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Area Conference on Employment and Social
Protection
CESifo Conference Centre, Munich
29 – 30 June 2001
Efficiency Wages, Job Security and Training
by
Margarita Katsimi
Efficiency Wages, Job Security and Training
Margarita Katsimi
(Athens University of Economics and Business and CESifo)
June 2001
ABSTRACT
This paper considers the optimal level of rm-specic training by taking into account the positive eect of training on the expected duration
of workers current employment. In the framework of an eciency wage
model, a short expected job tenure represents a disamenity that reduces
the penalty from shirking. As this disamenity increases, workers will have
an incentive to continue providing a positive level of eort only if they
are compensated by an increase in the wage rate. Firm-specic training
will have two eects on wages: a positive direct eect since workers must
be compensated for the higher level of eort implied by training and a
negative indirect eect because trained workers face a lower probability of
being red in a recession. The existence of the second eect will partly or
totally oset the negative impact of economic uncertainty on investment
in rm-specic human capital.
JEL Classification Numbers: J41, J33, J24.
Keywords: eciency wages, rm-specic training.
Address for correspondence: Margarita Katsimi, Athens University of Eco-
nomics and Business, Department of International and European Economic Studies,
76 Patision Avenue, Athens 10434, Greece. E-mail address: [email protected].
I am grateful to Gyl Zoega, Steve Satchell and Alison Booth for valuable comments and
suggestions on an earlier version of this paper. Preliminary version.
1. Introduction
As early developments of the human capital theory predict, uncertainty about
future employment has a negative impact on investment in rm-specic training.
According to Becker (1962, 1964) and Oi (1962) a rm will be reluctant to invest
in rm-specic training since quitting implies the inability to recoup the nancial
outlays. Similarly, workers will be reluctant to bear the cost of this investment if
there is a positive probability of being dismissed and not benet from investment
returns. The probability of both ring and quitting will decrease if investment costs
and rents are shared between workers and rms. The incentive to share the investment in rm-specic human capital is investigated by Hashimoto (1979, 1981). In
Booth and Chatterji (1989) the redundancy payment is part of the rm's optimal
contract to induce workers to undertake specic training in sectors where there is a
positive probability of being dismissed. This paper shows that the negative causality
between rm-specic training and employment uncertainty runs both ways: Firstly,
employment uncertainty has a negative eect on rm-specic training because it
reduces expected returns. Secondly, rm-specic training can reduce employment
uncertainty because rms which have invested in rm-specic training will be more
reluctant to re workers in a recession since this will imply losing some of their investment return. In the framework of an eciency wage model, the negative impact of
rm-specic training on future employment uncertainty will have a negative impact
on wages, thereby osetting some of the initial investment cost.
The idea that job security will have a negative impact on eciency wages has been
analyzed by Katsimi (1995), Saint-Paul (1996) and Fella (2000).1 All authors base
their arguments on dierent versions of the Shapiro and Stiglitz (1984) model which
shows that in an environment where employers are unable to monitor workers' onthe-job eort costlessly, unemployment can induce workers to provide a positive level
of eort. In this framework, a short expected job tenure represents a disamenity that
Empirical evidence suggesting a wage premium based on the job's unemployment risk has been
found by Abowd and Ashenfelter (1981), Adams (1985) and Li (1986). Research on this topic dates
back to the pioneering work of Hall (1970, 1972).
1
1
reduces the penalty for shirking. As this disamenity increases, workers will have an
incentive to continue providing a positive level of eort only if they are compensated
by an increase in the wage rate. The optimal incentive wage will increase with the
risk of being red in a recession. In other words, the cost of labour decreases when
the rm is expected to retain its workforce in a recession. This, however, requires
either that the rm can commit to a low ring policy or that workers expect that
low ring is the optimal future employment policy of the rm. In Saint-Paul (1996),
rms' commitment to a future level of employment is represented by the fact that
employment is set one period in advance. In Katsimi (1995) and Fella (2000), the
imposition of redundancy payments by the government leads to a higher level of
expected future employment in a recession.
This paper considers the case where the above commitment mechanism is endogenous. In the absence of an imposed turnover cost such as a redundancy payment, a
prot-maximizing rm may have an incentive to choose an action that will increase
the cost of dismissing the existing workforce in a recession. In that context, the level of
rm-specic training can be viewed as a `commitment' to higher future employment in
a recession. Given that rms' ability to commit to higher future employment implies
lower wages a prot-maximizing rm may voluntarily choose to invest in rm-specic
training even if the marginal cost of this investment exceeds the expected marginal
return.
The model presented in this paper builds on Shapiro and Stiglitz (1984) by endogenizing workers' horizon on their job and allowing for investment in rm-specic
training.2 Production takes place in a stochastic environment and workers are risk
neutral. Workers' expected job tenure depends on the characteristics of the stochastic environment. An increase in the variance of output will decrease the level of
employment that workers expect to be sustained in a recession. Each worker will now
nd that there is a higher probability of loosing his job and this will put an upward
pressure on wages and unemployment.
2 In the following analysis, expected job tenure is dened as the expected duration of worker's
current employment which is a measure of job security since there are no quits.
2
Specic human capital is treated as a team investment concerning all workforce
and involves costs and returns only for the rm. For simplication we neglect the
uncertainty stemming from quitting. Uncertainty about the future state of the economy decreases both the expected return and the cost of investment in specic human
capital. Since workers are uniformly trained at an optimal level, ring workers in a
recession implies the loss of some of the return of training. If a recession occurs in the
period when the investment return is realized, a reduction in employment implies the
loss of the return from the human capital acquired by the dismissed workers. As a
result, a positive level of training in the previous period will increase employment in a
recession. A higher level of expected employment in a downturn of the economy will
decrease the probability of being red in a recession, thereby, lowering wages. This
negative impact on eciency wages represents a reduction in the cost of human capital investment. This implies that there is a direct positive eect of training on wages
and an indirect negative eect due to its negative impact on the probability of being
red in a recession. Uncertainty about the future state of the economy decreases the
expected return to training, but, on the other hand, it also decreases the cost of training indirectly through improving job security. In equilibrium, the rm will choose a
positive level of investment in specic human capital even if the marginal cost of this
investment exceeds its expected marginal return. Moreover, if the negative indirect
eect of training on eciency wages is stronger than the expected loss of investment
returns due to a reduction in the workforce, uncertainty about the future state of the
economy may lead to a higher optimal level of rm-specic investment.
The rest of the paper is organized as follows: In section 2, wage and employment
determination is discussed in a simple two-period model. Firm's decision to invest in
rm-specic human capital is described in section 3. The last section concludes.
2. Wage and Employment determination
There are two periods and the economy is characterized by the following production function in each period:
3
Yt = gNta t
(1)
where Y is the level of output, N denotes the level of employment, is a log-normal
productivity shock with mean zero and variance 2 and the subscript t denotes the
time period, t = 1; 2.
Firms set wages unilaterally in order to maximize prots. There is asymmetric
information between employers and employees about the on-the-job eort of the latter: the monitoring technology is imperfect. Workers are risk neutral and their utility
depends on the amount of goods they can consume with their wage, w, and on their
job eort, e. The utility function of the j th employed worker in each period is given
by:
Ujt = wt ; et
(2)
While unemployed, workers receive an unemployment benet, d, so that the utility
of an unemployed worker is given by
Vt = d
(3)
Table 1 summarizes the timing of events.
At the beginning of period 1, rms observe the value of the productivity shock,
t , and set employment so that wages satisfy the non-shirking condition.3 Then,each
worker decides either to shirk and provide minimal eort (e = 0) or not to shirk in
which case he provides some xed positive level of (e = e) as in Shapiro and Stiglitz
(1984).4 If a worker chooses to shirk, there is a probability p that he will be caught
and dismissed during each period. Firing workers who shirk is optimal for the rm
since a punishment in the form of a wage reduction would simply induce all workers
to shirk again.
We will assume that in the rst period takes its expected value, so that in the second period
there is a recession if decreases and a boom if increases.
4 Note that g = e
c.
3
4
In the second period, rms reset wages after observing the productivity shock
and adjust their workforce so that the marginal productivity condition for prot
maximization is satised. Again, there is a probability p that the eort level of each
worker will be minitored, in which case if e = 0 the worker will be red. We assume
that although wages are set at the beginning of each period they are paid by the
end of the period, so that shirking involves a cost throughout the last period.5 If
there is a boom in the second period, 2 > E (), unemployed workers will get a job
with probability z. In case of a recession in the second period, 2 < E (), employed
workers will lose their job for cyclical reasons with probability q. Thus,uncertainty
in rst period results from the unknown value of the productivity shock in the next
period.
We denote by q the probability that a worker will lose his job in period 2 conditional on there having been a negative productivity shock:
q = N1 ; E (NN2 jv < 0)
(4)
1
where v = log()
Clearly, the lower the expected level of employment after a negative productivity
shock, E (N2jv < 0), the higher the probability that a worker will be red.
Both workers and employers are forward-looking: workers decide on their level of
eort by taking into account rms' current and future optimal behaviour and rms
decide on the level of training, wages and employment by taking into account workers'
current and future incentives.
2.1. The last period
Workers will provide the amount of eort that maximizes their utility. After the
realization of the productivity shock in period 2, there is no uncertainty for workers
One can also include a third period where individuals are out of the labour force and consume
the wage of the second period.
5
5
who do not shirk. The utility of not shirking in the last period is given by equation(2)
when e = e. The utility of the worker who shirks (e = 0) will be higher than the
utility of the worker who doesn't shirk (e = e), as long as he is employed. From
equation (2) we obtain:
U NS = U S ; e
(5)
Shirking involves the risk of being caught and red with probability p. Each
worker will choose a positive level of eort as long as the utility from not shirking
exceeds the expected utility from shirking. The non-shirking condition (NSCC) can
be written as:
U2N EU2S
(6)
If there is a boom in the second period, 2 > E (), the expected utility from
shirking is given by
EU2S = (1 ; p)U S + p[zU s + (1 ; z)V ]
(7)
Setting equation (6) equal to zero and solving for w2, gives the lower level of real
wage at which workers will not have an incentive to shirk, w2B :
w2B = d + p(1 e; z)
(8)
Each prot maximizing rm will increase its workforce until w2 equals he marginal
product of labour :
agN2a;1 = w2B
(9)
If there is a recession in the second period, 2 < E (), workers who get red for
shirking cannot nd another job since all rms face the same stochastic environment:
EU2NS = (1 ; q)(U S ; e) + qV
(10)
6
Moreover, workers who do not shirk can still get red for cyclical reasons:
EU2S = (1 ; q)[(1 ; p)U S + pV ] + qV
(11)
The lowest wage that satises the NCS is:
w2R = d + pe
(12)
By comparing equations (8) and (17) one can see that the eciency wage in a
recession will be lower than in a boom, since the penalty associated with unemployment is higher in a recession (z = 0). The NSC is represented graphically in gure
1. At any wage rate above w each worker is better o by not shirking. At w rms
induce workers to provide a positive amount of eort at the lower cost.
Solving the prot maximization condition for N , gives the equilibrium level of
employment:
+ e) a;1
N2R = ( pbpga
(13)
1
By taking the conditional expectation of (13), we obtain:
+ e) a;1 E ( 1;a )
E (N2jv < 0) = ( pbpga
1
(14)
1
Proposition 1: An increase in the variance, 2 , of the productivity shock will
have a negative impact on expected period 2 employment in a recession, E (N2 jv < 0).
Proof: See Appendix.
2.2. The rst period
At the beginning of the rst period, each worker selects an eort level in order to
maximize his expected utility in the two periods by taking into account the expected
eciency wage of the next period. A worker who decides not to shirk in the rst
7
period will always face a probability of being red in the next period in the presence
of a negative productivity shock. Thus, the expected utility of not shirking in the
two periods is given by
EU1N = U1N + h[qV + (1 ; q)U2N (w2R)] + (1 ; h)U2N (w2B )
(15)
where w2B and w2R are given by equations (8) and (12) respectively, h is the probability of a recession, and q is the probability of being red in a recession dened by
equation (4).
Workers can lose their job in the rst period only due to shirking. If this is the
case, they will nd a job in the second period with probability z if the economy is in
an upturn.
In the second period, workers can lose their job either due to shirking if the
economy is in an upturn or both due to shirking and for cyclical reasons, if the
economy is in a recession. In the case of a boom, unemployed workers will nd a job
with probability z whereas in the case of a recession unemployed workers will remain
unemployed.The expected utility from shirking in the two periods can be written as:
EU1S = (1 ; p)fU1S + h[(1 ; q)(1 ; p)U2S (w2R) + (1 ; q)pV + qV ]
+ (1 ; h)[(1 ; p)U2S (w2B ) + p[zU2S (w2B ) + (1 ; z)V ]]g
+ p[V + (1 ; h)[zU2S (w2B ) + (1 ; z)V ] + hV ]
(16)
The terms in the squiggled brackets on RHS of equation (16) states the expected
utility of a shirker who does not get monitored in the rst period and the remaining
terms give his expected utility when he gets caught and is red in period 1.
By using equations (15) and (16), the NSC in the rst period can be written as
w1 d + e + pe hq(1 ; p)
(17)
8
The wage that satises the NSC will depend negatively on the expected cost of being unemployed: w1 will increase with unemployment benets, d and the probability
of a boom, (1 ; h). Moreover, the eciency wage will decrease with the probability
of being caught while shirking, p. A better monitoring technology will increase the
unemployment probability for each worker who decides to shirk, leading to a lower
expected utility of shirking. Similarly, a decrease in the disutility of eort, e, will
imply a lower opportunity cost of not shirking, which will lower w1 .
One can see that, the probability of nding a job in a boom will not aect the
eciency wage of the rst period. The positive eect of z on w1 will be completely
oset by its positive eect on the second's period wage in a boom, w2B . The latter
will decrease w1 by raising the expected opportunity cost of being unemployed in the
second period.
Finally, the eciency wage will depend positively on the probability of being red
for cyclical reasons. As the probability of being red in a recession increases, expected
job tenure falls and so does workers' expected utility from being employed. Workers
view a long job tenure as a form of compensation. Thus, if for any reason expected
job tenure decreases, wages should increase for workers expected utility to remain
constant and vice versa. In the context of this model, a long job tenure implies a low
value of q and h. One can see from equation (4) that the probability of being red
in a recession, q, depends negatively on the expected level of employment after the
realization of a negative productivity shock, E (N2jv < 0) . In gure 1 the NSC is
satised at a wage rate equal to w. As expected job tenure increases, the expected
utility from non shirking will now exceed the expected utility from shirking. This
implies that the NSC is now satised for a lower level of wage. The NSC shifts to the
left and the level of the eciency wage decreases to w0 .
From Proposition 1 and equation (4) follows that w1 will depend positively on
. Thus, an increase in the variance of the productivity shock will shift the NSC in
gure 1 to the right and the eciency wage will increase to w00 .
9
By substituting equation (4) in (17), one can see that the eciency wage will be
a positive function of employment: as employment increases, the probability that a
worker will be red if there is a recession in the next period becomes higher. The
positive relationship between employment and the wage rate that satises the NSC is
described in gure 2. The LD line gives us the expected marginal product of labour.
We assume that the productivity shock in the rst period equals its expected value
so that the equilibrium level of employment is determined at the point where the
marginal productivity condition is satised:
agN1a;1 m = w1
(18)
where m = E (). Employment in the rst period is determined at point E in
gure 2.
3. Firm-specific training
We will now consider rms' decision to invest in specic training for the whole
labour force. Training requires an additional level of eort for each worker in the rst
period so that
e1 = e + b:
(19)
Given that shirking is a choice, workers will provide this higher level of eort
during the training period only if the wage they receive satises the non-shirking
condition. This implies that rms bear the total cost of training by compensating
fully their employees for their higher level of eort in the rst period. Returns to
training are realised in the second period. We assume that these returns by the rm
are not threatened by the possibility of a premature quit. An increase in the per
worker eort by b due to training in the rst period will increase productivity by r(b)
in the next period. r(b) is a twice dierentiable, strictly concave function that can
10
represent an index of worker quality.6 This implies that uncertainty over investment
returns stems only by the uncertainty of the economic environment:7 The expected
return the rm attaches to training is
E (R) = hr(b)E (N2 jv < 0) + (1 ; h)r(b)N1
(20)
The introduction of training makes the prot maximization decision of the rms
dependent across the two periods. Expected prots in the two periods are given by
E () = 1 + E (2 )
= Y1 ; w1T N1 + E [Y2 ; w2N2] + hr(b)E (N2 jv < 0) + (1 ; h)r(b)N1(21)
where w1T is derived by substituting equation (19) in the NSC of the rst period
and soling for w1.
w1T = d + e + pb + pe hq(1 ; p)
(22)
In period 2, there is no uncertainty and employment must satisfy the following
FOC:
gaN2a;1 + hi r(b) = w2i
(23)
where i = R; B , hR = 1 and hB = 0.
Solving equation (23) for N2 gives the equilibrium level of employment in the
second period for i = R:
e ; r(b)p ) a;1
N2 = ( pd + pga
(24)
1
According to Hart and Moutos (1995), this index may represent the speed at which the product
is produced or the number of salable units achieved at a given rate of production so that more
investment leads to more saleable units.
7 Hashimoto (1979, 1981) among others investigates the importance of uncertainty over investment
returns to specic training when there is uncertainty over r(b).
6
11
From equation (24), it is easy to see that employment in a recession will depend
positively on the level of b so that the introduction of training will lead to higher
employment in period 2, #N#b2 > 0. Firms will be more reluctant to re workers after
a negative productivity Shock, since this is associated with losing part of the rent
created by training. Moreover, by taking the conditional expectation of equation
(24) we can see that the level of training will have a positive eect on the level of
expected employment in a recession.
#E (N2 jv < 0 ) > 0
#b
One can see from equation (12) that an increase in E (N2jv < 0) will have a
negative impact on the eciency wage in the rst period.
In period 1, rms choose the level of employment and training that maximizes
ex-ante prots, given the level of the real wage that satises the NSC. The rst order
condition with respect to employment from equation (21) is:
gaE ()N1a;1 + (1 ; h)r(b) = w1T + w1TN1 N1
(25)
Solving for employment in the rst period (25), gives:
dp ; r(b)p(1 ; h) ) a;1
N1 = ( e(p + h(1 ; p)) +pcbe+
am
1
(26)
The rm's choice variable for investment in specic training is b. After some
rearrangements, the rst order condition with respect to b can be written as:
hc(1 ; p)e
F = r(b)bE (N2 jv < 0) (1 ; a)(
e + dp ; pr(b))
; f Np1 ; r(b)b[hE (N2 jv < 0) + (1 ; h)N1 ]g = 0
12
(27)
The rst part of equation (27) reects the decrease in labour cost due to the
reduction of the dismissal probability for cyclical reasons and the remaining part
represents the dierence between the marginal cost of training and the expected
marginal return of investment in the second period. Solving equations (26) and (27)
for N1 and b, gives the optimal values of employment and investment in rm-specic
training.
Proposition 2:
Assuming that b0 is the level of b that equalizes marginal cost with expected marginal
return to training, the negative impact of rm's investment in training on workers'
expectations for future employment will increase the optimal level of investment in
rm-specic training , b , so that b > b0
Proof: Assume that b0 is the level of training which equalizes marginal cost with
expected marginal return to investment. If one substitutes b0 in equation (27), the
second term of the equation will equal zero. Given that the remaining part of equation
(27) is positive for positive values of b, b = b0 does not satisfy equation (27). F = 0
will be satised for a higher level of b if Fb < 0. The derivative of equation (27) with
respect to b is negative since E ()bb < 0.8
Finally, we want to compare the level of b derived by equations (26) and (27) with
the optimal level of training in the absence of uncertainty, h = 0.
Proposition 3:
Uncertainty will lead to a higher level of investment in rm-specic training if the
negative impact of investment returns on eciency wages exceeds the expected loss of
investment returns due to a reduction in the workforce in a recession.
Proof:
The stability condition E ()N1 N1 < 0 and E ()N1 N1 E ()bb ; E ()N1 b E ()bN1 > 0 is satised
for reasonable parameter values.
8
13
If h = 0, then equation (27) becomes F = 1p ; r(b)b = 0. Assume that b satises
F = 0. By substituting b in equation (26) and then in (27) we obtain:
#w1T ) ; h( N1 (b) ; E (N2(b)jv < 0) )
F (b) = #r
(b)
N (b)
1
(28)
Given that Fb < 0, b > b if F (b) > 0.
4. Conclusions
The model presented above examines the decision to invest in rm-specic training
in a stochastic eciency wage model. It investigates a neglected positive aspect of job
security provisions: the wage reduction associated with the lower unemployment risk.
A prediction of the model is that expected job tenure will decrease with the volatility
of output. A short expected job tenure will induce rms to oer high wages in order
for workers to have an incentive to provide a positive level of eort. A decrease in
the volatility of output through stabilization policy will lower wages and stimulate
employment. This result is consistent with the empirical ndings of Abowd and
Ashenfelter (1981), Adams (1985) and Li (1986), suggesting that industry dierences
in wages can be explained by dierences in unemployment risks.
Firms' investment in rm-specic training will have a negative eect on the eciency wage by decreasing the unemployment risk. This implies that in an eciency
wage framework, part of the investment cost will be oset by the reduction in labour
cost due to lower employment uncertainty. This indirect negative training eect on
wages will have a positive impact on rms' optimal level of investment in rm-specic
human capital and it will oset at least part of the negative eect of economic uncertainty on this investment.
14
5. Appendix
Proof of Proposition 1
We know that log() N (0; 2). One can write
v = log() as v = z where z N (0; 1).
Thus,
1
E ( 1;a jv < 0) = E (exp( 1 ;1 a z)jz < 0)
(29)
Given that pdf (z < 0) = 0:5, the conditional probability density function
of z is given by
(z) = 2pdf (z)
pdf (zjz < 0) = pdfpdf
(z < 0)
(30)
Thus (29) can be written as
E ( jv < 0) = 2
1
1 a
;
Z1
0
p1 exp( 1;;za ; 12 z2 )dz
2
(31)
By multiplying and dividing by p12 exp( (1;2a)2 ), (31)
can be written as
Z 1
1
E ( 1;a jv < 0) = 2exp( 2(1 ;1 a)2 2) p1 exp(; 21 (z + 1 ; a )2 )dz
0
2
= 2exp( 2(1 ;1 a)2 2)[1 ; ( 1 ; a )]
(32)
The derivative of (32) with respect to is given by:
2
[ 2 exp( 2 )[ (1 ; ( )) ; ( )]
1;a
2(1 ; a) 1 ; a
1;a
1;a
15
(33)
() is the quantity
Note that () = 1;(
)
known as the inverse of Mills' ratio or the hazard rate and that
d() = ()[() ; ] > 0
d
(34)
This implies:
(1 ; ()) ; () < 0
(35)
It is easy to see that (33) will always be negative.
16
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17
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18
Table1: TIMING OF EVENTS
Period 1
Period 2
The productivity shock
1 is realized
1 = E ()
The productivity shock
2 is realized
Firms set w1 and N1
Firms set w2 and N2
Workers choose e
Workers who choose e = 0
will get red with
probability p
Workers who choose e = 0
get red with probability p
If 2 > E ()
unemployed workers
get a job with probability z
If 2 < E ()
employed workers
lose their job with probability q
19
Figure1: The non-shirking condition
EU N ; EU S
0
w0
w
20
w00
w
w
Figure2: The equilibrium level of employment
LD
w
1
NSC
E
N1
21
N