomes very
low even for fairly short planning horizons.

I will therefore focus on the solution to the three-period
case. Once this case is understood, the extension to a longer planning
horizon is conceptually trivial (although computationally cumbersome,
because it requires numerical integration in progressively higher
dimensional spaces). The numerical simulations discussed below indicate
that increasing the planning horizon beyond three periods would have
essentially no impact on the results .4/

In the three=period case, the firm's problem can be written:

5) max V(1) = 4, + E,(m2)/(148) +# E,(m3)/ (146)?

Ly

S.t. TM, = ¥(L,;D,) * wh, > c max(0, BL, ~ L,)
TM2 = Y(L25D2) ~ wh, > c max(0, BL, ~ L2)
T; = Y(L3;D,3) ~ wh, - c max(0, BL, > L;)

where D, is known but subsequent realizations of the demand shift
variable are stochastic with cumulative probability function F(D,,D,).
The expectation is conditional on all information available in period
one, so when the demand shift is autocorrelated this probability
function depends upon D,.

When determining period-one employment, the firm must of

course consider the period=two and periodsthree employment decisions


53

Footnotes

* Division of International Finance, Federal Reserve Board. This paper
represents the views of the author, and should not be interpreted as
reflecting the views of the Board of Governors, or of any other members
of its staff.

1/ For influential examples of this approach, see Sachs(1979, 1983) and
Artus (1984),

2/ See, in particular, Blanchard et. al. (1985), OECD (1983), Krugman
(1982), and Nickell (1979). oo

EM This possibility is raised in OECD (1985) p.195, which views the

Chrysler and Uniroyal union contracts as’ evidence that collective
bargaining contracts trade off wages for job security.

4/ This is true for simulations in which firm's quit rate, b, is not
much larger than o, the standard deviation of fluctuations in the MPL
curve. If the rate of workforce attrition is much lower than this
measure of the variability of labor demand, then it is possible that
extending the planning horizon would have a larger effect.

5/ This assumes no "vintage" effects, that is, that the probability of
workers' leaving the firm is independent of how long they have been
employed with the firm, This assumption is clearly imprecise,
especially for retirements. However, a more realistic and complicated
assumption would have a very minor impact on the results.


51

TABLE NINE
PERIOD ONE LABOR DEMAND SHOCK
Low Base High
Demand Case Denand
Dy= 95 Dy= 100 Dy= 105
C= 20
L, = 95.0 0. 84 0.28 0.07
97.5 2.06 0.83 0.27
100.0 4,22 2.07 0.83
102.5 7.29 4,27 2.10
105.0 10.75 TM 4,36
c = 40
L, = 95.0 0. 93 0.30 0.08
97.5 2.40 0.93 0. 30
100.0 5.27 2.43 0.94
102.5 9.94 5.1 2.31
105.0 16.20 10.29 5.54
Cc = 60
Ly = 95.0 0.93 0.30 0.08
97.5 2.42 0.93 0.30
100.0 5.40 2.43 0.95
102.5 10.46 5.4 2.54
105.0 17.84 10.29 5.82
Cc = 80
L, = 95.0 0. 93 0.30 0.08
97.5 2.42 0.93 0.30
100.0 5.41 2.46 0.95
102.5 10.51 5.57 2.54
105.0 18.07 10.90 5.84
C = 100
L, = 95.0 0.93 0.30 0.08
97.5 2.42 0.93 0. 30
100.0 5.41 2.46 0.95
102.5 10.51 5.58 2.54
105.0 18.09 10.95 5. 84


57

International Finance Discussion Papers

IFDP
NUMBER TITLES
1985
(partial listing)
272 Expected Fiscal Policy and the Recession
of 1982
271 Elections and Macroeconomic Policy Cycles
N
270 Assertion Without Empirical Basis: An
Econometric Appraisal of Monetary Trends
in ... the United Kingdom by Milton Friedman
and Anna J. Schwartz
269 Canadian Financial Markets: The Government's
Proposal for Reform
268 Was It Real? The Exchange Rate Interest
Differential Relation, 1973-1984
267 The U.K. Sector of the Federal Reserve's
Multicountry Model: The Effects of
Monetary and Fiscal Policies
266 Optimal Currency Basket in a World of
Generalized Floating: An Application to
the Nordic Countries
265 Money Demand in Open Economies: A Currency
Substitution Model for Venezuela
264 Comparing Costs of Note Issuance Facilities
and Eurocredits
263 Some Implications of the President's Tax
Proposals for U.S. Banks with Claims on
Developing Countries
262 Monetary Stabilization Policy in an Open
Economy
261 Anticipatory Capital Flows and the Behaviour
of the Dollar
260 Simulating Exchange Rate Shocks in the MPS
and MCM Models: An Evaluation
259 Trade Policy for the Multiple Product

Declining Industry

AUTHOR(S)

William H. Branson
Arminio Fraga
Robert A. Johnson

Kenneth Rogoff
Anne Sibert

David F. Hendry
Neil R. Ericsson

Garry J. Schinasi
Richard Meese
Kenneth Rogoff

Hali J. Edison

Hali J. Edison
Erling Varcal

Jaime Marquez

Rodney H. Mills

Allen B. Frankel

Marcus H. Miller

Arnold Kling

Arnold Kling

Catherine Mann


L,

Ly

L,

C= 20

GSSRVs

onouno

C= 80

= 95.0

97.5
100.0
102.5
105.0

C = 100

= 95.0

97.5
100.0
102.5
105.0

49

TABLE SEVEN
LABOR DEMAND ELASTICITY
Low Base High
Elasticity Case Elasticity
a= 10.0 a= 4.0 a= 2.0
0.47 0.28 0.15
1.29 0. 83 0.46
2.95 2.07 1.22
5.59 4.27 2.71
8.93 7M 5.15
0.65 0.30 0.15
1.92 0.93 0.47
4,65. 2.43 1.23
9.37 5.4 2.79
15.84 10.29 5.48
0.72 0.30 0.15
2.18 0.93 0.47
5.52 2.43 1.23
11.67 5.4 2.79
20.73 10.29 5.48
0.74 0.30 0.15
2.28 0.93 0.47
5.92 2.46 1.23
12.92 5.57 2.79
23.89 10.90 5.48
0.75 0.30 0.15
2.32 0.93 0.47
6.08 2.46 1.23
13.54 5.58 2.79
25.74 10.95 5.48


The total cost to the firm of overemployment is the triangle
ABC. An increase in BL, thus increases the total cost of overemployment
by the distance AB = a(BL,°D;), which means that in the case of
intermediate demand under discussion, an increase in L, raises the
expected cost of overemployment by Ba(BL2°D;).

The expected value of this marginal cost is therefore the
probability that the cost will be incurred (that is, that D, will »e
between BL, and BL,7¢c/a) which is [F,(BL2)“F,(BL27c/a)], times the
expected value of the marginal cost given that it does occur, which is
ELa(BL2-D;) | (BL,7c/a) < Ds < BL; J.

Having calculated the impact of an increase in period=two
employment on period-three profits, we can now characterize the firm's
period=two employment decision, The firm's objective in period two is
to maximize the discounted sum of expected period=two and period=taree

profits. The first order condition is:

dt. dE(13)
1) 0# + = 7448)
dbz dL,

where the expectation on the right hand side of (11) is given by

(10), and the marginal profitability of labor in period two is:

dn, a(D,*L,) +¢ if L, < BL,

12) a.”

a(D,*L2) if L, > BL,

Because the marginal impact on period-three profits of

an increase in period-two employment is necessarily negative,


4o

In Table Seven the impact of alternative assumptions about the
slope of the labor demand curve is examined. The steeper the slope, the
higher is the expected marginal cost due to the severance payments. The
reason for this is fairly straightforward. If the labor demand curve is
shallow, this means that the firm can be far away from the optimal. level
of employment with fairly minimal implications for profits. Thus, if it
has extra workers in a given period, it need not accept the cost of
firing them; it can hang onto them with only a small profit loss util
demand recovers and the size of the workforce dwindles. On the ot:her
hand, if the labor demand curve is very steep, being away from the
optimal level of employment has a large impact on profits. The firm must
either maintain its excessive workforce at a large cost in terms of
profits, or fire the excess and pay the severance cost. It is also worth
noting that, when the demand curve is steep, the cost of severance
payments is much more closely related to c. That is because, again, the
firm will more often be forced to fire workers when demand is low, making
the overall burden much more sensitive to the size of the payment.

It is important to note that the increase in the marginal cost
of labor due to an increase in a does not imply that the adverse :.mpact
on employment is greater; as the marginal cost increases, the sensitivity
of employment to the marginal cost decreases. In fact, for the cases
considered in Table Seven, the two effects are approximately offsetting.
In all three cases, the impact on employment, at c=40, is about one half
percent.

In Table Eight, I consider the impact of increasing p, t:he

autocorrelation of the demand shocks. The higher the autocorrelazion,


United Kingdom proposed that the adverse effects of employment
protection legislation be reduced by raising the qualifying period for
protection against unfair dismissal from six months to two years of
tenure with a firm,

However, even if there were consensus on the direction of the
impact of severance costs on employment, there is little evidence on its
magnitude. Especially if employment protection legislation serves a
useful social purpose, against which potentially negative effects on
employment must be weighed, the probable size of these employment
effects is important. The purpose of this paper is to provide a
framework for assessing the impact on labor demand of social policies
that. make firing workers costly. In Section II the existing literature
on the impact of severance costs on employment demand is surveyed. In
Section III a simple model of the firm's employment decision, in the
presence of significant severance costs, is presented and solved. In
Section IV the model developed in Section III is used to make judgements
about the likely empirical importance of severance costs for the

unemployment problem in Europe. Section V concludes.

II. Survey of the Literature

The empirical literature on the impact of labor market
rigidities in general, and severance costs in particular, is
surprisingly scarce, given the attention paid to the issue in policy

recommendations.


33

this parameter makes a difference, the conclusions are not highly
sensitive to p.

In the base case, the slope of the labor demand (marginal
product of labor) curve, a, is assumed to be 4, corresponding to a low
but nonnegligible estimate of the short-run wage elasticity of labor
demand of .25 (at the expected level of D,).

The rate of workforce retention, 8, is a crucial parameter, and
one on which comparatively little evidence exists. For the base case I
assume that 4 percent of the workforce voluntarily leaves in a given
year, so that 8=0.96. This is speculative, and can be justified as a
conservative estimate as follows. Assume that the working life is 40
years, and that over the past 4O years the workforce has been growing at
about; one percent per year. On these assumptions, the cohort that is
retiring accounts for about 2 percent of the workforce. The other reason
for voluntary workforce attrition is voluntary departures to change jobs.
If the probability of each worker changing jobs in a given year is two
percent, then roughly 20 percent workers would change jobs (voluntarily)
more than once in their career, 35 percent would change once, and 45
percent would stay with a single employer (unless fired at some point in
their career.) This is almost certainly an overstatement of workers!
attachment to their employer, and therefore an overstatement of the
impact of severance costs on the expected cost of a worker.

A recent study by the OECD (1985) sheds some light on this
important parameter. As Table One indicates, aggregate quit rates in
manufacturing seem to be falling, but are substantially higher than the 4

percent assumed in the base case:


The first term is what expected profits would be if there were
no severance costs. The second term is the expected cost of actual
severance payments in period three, which are only paid if D; is less
than (8L,~c/a). This cost of severance payments is zero if ¢ is zero,
but it also approaches zero (at least for the normal probability
function) as ¢ becomes very large. The reason for this is that as c
approaches infinity, there are no situations in which the firm would find
it optimal to fire a worker. Instead, it will always be forced to accept
the cost of excessive employment. The last two terms are the expected
cost of the excess employment induced by the severance costs.

Equation (9) gives the impact of the severance payments on
gross periodthree profitability. However, for the purpose of
determining labor demand, what matters is not the impact of severance
costs on total profits, but rather the impact of the severance costs on
the profitability of labor at the margin. This is, of course, strictly
true only if the firm in question remains in business. If firms produce
subject to a minimum expected profit condition, then the severance costs
may result in bankruptcies, with obvious implications for labor demand.
For tne remainder of this paper, I abstract from the bankruptcy issue and
focus on the labor demand response of firms that are not driven out of
business by the severance payments. The reader should bear in mind,
however, that the bankruptcy problem may be quantitatively significant.

The firm, in period two, thus cares about the impact on
period-two and -three profits of hiring an additional worker. The impact

on period=two profits is the marginal product of labor less the wage.


25

L2(D2) if D, < Bz-c/a
* - ~
14) La (DesLy) = 4 BL, if Da-c/a < D, < D2 BL,
L (D2) if D, > B,

where L,(D,) sets the marginal product of labor equal to (w=c+>),

L,(D,) sets the marginal product of labor equal to (w+o), and BD, solves:

15) B(ty) = Bfl, + cF ,(82L,-c/a) + ofP,(pLyro/a)-Fa( pth DIB ty -B( Dd Dsea)] }
where 2 = (D,,D, 8.t. Da=Dz, and (8?L,-c/a) < D, < B7L,), and F,(D,) is
the cumulative distribution function for D, conditional on D, being
equal to B,. 5, is the critical level of period-two demand at which the
firm finds it profitable to start hiring workers. It serves the same
purpose as $L2 in equation (7) and Figure One.

As expected, the presence of severance costs tend to increase
employment when demand is weak, and decrease employment when demand is
relatively strong. Thus, although the impact on employment depends upon
the state of the economy, it will certainly be true that employment will
be less variable in the presence of severance costs.

Period-One Emp loyment: Having determined employment policies
L,(D2,L,) and L3(D,,L2(D2,L,)), we can consider the firm's period-one
problem. The employment policies summarized in equations (7) and (14)
ean te used to determine period-two and period-three optimal profits as
a function of L,, D, and D,. The firm now takes the expectation of the

present value of expected profits in periods one through three, and


21

then employment is (D3;-c/a), and if D,; is above 8L,, then employment is
D,. In either case it is unaffected by L,. On the other hand, if D, is
between BL, and (8L,7c/a), then period=three employment is ®L,, so that
a unit increase in period=two employment raises optimal period~three
employment by 8.

If D,; is in the intermediate region, then the marginal
reduction in period=three profits due to a marginal increase in
period=three employment is, as illustrated in Figure Two, equal to

a(BL,.°D;).

Figure Two

. J_Bl2“Ds__
NXg [B w

Marginal loss due to excess employment

| = a(BL2-D;)

(wee)

Ds BLS D3+¢e/a,


34

TABLE ONE
QUITS PER 100 EMPLOYEES IN MANUFACTURING

Year: Austria Italy* Japan Sweden United States
1971 17 25 31
1972 16 22 38
1973 17 23 46
1974 14 26 yy
1975 12 23 25
1976 12 21 30
1977 30 12 18 32
1978 27 9 1 15 36
1979 28 10 12 21 35
1980 30 11 12 22 28
1981 28 1 1 17 24
1982 27 1 15
1983 10

* Manual workers only
Source: OECD (1985) p. 9

Even in countries with the lowest quit rates, they are almost
never below 10 percent.

What matters in this analysis is not the quit rate per se, but
the quit rate relative to the variability of demand. This is what
determines the likelihood that the company will experience a bad enough
demand realization that the severance costs will "bite," either through a
unprofitably large level of employment or actual, costly firings. Table
Two, from the same OECD study, compares employment declines, in percent,
and quit rates in several industries. The industries selected were those

with the most rapid employment declines.


16

employment would be profitable. The converse is true when employment is
above (D,+¢c/a).

In Figure 1c, period-three demand is high enough so that the
marginal product of labor curve passes through BL, above w. In this
case, the marginal product of labor equals the marginal cost at an
employment level greater than 6L,, so that the marginal cost is w, and
labor demand equals D,. Thus, when demand is this high, the firm
behaves as though there were no severance costs.

In Figure 1b, period=three demand is intermediate so that. the
MPL curve passes through BL, between (w-c) and w. In this case, the
marginal cost of labor depends upon whether the firm is contemplating an
increase or a decrease in employment. If the latter, then the change in
employment is associated with an increase in firing, so that a
reduction in employment from BLo would save the firm (w-c) in labor
costs, but cost the firm a reduction in output equal to the marginal
product of labor, which is, in this case of intermediate demand, greater
than (wec), Thus, it would not pay to reduce employment from BL,. On
the other hand, an increase in employment from BL, requires hiring new
workers, and does not lead to a reduction in the level of firings.

Thus, the marginal cost of increasing employment is w, which, in this
intermediate demand case, is greater than the marginal product of labor.
Consequently, in the intermediate demand case, the firm's optimal
employment is BL..

The above discussion can be summarized in the following

period-three labor demand schedule:


Throughout the analysis, it will be assumed that the real wage
is exogenously given at a level too high to sustain full employmen:.
Thus, labor is supplied with perfect elasticity at the prevailing,
excessive, real wage, and employment is determined by labor demand. The
focus of this analysis is not the "natural" or "full-employment" rate of
unemployment, which is presumably determined by job search
considerations that lie beyond the scope of this paper. I confine
myself to the specific question: in the presence of unemployment due to
a failure of markets to clear in the short to medium term, what will be
the effect on employment of social policies that make it costly to fire
wor kers?

The analysis is partial equilibrium; while I model the firm's
determination of output and employment given demand for the firm's
output, I do not consider the impact of the firm's employment decision
on the level of aggregate demand. Nor do I model the firm's inventory
or fixed investment decision, an omission that is potentially
significant. To the extent that high labor costs cause firms to
substitute capital for labor, the analysis will understate the reduction
in labor demand caused by severance restrictions. The restricted
analysis can be justified as a reasonable preliminary to a more complete
analysis, providing an indication of the incentive caused by severance
restrictions to substitute capital for labor.

Finally, this paper does not consider the implications of
severance payments for labor supply or wage=setting behavior,
considerations of obvious importance, The impact of firing costs for

labor supply are unclear, In particular, it would seem to depend upon


31

3) The joint distribution of D,, D2, and D;. I assume that
they are jointly normally distributed, with a standard
deviation of o, and an autocorrelation parameter of p. The
(unconditional) expected level of the labor demand shift
parameter is labelled Tt (as noted above, this is-normalized at
100 for period one), Tt is assumed to grow at a constant rate
&, so that the expected level of period-two and period~three
demand conditional on the (known) level of period-one demand

ean. be written:

25) E, (D2) = (1+g)T, + p(D,-T,)

26) E, (Ds) = (1+g)?T, + p?(D,°T,)

4) The short-run wage elasticity of labor demand, which (given

the normalizations discussed above) 1/a.

5) The rate at which workers leave the firm voluntarily, which
is 1°86. This, along with o, is one of the most important

parameters.

6) The firm's discount rate, 5. Estimates of the cost of the
severance restrictions are not sensitive to this parameter, so

I specify 6 = .1 for all of the calculations that follow.


28

An additional difference between the two=period and the
three-period analysis is that the firm must, in period one, consider the
impact of its employment decision not only on next period's expected
profits, but also on expected profits two periods into the future. ‘he
derivative of expected period=three profits with respect to period-one

employment is:

4e(n,) BL, BD, B*L,*c/a Dy
a: -s7{aS _ f (BL, *D,)f(D,,D,)dD,aD, 40 S _ Sf f(D2,D,)dD, dD, }
2 8?L,*c/a D.-c/a fated Dare/a

Or, more intuitively:

21) So = -87{a ProblD,,Dsé Gsqa)lB2L,7E(Ds | D2,Ds€ M5q)] +

+e Prob[D,,Ds€ Msp]}

where:
Qsq = {[D2,Ds | (Ba-c/a) < Dy < By and (BLy*C/a) < Dy < B7Ly}

Qsp = {D2,D3 | (Ba-c/a) < Dz < B, and Dy < B7L,%0/a }

that is, 234 is the region of realizations for D, and D, such that there
are no hirings or firings in either period two or period three. ,b is
the region in which there are no hirings or firings in period two, and
there is firing in period three.

The intuitive explanation of this expression is fairly

straightforward, The first term of (21) is the impact of an increase in


evidence that employment fluctuated less, and hours more, in response to
demand fluctuations after the introduction of the Act.

With respect to the level of employment demand, rather than
its cyclicality, the evidence is somewhat weaker. Nickell (1979)
formalizes a model in which flows into unemployment are directly reduced
by employment protection legislation, with an offsetting reduction in
flows from unemployment into employment. The latter effect occurs
because firing costs give firms an increased incentive to screen workers
more effectively, because it is expensive to get rid of bad workers.

The econometric results in that paper provided weak evidence that
employment protection legislation reduced equilibrium employment, and
increased the equilibrium unemployment rate. However, the proxy for
increases in employment legislation was a time trend, which undermines
confidence in the link between his regressions and severance costs.

In his 1982 paper, Nickell used as a proxy for severance costs
the number of unfair dismissal cases brought before industrial
tribunals, an important, though not the only, cost of firing workers in
Britain. This paper found that the increase in unfair dismissal cases
from 1966 to 1976 actually lowered the equilibrium unemployment rate by
almost a full percentage point, though in a later paper (Nickell (1985))
he argues that this result is very tentative.

The theoretical framework that follows provides further reason
for viewing these aggregate time~series regressions skeptically. First,
it is shown that the impact of firing costs on employment demand depends
upon the state of demand; in high demand conditions employment should be

lower than it would be in the absence of severance costs, but in low


Two kinds of evidence may be identified: surveys of employer
attitudes, and more formal, econometric tests. Neither provides
unambiguous answers, There have been several surveys of employer
attitudes in the United Kingdom. Early surveys, such as Daniel and
Stilgoe (1978) and Clifton and Tatton=Brown (1979) tended to downplay
the importance of employment protection legislation to employers.
However, there was an exception in the Wilson Committee survey on
investment attitudes, in which employers expressed strong opposition to
such legislation, citing the consequent difficulties in adjusting the
size of the workforce to changes in economic conditions. A more recent
report by the Confederation of British Industries, however, found that
"removing or relaxing redundancy entitlement or individual employment
rights would not generally lead to higher employment, but lifting the
burden placed on smaller firms might help. (C.B.I (1984) p.3, quoted in
Nickell (1985))

Formal econometric studies are scarce. Several authors have
noted that firing costs would provide an incentive to shift labor
fluctuations from employment changes toward changes in hours. Ina
erossscountry study, Kaufman (1979) found that in European countries,
output fluctuations tended to generate larger changes in hours, and
smaller changes in employment, than they do in the United States, and
interpreted this as evidence that severance costs were important.
Nickell (1979) estimated hours and employment equations for two periods:
1955 to 1966, and 1967 to 1976, which correspond to the periods before

and after the Redundancy Payments Act was introduced. He found weak


17

Ds + c/a if Dy < BL, + c/a
*
7) bs = BL, if BL,-c/a < D, < BL,
D; if D, > BL,

To summarize, the impact of the severance costs in period
three depends upon in which of three regions is the period-three demand
shock. If demand is high enough, then there is no effect on the firm's
employment or profits. If demand is intermediate, there is no firing,
but because the firm is induced to employ an uneconomically large
workforce, the firm's profits are reduced, If the demand shock is bad
enough, so that the excess of the wage over the marginal product of
labor exceeds the firing cost, c, then the firm does fire workers, and
its profits are reduced both because of actual severance payments, and
because of an excessively large labor force.

A notable feature of this labor demand schedule is that the
optimal level of employment is always greater than or equal to what it
would be in the absence of severance costs. This is because of the
unrealistic assumption that the firm's planning horizon does not extend
beyond the current period. We shall see that the impact of severance
costs on employment is less positive when the firm does have to plan
ahead.

Period-Two Employment: Having determined its period-three
employment policy as a function of period=two employment and the
period-three demand shock, and the consequences for period-three
profitability, the firm can turn to the period-two employment decision.

Using equation (7) to substitute for L,, it is possible to derive an


periods of low demand, when the firm would otherwise want to lay off
employees, imposing a cost of firing will result in fewer layoffs. The
Severance costs will, then, fulfill the objective of raising employment
in states of low demand. However, the very effectiveness of the
severance payments policy, by leading the firm to employ an excessive
number of workers and by imposing actual severance payments, will reduce
prof:ts. The firm will, when deciding whether to hire a worker ,
consider not only the current wage that must be paid, but also the
reduction in future profits associated with the Prospect that the
severance costs will "bite" in the future. Thus, severance costs impose
on the firm an additional expected marginal cost of employment, which
will tend to decrease employment demand when the firm would otherwise be
hiring.

The purpose of the following model is to capture this element
of labor costs, to characterize the nature of the firm's employment
decision when the costs are significant, and to make an assessment of
the likely magnitude of the costs. The magnitude will, of course,
depend on a variety of structural factors including the variability and
trend growth rate of labor demand, the shorterun wage elasticity of
labor demand, the size of the severance Payment, the rate of attrition
of the firm's labor force due to retirements and other forms of
voluntary worker departure, and the persistence of demand shocks. While
these parameters cannot be known with certainty, plausible bounds on the
likely magnitude of the significance of severance payments can be

determined.


23

the firm will be induced to reduce period=two employment in
order to offset the adverse implications for expected
period=three profits of high period-two employment, at the
expense of period=two profits.

For notational convenience, define $(L,) as the
discounted reduction in expected period-three profits from a

marginal increase in period=two employment:

13) (La) = ~ BGM) 7 (145)
dL,

Ther. the derivation of the optimal period-two labor demand from the
first-order condition (11) can be illustrated by Figure Three, which is
analogous to Figure One, above. As in Figure One, the first order
conditions are met at the intersection of the marginal product of labor
curve and the marginal cost of labor curve. However, in this case the
firm's marginal cost of labor curve includes a term reflecting the
adverse impact on future profitability of an increase in the current
period's level of employment. As in the period=three analysis,
employment is higher in low-demand realizations than it would be in the
absence of severance costs, where "low" means relative to ®L,. However,
in contrast to the period=three analysis, employment is reduced in high-=
demand conditions compared with what it would be without severance
restrictions.

Formally, the firm's period=two employment policy can be

sumiarized as follows:


Labor Market Rigidities and Unemployment:
The Case of Severance Costs

Michael K. Gavin
Division of International Finance
Federal Reserve Board
Washington, D.C. 20551

Revised: June, 1986

This paper represents the views of the author, and does not necessarily
correspond with the views of the Board of Governors, or any other
members of its staff.


L,

Li

li

L,

C= 20

= 95.0
97.5
100.0
102.5
105.0 .

= 95.0
97.5
100.0
102.5
105.0

45

TABLE THREE

BASE CASE
Expected Expected Expected
Firing Overemployment Total
Cost Cost Cost
0.06 0.22 0.28
0.23 0.60 0.83
0.76 1.30 2.07
2.02 2.25 4.27
4.35 3.05 Te
0.00 0.29 0.39
0.02 0.90 0.93
0.12 2.31 2.43
0.49 4,92 5.41
1.64 8.66 10.29
9.00 0.30 0.39
0.00 0.93 0.93
0.01 2.46 2.45
0.04 5.53 5.57
0.19 10.71 10.99
0.00 0.30 0.30
0.00 0.93 0.93
0.01 2.46 2.46
0.04 5.53 5.57
0.19 10.71 10.99
0.00 0.30 0. 36
0.00 0.93 0.93
0.00 2.46 2.°6
8:8? 18:88 18:58


10

Ly is the amount of labor utilized by the firm.

Thus Dy is, by normalization, the labor input that equates the
real wage with the marginal product of labor. This is no more than a
convenient normalization. There is, in particular, no implication that
the marginal product of labor schedule is causally related to the real
wage. Equation (1) can be viewed as a reduced form consistent with a
variey of structural interpretations. For example, Dy may be thought of
as deriving from shifts in the demand for the firm's output.
Alternatively, and in a more classical vein, D_ may represent
fluctuations in the technical conditions of production. All that
matters for my purposes is that there is an amount of labor, Dy, that
would be optimal in period t if the wage were the only labor cost to the
firm, that this optimal level of employment fluctuates stochastically
over time, and that deviations of actual employment from the ortimal
level reduce the firm's profits at an increasing rate.

However, the point of this excercise is to explore firm
behavior when the wage is not the only labor cost faced by the firm.
When firms fire workers they must pay substantial severance and,
sometimes, legal costs. It will be assumed that the firm must pay a
a fixed amount, c, for each worker fired. Assuming that the firm's
workforce "decays" at a constant rate b, as a result of retirement or
other forms of voluntary departure, the number of firings can te

written:

2) firings = max(0, (1-b)Lt-1 > Le)


which of several competing labor~supply paradigms is correct. The labor
contracting literature, exemplified by Azariadas and Stiglitz (1983),
views firms as bargaining with atomistic workers. This paradigm
stresses the risk-sharing aspects of labor contracts, and it is likely,
though it has not been demonstrated, that the increase in employment
security generated by the firing costs would be at least partially
offset by a reduction in the real wage that must be paid to workers. 3/

On the other hand, recent work by Lindbeck and Snower (1984)
shows, in the context of a laborsunion bargaining model, that firing
costs can increase a union's bargaining power, and help explain
excessive real wages and resultant involuntary unemployment. It may
welll be that the most important impact of severance costs on employment
operates through changed real wage demands, rather than lower labor
demand at a given real wage. This important extension is left for
future research.

The firm is viewed as having a short-run demand for labor
schedule, the marginal product of labor, that includes a stochastic
shift parameter Dy. The current value of this parameter is known to the
firm, but future values are uncertain. For notational convenience, I

normalize the marginal product of labor schedule as follows:

1) MPL»= w+ o(D,-L,)

where: wis the (fixed) real wage,

Dy is the demand shift parameter,


it
a
—

@ :490yg pueweq z0qe7
a) T T T T T T T T T T — T T T T T T T

it oll 001 06 : » 08
og

06

oor

n n | n L. 1 n oz

a 1 1 1 | \ 1 t 1 | i L
suofjdunssy ose) eseg

INSHAOTdWI GNV GNVNAd ANO-dOLWad NUAMLAG dINSNOLLV1au
unod FuNdTA


30

This theoretical statement of the firm's employment policy is
of limited interest if the impacts are empirically small. To explore the
empirical significance of these social policies, the next section of the
paper assigns plausible values to the parameters identified in this

section as key determinants of the cost of severance restrictions.

Iv. Empirical Assessment

We are now in a position to discuss the implications of
severance restrictions for labor demand in more quantitative terms.
While it would be possible, in principle, to examine the algebraic
equations derived above for general insights, it would be difficult, and
it would be impossible to make any statements about the quantitative
significance. Instead, I will attach plausible values to the key
determinants of the costs discussed above, to obtain insights into the
actual impact of severance restrictions. To do so, it will be

necessary to obtain estimates of several important parameters, namely:

1) The actual size of the severance cost, c. (Without loss of
generality, I normalize so that the wage equals 100, so that
the cost of severance restrictions should be interpreted as a

fraction of the annual wage.)

2) D,, the labor demand shock. I normalize so that the
expected value of D, is 100; numbers less than 100 are

interpreted as "recessions", numbers greater as "booms."


C= 20

L, = 9

Se
ouounsd

10:
105

f= 40

L, = 95.0
97.5
100.0
102.5
105.0

C= 60

L, = 95.0
7.5
100.0
102.5
106.0

C= 80

Li = 95.0
97.5
100.0
102.5
105.0

c= 100

L, = 95.0
97.5
100.0
102.5
105.0

46

TABLE FOUR
EXPECTED LABOR DEMAND GROWTH

Low Base High
Growth Case Growth
g=70.01 g=0.00 g=0.01
0.47 0.28 0.16
1.30 0. 83 0.52
2.98 2.07 1.40
5.71 4,27 3.11
9.18 TM 5.81
0.51 0.30 0.17
1.49 0.93 0.57
3.68 2.43 1.59
7.68 5. 3. 76
13.64 10.29 7.60
0.51 0.30 0.17
1.51 0.93 0.57
3.76 2.43 1.60
8.02 5.41 3. 83
14.82 10.29 7.89
0.51 0.30 0.17
1.51 0.93 0.57
3.76 2.46 1.60
8.05 5.57 3.83
14.97 10.90 7.92
0.51 0.30 0.17
1.51 0.93 1.30
3.76 2.46 2.98
8.05 5.58 5.71
14.97 10.95 9.18


29

period-ore employment on the expected period-three cost of
overemployment. This cost is non-zero only if (D,,D,) falls into the
region that I have labelled 2,4, which is to say, only if there are no
hirings or firings in both period two and period three. This makes
intuitive sense; for the first-period's marginal worker to affect the
cost of overemployment in period three, that worker must also be the
marginal worker in period three, which will not be the case if he is
fired or if additional workers are hired after him, making them the
marginal workers.

The second term is the increase in the expected cost of
period=tnree severance payments due to an increase in period=one
employment. This is non-zero only if there are no hirings or firings in
the second period, and if the demand realization is bad enough in the
third period to make firings optimal. Because the labor force in period
three that is left over from period one is lower due to attrition, (it
equals 87L,), this would require a very bad demand realization.

Having determined the expected marginal cost of period-one
employment, we can characterize the period-one employment decision.
This is broadly similar to the two*period decision, illustrated in
Figure Three and equation (14). In fact, (14) holds precisely if 9$(L,)

is defined as:

: _ - GEC) . dE(m,) 2
24) o(Ly) = “a, 708) aL, 7(1+8)

where the derivatives on the right side of (24) are given in equations

(20) and (21).


demand conditions it should be higher. Second, it is shown that proxies
for the costliness of severance restrictions which rely on the incidence
of firing, such as the number of unfair dismissal cases used by Nickell,
may for plausible parameter values be inversely related to the total
cost of the severance restrictions. This is because, as the cost. of
firing increases, firms find it optimal to do less firing. Thus, while
costliness of firing restrictions increases, the incidence of firing may
fall.

The empirical literature to date does not, therefore,
represent a consensus of any sort on the magnitude, or even the
direction, of the impact of severance payments on employment. Toa
large extent, this reflects the difficulty of finding adequate proxies
for the cost of employment protection schemes, and the low power of
aggregate time-series econometrics. The strategy followed in this
analysis is to ground the analysis more firmly in an explicit
theoretical model. While the theoretical construct is necessarily
incomplete, and therefore will not provide definitive empirical results,
it provides substantial insight into the empirical relevance of the
problem by articulating the link between severance costs, other
Structural parameters that characterize the economy, and the employment

decision.

III. The Model

The insight that I intend to capture in the following analysis

is simple. Severance costs can affect employment in two ways. In


20

The impact on period=three profits is the derivative of (9) with respect

to period=two employment. This can be written:

(10) SEG%a)  -08F,(BLa-c/a) ~aB [Fs (BL. )Fs(BL27¢/a) }{BL2-E(D,| Ds © 9)
2

Where 2 = [D, s.t. (BL,“c/a) < D3 < BL2]

The first term in the expression in the increase in the
expected cost of severance payments in period three due to an increase
in period-two employment. An extra employee hired in period two implies
8 extra employees in period three (ignoring indivisibilities)>/, and if
he is fired it will cost the firm cB. The probability that demand will
be low enough to cause workers to be fired in period three is
F,(8L,~c/a), so the expected increase in period-three severance payments
due to an increase in period-two employment is the first term of (10).
It is increasing in L,, and is increasing in the variability of the
labor demand shock (D,) if BL, is less than the expected value of ),.

The second term is the change in the expected cost of excess
period=three employment from a change in period=two employment. Tnis
term follows from mechanistic differentiation of (9), but it can be
understood intuitively as well. An increase in L, affects period* three
employment (and through employment, profits) only if the marginal worker
in period 2 is also the marginal worker in period 3. This occurs only
if D,; is in the intermediate case discussed above, that is, only if in

period three there are no hirings or firings. If D,; is below (8L,~c/a),


IFDP
NUMBER

284

283

282

281

280

279

278

27T

276

275

274

273

56

International Finance Discussion Papers

TITLES

1986
Labor Market Rigidities and Unemployment :
the Case of Severance Costs

A Framework for Analyzing the Process
of Financial Innovation

Is the ECU an Optimal Currency Basket?

Are Foreign Exchange Forecasts Rational?
New Evidence from Survey Data

Taxation of Capital Gains on Foreign
Exchange Transactions and the Non-neutrality
of Changes in Anticipated Inflation

The Prospect of a Depreciating Dollar
and Possible Tension Inside the EMS

The Stock Market and Exchange Rate Dynamics

Can Debtor Countries Service Their Debts?
Income and Price Elasticities for Exports
of Developing Countries

Post-simulation Analysis of Monte Carlo
Experiments: Interpreting Pesaran's (1974)
Study of Non-nested Hypothesis Test Statistics

A Method for Solving Systems of First Order
Linear Homogeneous Differential Equations
When the Elements of the Forcing Vector
are Modelled as Step Functions

International Comparisons of Fiscal Policy:
The OECD and the IMF Measures of Fiscal
Impulse

An Analysis of the Welfare Implications of
Alternative Exchange Rate Regimes: An
Intertemporal Model with an Application

AUTHOR(s)

Michael K. Gavin
Allen B. Frankel
Catherine L. Mann
Hali J. Edison

Kathryn M. Dominguez

Garry J. Schinasi

Jacques Melitz
Michael K. Gavin
Jaime Marquez

Caryl McNeilly

Neil R. Ericsson

Robert A. Johnson

Garry Schinasi

Andrew Feltenstein
David Lebow
Anne Sibert

Please address requests for copies to International Finance Discussion

Papers, Division of International Finance, Stop 24, Board of Governors of
the Federal Reserve System, Washington, D.C. 20551.


37

The base case provides some other interesting insights into the
structure of the severance cost problem. It is surprisingly insensitive
to the size of the severance payment, once that payment reaches about 20
percerit of the annual wage. This is because, at such high severance
costs, it very seldom pays actually to fire a worker. For example,
suppose employment is 100 in period one. In period two it will, because
of voluntary worker departures, be only 96. It doesn't pay to fire a
worker until demand is c/a, or 40/4 = 10 units below 96, that is, unless
demand in period 2 falls below 86. This is almost three standard
deviations below the expected level of period=two demand, and the
probability of demand being so low is slight. So, the expected cost of
the severance payments is primarily due to anticipated overemployment,
rather than actual severance payments, and this overemployment cost is
relatively insensitive to c.

It is interesting to note the inverse relation between the
expected cost of actual severance payments, the first column of Table
Three, and the payment per worker hired. This suggests that empirical
studies which use as a measure of the burden of the severance payments
policy some variable that is related to the number of firings undertaken
(for example, Nickell (1982)) are likely to run into the difficulty that
their proxy for the overall burden of severance payments is declining
when the actual burden is increasing.

An aspect that does not emerge from Table Three is that the
increase in expected labor costs due to the severance payments is almost
all due to costs expected to be incurred in period two; only about 15 to

20 percent of the increase in expected labor costs is due to costs


38

expected to be incurred in period three. This, again, is because the
attrition rate is large in relation to the standard deviation of the
demand shock, so the probability that demand will be bad enough in reriod
three to make the optimal labor force be below what is left over from
period one, 87L,, is very low. For this reason, it is apparent that
adding a fourth period to the firm's planning horizon would have a
neglibibly siall impact on these conclusions.

Sensitivity Analysis: Before evaluating in more detail tte
implications for employment of these estimates of the incremental
marginal cost of employment attributable to severance costs, I examine in
Tables Four through Nine the sensitivity of this cost to the various
assumptions that were made. In Table Four I examine the influence of
expected labor demand growth, which is the trend rightward shift in the
labor demand curve. Three cases are considered: the base case, discussed
above, in which the trend growth in employment is zero, a low growth case
in which it is expected to decline by one percent per year, anda high
growth case in which it is expected to increase by one percent per year.
Table Four indicates that the estimated burden of severance costs is
fairly sensitive to anticipated labor demand growth. An increase
(decrease) in the expected growth rate of one percentage point reduces
(increases) the marginal cost of labor by about one percentage point.
which, under the assumed labor demand elasticity, would increase. (reduce)
the firm's optimal level of employment by about .25 percent. Thus, as
Blanchard et. al. point out, the reduction in trend employment grow':h has
made a social policy that was reasonably costless in the high growth

years of the 1960s more costly now that trend demand growth has falilen.


TABLE TEN
OPTIMAL EMPLOYMENT: BASE CASE

Period~One
Demand Optimal
Shock: D, Employment
90.0 94.51
92.5 96.00
95.0 96.00
97.5 97.17
100.0 99.51
102.5 101.81
105.0 104.06
107.5 106.26

110.0 108.42


26

maximizes this with respect to period-one employment. Period-one profits

are:

16) a, = Y(D,,L,) > wh, ~ cmax(0, Blo oL,)

This is non*stochastic. The marginal period-one prefitability of

period-one employment is:

an, § 0 HY) if Ly > Blo
17) =
diy a(D, *L,) +e if Ly < Blo

Now consider period two. Expected period-two profits are:

+2 +0

18) E(mz) = SS ma(Dz,Ly,L2) f(Dz,Ds] D,) dDzdDy

22 20

where:
19) m2 = ¥(D,,L2(D2,L,)) “wh, ~c max(0, BLy~ La)

Differentiating (18) with respect to period~one employment, we obtain:

ht) ~f dw, (D2,L,) £, (Dz) dD,
1

so

-| {a(D,-L,(°))%42 = ¢ 4 max(0, BLicLz) | f2(D2) dda
a; a;


55

Kaufman, R. (1979) "Why the U.S. Unemployment Rate is So High," in
Michael Piore (ed.) Unemployment and Inflation:
Institutionalist and Structural Views, M.E. Sharpe, Inc. :
White Plains.

Krugman, P. (1982) "The Real Wage Gap and Unemployment," Annales de
L'INSEE, no. 47748

Lindbeck, A. and D. Snower (1984) "Involuntary Unemployment as an
Insider-Outsider Dilemma," University of Stockholm Institute
for International Economic Studies Seminar Paper No. 282

Metcalf, D. (1985) "An Analysis of the Redundancy Payments Act," Centre
for Labour Economics Working Paper No. 606

Nickell, S.J. (1979) "Unemployment and the Structure of Labor Costs,"
Carnegie Rochester Conference Series on Public Policy,
(Supplement to Journal of Monetary Economics.) no. 11

oeee (1982) "The Determinants of Equilibrium Unemployment in
Britain," Economic Journal September

eeee (1985) "The Government's Policy for Jobs: An Analysis,"
Centre for Labour Economics, London School of Economics
Discussion Paper no. 222. August

OECD (1982) Positive Adjustment Policies: Managing Structural Change,
Paris

woes (1985) " Labour Market Flexibility," manuscript, Paris.

Puig, J.P., M.T. JoinsLambert, and J. Maurice (1984) "Communication de
la Delegation Francaise Sur Les Perspectives D'Emploi A Moyen
Terme et les Politiques d'Emploi en France," mimeo, INSEE

Sachs, J. (1979) "Wages, Profits, and Macroeconomic Adjustment: A

Comparative Study." Brookings Papers on Economic Activity,
no. 2

aeee (1983) "Real Wages and Unemployment in the OECD Countries,"
Brookings Papers on Economic Activity, no. 1

Symons, J. and R. Layard (1984) "Neoclassical Demand for Labor
Functions for Six Major Economies," Economic Journal,
November .

Thurow, L. (1985) "A Time to Dismantle the World Economy," The
Economist 9-15 November

Wilson Committee (1978) Research Report no. 1


general rubric of "labor market rigidities.") Thus, previous studies on
the European real wage problem may well underestimate the impact of
excessive labor costs, broadly defined, on the European unemployment
problem.

A form of labor market rigidity that is often mentioned in
this context is the high cost of firing workers in Europe, compared both
with the cost in the United States, and with the European situation in
the early 1960's.2/ There is little doubt that it is much more
expensive and difficult to fire workers in Europe than in the Un:ted
States. This is established, for example, in Kaufman (1979), which
documents separation costs in Europe in some detail, showing that. they
are substantially higher than in the United States. Although Kaufman
actually argued that these severance costs were a reason for supposing
that unemployment should be lower in Europe than in the United Sates,
the recent situation in Europe has led many observers to argue that the
inability to fire workers in future recessions would make firms
reluctant to expand employment during years of normal or high demand,
thus reducing labor demand and, in a context of rigid real wages,
increasing unemployment. Thurow (1985) expresses a typical view:

{in America, firms] can easily fire unneeded workers.

Advance notice need not be given; severance pay need not be

paid. Workers can be hired with the knowledge that if they

are not needed they can easily be fired. . .. In Europe
firings range from difficult and expensive to impossible.

This makes it much riskier and expensive to go into business.

What is a reasonable risk in America where labour is a

variable cost becomes an unreasonable risk in Europe wnere

it is an overhead fixed cost.

These concerns have led to policy responses in some countries.

For example, in a 1985 White Paper on employment, the government of the


4y

burden of the firing costs. To reduce Significantly the impact of firing
costs it would be necessary to lower them to a very low level. (This
eonclusion is, of course, sensitive to the parameter values assumed
above, and in particular to the short-run wage elasticity of labor demand.
A very low elasticity would tend to undermine this conclusion.)

Before taking these policy conelusions seriously, of course,
there needs to be more adequate empirical grounding for the scenarios
presented above. In addition, it would in principle be desirable to
expand the theoretical model to incorporate important aspects of the
labor market such as heterogeneity of labor. Perhaps a more important
issue is the impact of severance costs on average profits, and therefore
entry and exit of firms. This issue was raised above, but not seriously
addressed.

Finally, the impact of severance costs on labor supply and wage
bargaining should be addressed. As noted above, the effect of severance
costs on workers' wage demands will probably depend upon the theoretical
paradigm used to model the bargaining process. Some work has been done

in this area, and more work is called for.


42

At D,=100, its average value, the severance costs reduce
employment by about one-half percent. As demand increases the expected
future cost of severance payments rises, and the impact on employment
becomes greater. At D,=105 employment is about one percent lower and at
D,=110 it is about 1-1/2 percent lower than it would be in the absence of
the severance costs.

For unfavorable demand shocks employment is higher than it
would be in the absence of the severance Payments. At D,=95 employment

is increased by about one percent, and at D,=90 it is increased by almost

five percent.

V. Summary and Conclusions:

This paper presents a simple formulation of the firm's
employment decision in the presence of firing costs, which is solved for
the firm's optimal employment decision. In this way, the key structural
parameters that determine the importance of severance costs for
employment are identified. Although a detailed empirical application
remains to be done, the quantitative significance of the problem is
investigated for plausible parameters, and the sensitivity of the
conclusions to alternative assumptions is explared.

The analysis has implications for future empirical work on this
topic. First, future work should recognize that the impact on employment
depends very much on whether the firm would or would not, in the absence
of firing costs, want to be firing workers, that is, whether labor demand

is greater than or less than the workforce left over from the previous


because the impact of periodsone employment on the firm's value depends,
through the firing cost terms, on future employment levels, This is a
straightforward problem in dynamic programming; to solve it the firm
first considers the period-three employment decision. It determines the
optimal. period-three employment policy as a function of D, andL,. It
then uses this to determine the optimal period=two employment policy by
taking the expectation of period-three profits over D,, and maximizing
the discounted sum of period-two and -three profits. This gives
period=two employment as a function of L, and D,, which is used to
calculate expected period-two and «three profits as a function of L,.
The optimal period-one employment is then the one that maximizes the
discounted sum of period-one, “two, and ~three expected profits, taking
into account the impact of period-one employment on future periods’
employnent and, therefore, profits.

Period-Three Employment: In period three, labor demand will

be adjusted to maximize period-three profits, because there is by
assumption no fourth period to worry about. Differentiating

period-three profits with respect to period~three employment, we have:

an (w+ a(D; -L3)) - w if BL, <L,
om
6) aL,
(w+ a(D; ~ L3)) = (wee) if BL, > Ls;

If BL, <L,, then a change in employment involves no firing,
only hiring, so that the marginal cost of employment is the real

wage, W. It thus pays the firm to employ up to the point that the wage


54

References

Artus, J. (1984) "The Disequilibrium Real Wage Rate Hypothesis: An
Empirical Investigation," I.M.F. Staff Papers, June

Azariadas, C. and J.E. Stiglitz (1983) "Implicit Contracts and Fix-Price
Equilibria," Quarterly Journal of Economics

Balassa, B. (1984) "The Economic Consequences of Social Policies in the
Industrial Economies," Weltwirtschaftliches Archiv

Blanchard, 0O., R. Dornbusch, J. Dreze, H. Giersch, R. Layard, and M.
M. Monti (1985) "Employment and Growth in Europe: A Two*Handed
Approach," mimeo, prepared for the Center for European
Studies. April

Bruno, M. and J. Sachs (1981) "Supply vs. Demand Approaches to the
Problem of Stagflation," in H. Geirsch (ed.) Macroeconomic
Policies for Growth and Stability. Kiel

C.B.I. (1984) "Attitudes Towards Employment," C.B.I. Social Affairs
Directorate, November

Clifton, R. and C. Tatton-Brown (1979) "The Impact of Employment

Legislation on Small Firms," Department of Employment Research
Paper, no. 6

Daniel, W.W. and E. Stilgoe (1978) The Impact of Employment Protection
Laws, Policy Studies Institute

Gennari, J. (1985) "Job Security: Redundancy Arrangements and Practices
in Selected OECD Countries," manuscript prepared for the
Directorate for Social Affairs, Manpower and Education, OECD

Grubb, D., R. Jackman, and R. Layard (1983) "Wage Rigidity and
Unemployment in the OECD Countries," European Economic Review

o--, R. Jackman, and J. Symons (1982) "Wages, Unemployment and Incomes
Policy," CLE Working Paper, no. 479 London School of
Economics

Hamermesh, D.S. (1985) "Job Security Policy and Labour Demand: Theory
and Evidence," manuscript prepared for the Directorate of
Social Affairs, Manpower and Education, OECD


15

FIGURE ONE

Case a:
Low Demand Realization

(D, < BL,*c/a)

Case b:
Intermediate Demand

(BL27c/a < D, < BL)

Ds BL, (D3+c/a)

Case c:
High Demand Realization

(Ds > BL)

BL. Ds (D3+c/a)


Labor Market Rigidities and Unemployment
The Case of Severance Costs

by

Michael K. Gavin*

i. Introduction:

The proposition that the current unemployment problem in
Europe is largely or even entirely due to excessive real wages has
become, if not the conventional wisdom, then at least the working
hypcthesis of choice for many analysts and, especially, policy advisors.
Under this hypothesis employment is determined by labor demand;
consequently, much of the recent empirical research on unemployment has
focused on the determinants of labor demand. With the resultant
estimates of a labor demand schedule, analysts have estimated the real
wage consistent with full employment, and have attributed the existing
unemployment to the calculated "real wage gap."l/

These studies use as the firm's cost of employing labor the
measured real product wage, including labor taxes paid by the firm.
However, many observers have argued that nonwage labor costs resulting
from various social policies and labor market rigidities have
significantly depressed labor demand in many European economies, (See
Balassa (1984) for a rather emphatic attribution of European

unemployment to various social policies, many of which fall under the


36

bad, but not catastrophic demand shocks are optimally handled by neither
hiring nor firing, but keeping employment at the level that is left over
from the previous period. This warns against interpreting the employment
declines in Table Two as representing fluctuations in the simple labor
demand curve, that is, in the context of the theoretical model offered in
this paper, the MPL curve.

We return now to the simulation experiments. On the basis of
these base case assumptions, Table Three calculates the expected marginal
cost of severance restrictions for severance payments ranging fron 20 to
100 percent of the annual wage. The calculations were accomplished by
carrying out numerically the two-dimensional integrations in equaions
(15), (20), and (21). (A copy of the FORTRAN computer program used to do
this integrating is available from the author on request.)

These numbers are estimates of the quantity $(L,) defined in
equations (20), (21) and (24), and should be interpreted as a percent of
the annual wage. Thus, if it costs 40 percent of the annual wage to fire
a worker, then at an employment level of L,=100, the expected marginal
cost of an additional worker is roughly 2°1/2 percent higher than it
would be in the absence of severance costs. With the assumed labor
demand curve, employment would be reduced as a consequence by about 1/2
percent if, of course, the labor force left over from the previous period
is small enough so that the firm is in the "high demand" case of. Figure
Three. This effect on costs and employment, while perhaps marginal in
the context of the current unemployment problem in Europe, is far from

trivial.


24

FIGURE THREE

Case a:
Low Demand Realization
wt o(Le) .
(D, < B,-c/a)

ULL Lee (wee)
Le
Da (Dz+¢e/a) BLy
Case b:
MCL: wt o(L,) Intermediate Demand
a, OS w (Bare/a < Dy < B,)
— —wrero(Le)
ong a E,W (wee)
PL
Da BL, (D,+¢e/a)
CL Case ec:

wW+(L2) High Demand Realization

w (D; > Da)

—wee+o(L2)

BL, D2 (Da+¢e/a)


ABSTRACT

It is frequently alleged that the persistent, high rates of
unenployment in many European countries are due, at least in part, to
var:ous labor market rigidities. One of these rigidities is the high
cost, of firing workers, compared with the cost in the United States, or
in Europe in the early 1960s.

This paper assesses the empirical importance of severance
cosss on labor demand. A partial equilibrium model of the firm's
emp:.oyment decision in the presence of significant severance costs is
fornulated and solved. The theoretical section of the paper identifies
the following determinants of the impact of severance costs on labor
demand: (1) the size of the required severance payments, (2) the
variability and persistence of shocks to labor demand, (3) the expected
rate of growth of labor demand, (4) the rate at which workers
voluntarily leave the firm to retire or take other jobs, (5) the wage
elasticity of labor demand, and (6) the firm's discount rate.

The analytical framework is then used to evaluate the impact
of severance costs on the expected cost of hiring a worker, and hence on
labor demand. These costs are evaluated for a plausible base case, and
the sensitivity of the conclusions to alternative assumptions is
investigated.


NT

TABLE FIVE
LABOR DEMAND SHOCK VARIABILITY
Low Base High
Variability Case Variability
S40 9 5.0 o= 6.0
C= 20
+0 0.07 0.28 0.54
97.5 0.33 0.83 1.46
100.0 1.20 2.07 2.39
102.5 3.26 4,27 5.95
105.0 6.81 TM 7.80
c= 40
= 95.0 0.07 0.30 0.75
97.5 0.34 0. 93 1.78
100.0 1.28 2.43 3.75
102.5 3.71 5.41 7.03
105.0 8.53 10.29 11.71
Cc = 60
= 95.0 0.07 0.30 0.76
97.5 0.34 0.93 1.82
100.0 1.28 2.43 3.90
102.5 3.73 5.4 7.51
105.0 8.69 10.29 13.00
Cc = 80
= 95.0 0.07 0.30 0. 76
97.5 0.34 0.93 1.82
100.0 1,28 2.46 3.92
102.5 3.73 5.57 7.58
105.0 8.69 10.90 13.25
C = 100
= 95.0 0.07 0.30 0..76
97.5 0.34 0.93 1,82
100.0 1.28 2.46 3.92
102.5 3.73 5.58 7.58
105.0 8.69 10.95 13.28


32

Base Case: It can hardly be hoped that the parameters chosen
in the following calculations will be uncontroversial; consequently I
will present the calculations for a reasonable base case, and will then
explore the sensitivity of my conelusions to variations in the important
parameters, At the very least, this will demonstrate which of the
parameters have most influence on the conclusions, so that a more
systematic empirical examination will know on which aspects of the labor
market to focus.

Because the severance cost per fired worker, c, is the center
of concern, I prefer not to make assumptions about its magnitude ancl will
instead discuss the impact of the severance costs for a range of
estimates for c, ranging from 20 percent to 100 percent of the annual
wage. This permits conclusions to be drawn about the impact of policies
designed to reduce the cost of firing workers.

For the base case, it is assumed that D,, the period-one labor
demand realization is 100, that is, the economy is neither in a recession
nor a boom. Later I explore in more detail the relationship betweer: D,
and employment in the presence of severance restrictions.

As for the distribution of D, and D,, I assume that expected
labor demand has a growth rate of zero, in line with the stagnant
employment experience in Europe during the past ten years. The labor
demand variability parameter, o, is set at 5. Thus, in the absence of
severance costs, it is assumed that the standard deviation of employment
would be about 5 percent of employment. This, as the sensitivity
analysis below demonstrates, is one of the most important assumptions.

The autocorrelation of the demand shock, p, is assumed to be 0.5. While


MY

the higher the expected cost of the severance payments. This is because,
when the autocorrelation parameter is higher, a bad demand realization in
period two, when no hiring is done, is likely to be followed by another
bad one in period three. This makes it more likely that the severance
eosts will apply in the third period, thus raising the contribution of
period-three expected costs to the total, from a minor amount in the case
when p=0.0 to on the order of 1/3 of the total when p=0.95.

Finally, in Table Nine I consider the impact of period-one
labor demand shocks. A reduction in period-one demand raises the
expected marginal cost of employment for a given level of period-one
employment. This is only because demand is assumed to be autocorrelated,
so that a bad period-one demand shock tends to be followed by a bad
period=two demand shock. When demand is not autocorrelated, this shift
in the $(L,) schedule does not occur.

Impact _on Employment: These calulations of the addition to the
mar ginal cost of labor due to the severance costs add insight into the
potential magnitude of the problem, but they do not directly answer the
question that ultimately concerns us; what is the impact on employment?
The discussion has, at least, clarified that the answer is not
unambiguous; it depends upon whether the current state of labor demand is
high or low relative to the size of last period's level of employment.

To illustrate this, Table Ten and Figure Four give the optimal level of
employment as a function of D,, under the base case assumptions discussed

above, assuming also that L,=100 and that C=20.


27

D, D.-¢/a .
= J *Ba(BL,-D,) f2(D,) dD, ~ Sf Ba f2(D2)dD,
D.-c/a 20

. dE + « =

20) SG) = <8 {cF,(B,-c/a) + alF2(B.)-F2(B.-c/a) HBL,-E(D2 | D2 € 22)J}
where 5, was defined above, F,() is the cumulative probability
distribution function for D, conditional on D,, and 2, is defined as

follows:
2, = (Dz | (B,-c/a) < D, < 52)

Comparison with equation (10) indicates that the impact on
next-period profits of an increase in this period's employment in the
three period problem is similar in some respects to that in the
two=period problem, The difference is the replacement of BL, with D.,
which, with D, > BL,, increases the adverse impact of an increase in
this period's employment on next period's expected profits. The
intuition for this effect is that, with a third period to worry about,
period=two employment will be lower (for a given realization of the
labor demand shock) than it would be if the next period were the last in
the planning horizon. This means that, for a given level of period=one
employment, the probability that the firm will in the next period want
to fire some of the workers is increased relative to what it would be in

the absence of a third period.


The firm's profits in period t can then be written:
3) me = Y(LesD_) + whe + ¢ max(0, BLE-7 > Ly)

where B = (1-b) is the firm's rate of workforce retention.
The firm's period-one problem, then, is to maximize the

present value of expected profits:

4) max V(1) = EL{ E me (1+6)7t+1}
Ly te1

where the expectation is conditional on all information available as of
pericd one, including the period-one demand realization, D,.

Although the maximization (4) is, in principle, conducted over
an infinite horizon, I solve the problem as though the firm's planning
horizon were finite. For plausible parameters, the solution to the
finite horizon case will be essentially the same as the infinite horizon
case. This statement is not formally proven, but it can be justified as
follows, The firm's period-one employment decision is affected by
period=n outcomes only to the extent that the period-one marginal worker
affects the nth period's optimal labor demand or firing decision. This
will occur only if the period-one marginal worker is also the period-n
marginal worker, which requires (1) no hiring between period one and
period n, (2) no firing between period one and period n, and (3) a bad

demand realization in period n so that the optimal labor demand is below


48

TABLE SIX
LABOR FORCE ATTRITION RATE
Low Base High
Attrition Case Attrition
B= 0.97 B=0.96 B= 0.95

c= 20

Ly = 95.0 0.46 0.28 0.17
97.5 1.29 0.83 0.53
100.1) 3.01 2.07 1.39
102.5 5.81 4,27 3.06
105.10 9.36 7M 5.69
C= 40

L, = 95.9 0.50 0.30 0.18
97.5 1.49 0.93 0.57
100.0 3.71 2.43 1.58
102.5 7.81 5.41 3.70
105.0 13.95 10.29 T3
C= 60

L, = 95.0 0.50 0.30 0.18
97.5 1.50 0.93 0.57
100.0 3.79 2.43 1.59
102.5 8.17 5.4 3.76
105.0 15.18 10.29 7.71
c= 80

L, = 95.0 0.50 0.30 0.18
97.5 1.50 0.93 0.57
100.0 3.79 2.46 1.59
102.5 8.19 5.57 3.77
105.0 15.33 10.90 7.73
Cc » 100

L, = 95.0 0.50 0.30 0.18
97.5 1.50 0.93 0.57
100.0 3.79 2.46 1.59
102.5 8.19 5.58 3.77
105.0 15.34 10.95 7.74


50

TABLE EIGHT
LABOR DEMAND SHOCK AUTOCORRELATION

Low Base High
Autocorrelation Case Autocorrelation
p= 0.00 p=0.50 p= 0.95
C= 20
L, = 95.0 0.26 0.28 0.36
97.5 0.77 0.83 1.01
100.0 1.91 2.07 2.35
102.5 4,03 4,27 4.59
105.0 7.26 TM 7.60
C= 40
L, = 95.0 0.28 0.30 0.42
97.5 0.84 0.93 1.23
109.0 2.17 2.43 3.04
102.5 4,85 5.4 6.34
105.0 9.53 10.29 11.34
C = 60
L, = 95.0 0.28 0.30 0.43
97-5 0.84 0.93 1.26
100.0 2.18 2.43 3.14
102.5 4.92 5.41 6.70
105.0 9.84 10.29 12.41
Cc = 80
L, = 95.0 0.28 0.30 0.43
97.5 0. 84 0.93 1.26
100.0 2.18 2.46 3.14
102.5 4.92 5.57 6.73
105.0 9.85 10.90 12.54
C= 100
L, = $5.0 0.28 0.30 0.43
97.5 0. 84 0.93 1.26
100.0 2.18 2.46 3.14
102.5 4.92 5.58 6.73

105.0 9.85 10.95 12.54


14

equals the marginal product of labor, so that L,=D, as it would be
without severance restrictions. If, however, 8L, > Ls, the marginal
cost of labor is not w, but (wee). This is because changes in
employment correspond to changes in the number of workers fired, not
hired, so that an increase (decrease) in employment saves (costs) the
firm c in severance costs. The appropriate employment policy, then, is
to set the marginal product of labor equal to the wage net of the
severance cost. Thus, for adverse demand shocks, the firm will indeed
be induced to increase employment, relative to the no-severance cost
level, as a result of the severance costs.

The derivation of the firm's optimal period=three labor demand
can be derived from firsteorder conditions (6) with the help of Figure
One, which depicts the marginal product of labor, MPL, and the marginal
cost of labor which is the solid locus MCL. The first order conditions
(6) are satisfied at the intersection of the period=three MPL curve and
the MCL curve.

If, as in Figure 1a, demand is low enough so that the MPL
curve cuts the BLo curve below (wee), then the optimal level of
employment is less than BL,, So that the marginal cost of employment is
(wee) and the optimal level of employment is (D3+¢/a). If fewer
workers were employed, the gap between the marginal product of labor and
the wage would be less than c, the cost of firing a worker. Then an
increase in employment, which means firing fewer workers, would lead to
a "production loss" of (w*MPL) and a "severance cost" gain of c on each

worker retained. Since (w*MPL) is less than c, such an increase in