HB31
.M415
working paper
department
of economics
THE STRUCTURE OF WAGES AND
INVESTMENTS GENERAL TRAINING
Daron Acemoglu
Jorn-Steffen Pischke
No.
97-24
November, 1997
massachusetts
institute of
technology
50 memorial drive
Cambridge, mass. 02139
WORKING PAPER
DEPARTMENT
OF ECONOMICS
THE STRUCTURE OF WAGES AND
INVESTMENT IN GENERAL TRAINING
Daron Acemoglu
Jorn-Steffen Pischke
No.
97-24
November, 1997
MASSACHUSEHS
INSTITUTE OF
TECHNOLOGY
50 MEMORIAL DRIVE
CAMBRIDGE, MASS. 02139
The Structure
and Investment
Daron Acemoglu
MIT
of
Wages
General Training
in
Jorn-Steffen Pischke
MIT
*
and University of Chicago
November 1997
Abstract
In the standard model of
for general training.
firms
may
human
When
capital with perfect labor markets, workers
pay
labor market frictions compress the structure of wages,
invest in the general skills of their employees.
The reason
is
that the
wage structure turns "technologically" general skills into "specific" skills. Labor market frictions and institutions, such as minimum wages and
union wage setting, are crucial in shaping the wage structure, and thus have an
important impact on training. Our results suggest that the more frictional and
regulated labor markets in Europe and Japan may generate more firm-sponsored
distortion in the
general training than the U.S..
Keywords:
Imperfect Labor Markets, General
Human
Capital,
Firm Sponsored Training
JEL
Classification: J24, J31, J41
We
thank Kevin Lang, Sherwin Rosen, Eric Smith, Robert Topel, Michael Waldman, and varFinancial Support from the German Federal Ministry for
Research and Technology and National Science Foundation Grant SBR-9602116 (Acemoglu) is gratefully acknowledged.
*
ious seminar participants for comments.
Digitized by the Internet Archive
in
2011 with funding from
Boston Library Consortium IVIember Libraries
http://www.archive.org/details/structureofwagesOOacem
Introduction
1
In the standard theory of
human
capital as developed
and
human
distinction between general
specific
the current employer are specific whereas
by Becker (1964), there
capital. Skills
skills
this paper,
human
capital,
which are as useful with some other
and employers have no incentive to
we develop the theory
of hiiman capital
when
all
the benefits of
invest in these skills. In
labor markets are imperfect. In
contrast to the standard theory, labor market frictions imply that firms
to invest in the general skills of their workers.
a sharp
which are only useful with
employer are general. In competitive labor markets, workers capture
their general
is
In particular,
if
may be
willing
these frictions distort
the structure of wages within the firm away from the competitive benchmark and to
the benefit of unskilled workers,
with general
general
skills.
skills,
We
credit
it
will
be profitable
for the firm to
find that contrary to conventional
wisdom,
market problems are neither necessary nor
labor market imperfections which
make
provide workers
for firms to
sufficient.
pay
for
The key
is
technologically general skills effectively specific,
because trained workers do not get paid their
full
marginal product when they change
jobs.^
The
link
between the structure of wages and training enables us to investigate the
impact of labor market institutions on human capital accumulation. There are important
differences
between labor market institutions of Anglo-Saxon economies. Continental
Europe and Japan. For example,
in contrast to the U.S.
Sweden unions play a very important
fioors set
role in
and the U.K.,
Germany, and
wage determination, and there are wage
by minimum wages and unemployment
benefits.
Many
these institutional differences compress the structure of wages
1996,
in
economists believe that
Blau and Kahn,
(e.g.
Edin and Topel, 1997). Comparisons of wage dispersion and returns to education
support this view. For example, in the raid 1980s, the log difference of ninetieth and tenth
percentile wages
was
1.73 in the U.S., 1.11 in the U.K. as
0.67 in Sweden, 1.22 in France and 1.01 in Japan
believe that distorted
in
human
opposed to 0.83 in Germany,
(OECD,
1993).
Many
wage structures reduce not only employment, but
capital (e.g.
Lindbeck, et
compressed wage structure
will
al.
1993).
economists
also investments
In contrast, our theory predicts that a
induce firms to pay for training, even though the
technologically general. Therefore, the
European and Japanese labor market
skills
are
institutions
^In the standard theory, firms pay for skills that are specific, and which skills are specific is determined
by technology, hi contrast, we focus on skills that are technologically general, in the sense that absent
frictions, they will be as useful with other employers. Market structure and institutions determine, in
equilibrium, which skills are turned into effectively "specific" skills. Becker (1964) realized that this
may happen when he wrote that "in extreme types of monopsony ... job alternatives for trained and
untrained workers are nil, and aU training, no matter what its nature, would be specific to the firm."
(p. 50, 3rd ed.), but did not pursue this further.
may
contribute to, rather than reduce,
human
capital accumulation. In line with these
predictions, the incidence of training appears to be higher in
the U.S.:
OECD
(1994, Table 4.7) reports that 23.6 percent of
Germany and
71.5 percent of those in
training.
By way
67.1 percent of
new
young workers
hires in
in the U.S.,
which has a
any formal
less distorted
wage structure and
less training
than
evidence that firms bear part of the cost of investments in
is
technologically general
in France,
seven years of labor market experience.^
first
other countries, there
in
Japan receive formal
of comparison, only 10.2 percent of U.S. workers receive
training during their
Even
Europe and Japan than
For example, Barron, Berger and Black (1997) report
skills.^
that productivity growth associated with training exceeds wage growth by a factor of
ten,
even though firms claim that most of this training
Further,
many temporary
is
valuable at other employers.
help agencies in the U.S. also provide general training to
employees, such as computer and typing
and
1993). Studies of the costs
skills,
and bear the monetary
new
costs (Krueger
prodiictivity of apprentices have also typically concluded
that apprentices do not pay for the
Ryan
In particular,
full cost of training.
(1980)
reports sizeable net costs of apprenticeship training in a U.S. shipyard. Similarly, von
Bardeleben, Beicht, and Feher (1995) find that the net costs of training are substantial
in large
German
firms,
even though the content of these programs are highly regulated
and apprentices are given exams by outside boards, which implies that the
skills
are
mostly general.
The main
idea of our paper can be explained using Figure
of a worker, /(r), as a function of his
employer and work
for
that he will receive his
/(r)
—
skills, r.
another firm, and in the process, he incurs a cost A. Assuming
full
product upon quitting, the worker's outside option
So the worker receives
i(;(t)
=
/(r)
— A.
incentive to invest in the worker's skills because
irrespective of the value of r.
as the special case with
the general
is
A =
skills of their
The
0,
>
r.
is
v{t)
=
and keep the
In this case, the employer has no
its profits
are equal to /(r)
— w{t) =
A
be thought of
so in competitive markets, employers do not invest in
employees. Next consider the case where the wage structure
skilled workers), that is /(r)
— w{t) = A(r) and
now makes
greater profits from
as the dotted curve in the figure.
workers with high
this outside option
perfectly competitive labor market can
compressed (distorted against more
A'(r)
which draws the product
Siippose that this worker can quit his
A. Suppose that the current employer can pay
worker.
1,
The
firm
Therefore, as long as the costs of worker training are not too large,
^However, it has to be borne in mind that these training data are collected using different methods
and are not easily comparable.
^The evidence in Bishop (1987) suggests that in the U.S., wages across workers doing the same job
in the same firm differ much less than productivity, so that even in the U.S., the structure of wages is
distorted against more skilled workers.
f(T)
f(x)
^^^^__
/y<r \
f(T)
-A
W(T) =
f{T)
- A(T)
\
\
/
=
w(t)
,-----
Finn-sponsored
training
No
firm-sponsored
training
Figure
the firm will invest in
The main
r.
The Wage Structure and Training
1:
This
contributions of
is
the basic story of our paper.
om paper are the focus on how labor market imperfections
transform technologically general
the structure of wages and training.
distort the structure of
be discussed
may
Our
finding on
how
wages and encourage training are
in Section 2,
distorted, firms
and the
skills into specific skills
which
will also establish that
invest in general skills
link
we draw between
labor market institutions
also novel.
when the
and workers may
These
results will
structure of wages
not, even
is
when workers
have access to perfect credit markets.
Why
should the structure of wages be distorted against more skilled workers?
analyze this issue in Section
as imion
wage
setting
3.
We
show that a range
We
of labor market institutions, such
and minimum wages, and plausible
frictions,
such as search, infor-
mational asymmetries and efficiency wages, can lead exactly to this type of distortion.
Further, even
when
trading in the labor market
technologically general and specific skills
of their workers.
may
is
frictionless, the interaction
between
induce firms to invest in the general
skills
Therefore, our model predicts that in a variety of circumstances,
we
should observe firm-sponsored investments in general training. Moreover, such invest-
ments should be more common when labor market
structure of wages against
more
skilled workers.
frictions
and
institutions distort the
Other papers on firm- sponsored invest-
ment
in general training
have investigated much more specific models, some of those
we analyze
similar to the ones
and so they
in Section 3,
will
be discussed there.
Partial Equilibrium
2
The Environment
2.1
Consider the following two-period model. In period
how much
choose
r G
There
IR+.
is
to invest in the worker's general
no production
by
in this period
u!{t),
<
For example, u[t)
which
1,
the worker and/or the employer
human
and we denote the wage of the worker
in the first period,
conditioned on the training that the worker receives.
is
payment from the worker to the
represents a
the worker either stays with the firm and produces oiitput and
as a function of his skill level (training) r, or he quits
assume that with probability
to be productive together
q,
which we denote by
capital,
is
In period
firm.
2,
paid a wage rate, w{t)
We
and obtains an outside wage.
the firm and the worker receive a negative shock, cease
and separate. With probability
1
—
the worker and the
<?,
firm can continue their productive relation, q will therefore be a measure of turnover in
our model. There
is
no discoimting, and
all
agents are risk-neutral and have preferences
defined over the unique good of this economy.
—
Each worker produces output y
capital of other workers."*
The
/(r)
cost of acquiring r imits of
is
an increasing, differentiable and concave function.
skill is
c{t) in terms of the final
by the firm (although the worker can pay
c{r)
everywhere
is
and hmr^oo
c'{t*)
—
c'(t)
it
by having ^{t)
oo.
These ensure that the
good and
<
and convex, and
but serves to highlight the economic mechanism we are interested
may
We
we
will discuss
how
technologically specific
The
consider two cases below.
first is
worker cannot make any transfers to the firm
In terms of our notation, u){t)
^This assumption
human
capital
adjusted
freely,
H
is
not as restrictive as
and physical
capital
the output of a worker y
an optimizing firm
will
it
skills is
extreme,
0.
the presence of
in:
and general
providing him with
=
The second
0.
appears.
K, F{H,K),
human
capital.
skills interact.
human
For example,
if
case
is
for the
total output
is
exhibits constant returns to scale
human
capital,
K/H,
capital, nor
expenses
the perfect credit
/(r) will be independent of the level of
keep the ratio of physical to
=
the credit constrained regime where the
for
>
c(0)
given by
can he take a wage cut during training in order to compensate the firm
of training.
=
is
transform technologically general capital into firm-specific
In Section 3.6
incurred
is
assume that
c'(0)
>
cost of training, r*
assimiption that there are no (technologically) firm specific
frictions
We
0).
first-best training level, r*,
and from the assumptions on the
/'(r*),
The
for
strictly increasing, differentiable
=
number and human
/{t) independent of the
a function of
and
H. This
constant.
K
is
can be
because
markets regime where the worker
is
<
not affected by credit constraints, so uj{t)
is
possible.
Training in a Perfectly Competitive Labor Market
2.2
If
a worker quits after the
first
period, she receives a
wage
of v{t) in the outside labor
market. In this section, we take the outside wage structure v{t) as given and look at
the determination of the internal wage structure w{t).
labor market
is
=
competitive, which implies v{t)
To
/(r),
start with,
suppose that the
and the worker can
and
qiiit
take a job in the outside market at no cost. Therefore, workers have to be paid their
marginal product:^ iu{t)
full
Proposition
Then r
competitive.
Due
—
we
v[t)
=
/(r).
The
following result
are in the credit constrained regime
is
immediate:
and labor markets are
0.
to the severe credit constraints, the worker cannot be
training, so
is
1 Suppose
=
made
to bear the cost of
no investment takes place, even though the optimal amoimt of training,
strictly positive. It
is
sometimes asserted that credit constraints faced by workers
induce firms to invest in general training. Proposition
1
r*,
may
shows that credit constraints
are not sufficient for firm sponsored investments in training.
Before
we turn
to the core of our analysis,
it is
also useful to state the
of Becker (1964), that with perfect credit markets, first-best training
workers pay
for
main conclusion
is
achieved and
it.
Proposition 2 (Becker) Suppose we
bor murkets are competitive. Then t
are in the perfect capital markets regime
—
and
t*
cu{t*)
=
and
la-
—c{t*).
Note that the presence of separations with probability
q
is
of
no consequence because
the worker will get exactly the same returns for his general himian capital in the outside
market.
2.3
Frictional
In this section,
is,
Labor Markets with Credit Constraints
we model
frictional labor
despite that fact that r
firm,
he
section,
v{t)
will get a lower
we
and
general
wage than
discuss in detail
its
is
how
relation to /(r).
his
markets by assuming that v{t)
human
capital,
if
<
/(r).
That
the worker separates from the
marginal product in the current firm. In the next
different forms of frictions
For now, the fact that v{t)
'Recall that marginal product of the worker
is
and
<
equal to /(r) not /'(r)
institutions determine
/(r) imphes that there
is
a surplus that the firm and the worker can share
when they
are together.
We
we adopt the Nash bargaining approach.
exposition in this section,
For the
also start with
the credit constrained regime and return to the case of perfect credit markets below.
Asymmetric Nash bargaining and risk-neutrahty imply that w{t), the wage
current firm,
is
=
Iu{t)
where
/?
6
firm, that
[0, 1]
is
is
v{t)
how much profit
the firm would obtain
loss of generality,
important point to note
level of training
over the
wage
-
v{t)
rate.
ttq
(1)
,
is
the outside option of the
the worker
we normalize
ttq
to
left
and took alternative
0.
is
independent
a feature of the temporal structure of our economy.
is
chosen by the firm, and then the worker and the firm bargain
is
At
if
TTo]
that the equilibrium wage rate w{t)
is
of c{t), the cost of training. This
The
+ P [/(r) -
the bargaining power of the worker,
employment. Without
An
at the
this point the training costs are already sunk.
Profits of the firm are:
7t{t)
= {l-q)
[fir)
-
where we have incorporated the
separation,
and
the worker
is
(1
-
/?)(!
-
with probability
q) [/(r)
q,
-
v{t)]
-
c{r).
there will be an invohmtary
the costs of training are borne by the firm because
all
The
credit constrained.
=
c{t)
fact that
imposed that
also
-
w{r)]
firm chooses r to maximize
7r(r),
which gives the
first-order condition:
(l-/?)(l-g)(/'(f)-./(f))-c'(f)
The
necessary condition for f
capital of the worker,
is
7r'(0)
>
that
0,
>
tional,
P <
1,
and
q
<
1.
Then
are: /'(O)
as long /'(O)
in general skills.
This
the central result of our paper.
workers.
The
=
>
0,
human
necessary conditions for firm
v'{0)
and
(1
—
/3)(1
—
q)
>
0.
condition,
>
v'{0),
the firm
loill
invest a positive
In contrast to the case of competitive labor
may have an incentive to invest
/'(O) > '''(O), nests the key idea of
markets, in frictional markets, the firm
skills of its
(2)
are in the credit constrained regime, labor markets are fric-
amount
is
0.
for the firm to invest in the general
Since c'(0)
0.
sponsored investment in general training
Proposition 3 Suppose we
is
=
in the general
otu model;^
it
^The additional requirements that /3 < 1 and g < 1 are straightforward to understand. They ensure
that the firm gets some rents from the relation, that is some of the bargaining power is vested in the
firm
and the
relation does not
end with probability
1.
implies that the
wage structure
the firm to invest in the general
wage
pay w{t), that
will
it
structure
is
/'(r)
>
is
+
/3/'(r)
profits
distorted only
relevant to the firm
is
librium training,
wage
linked to the external
(1
-
(2)
to ensure f
wage structme
>
v'{t)
equivalent to
is
and the firm
<
>
/3
r*
and
=
(/?
is.^
wage structure encourages firms
than the
0,
v'{t*)
g
=
0,
>
0,
and
or
if
^>'{t*)
=
for training, equi-
first-best training level, r*.
>
g
pay
to
it
In
immediately follows from
are necessary but not sufficient
t*).
A key comparative static result is immediate.
Let
=
?;(t)
av{T)
+ b.
Then, everything
being equal, a reduction in a increases investment in training, r (see equation
else
the
structure, v{t). hi particular,
Therefore, /'(r)
P)v'{t).
f, is generally strictly less
that f
=
external
distorted
particular, as long as
equation
is
from trained workers. In other words, the internal wage structure
when the
Even though a
A
What
the worker.
w'{t), so that wages increase less with skills than does productivity
makes higher
is
=
implies w'{t)
(1)
skills of
the internal wage structure. However, the internal wage
is
endogenous, and
compressed at the point of no training, enconraging
is
(2)).
decrease in a reduces the outside option of skilled workers relative to the outside
opportunities of the unskilled, compressing the wage structure.
This implies that the
firm can capture additional rents from the skilled, so
more
skills.
Therefore, contrary to conventional wisdom, a
can improve
human
invests
it
in the worker's
more compressed wage structure
capital investments.
Another useful comparative
ately implies that df/dq
benefits from training
<
0.
static result
is
with respect to turnover,
q.
(2)
Therefore, turnover reduces training, because the firm only
when the worker
higher turnover makes this less
likely.
stays
It is
and produces
represents an important market failure
(e.g.
second period, and
in the
often argued that high turnover economies
such as the U.S. do not generate sufficient investments in worker
skills,
and that
Ward
(1992) find that the
with ten years of experience
Pischke, 1998) or two
are
much more
is
or f
suggests
'This
make
is
=
r* irrespective of the level of
why high
in
q.
it is
one (Acemoglu and
Germany, where young workers
formal training (see also
OECD,
1994).
But the
state-
failures are difficult to interpret against
the backgroimd of Becker's model of training: as
=
market, while
(Dustmann and Meghir, 1997)
ments regarding turnover, training and market
f
For ex-
median number of jobs held by male worker
six in the U.S. labor
likely to receive
this
Blinder and Krueger, 1996). Indeed, cross-
sectional comparisons reveal that high turnover countries have lower training.
ample, Topel and
immedi-
we
saw, in competitive markets either
Our model explains these
turnover causes low training, and
why
a feature of Nash Bargaining. Other bargaining solutions
this
may
correlations
and
represent a market
will give similar results,
the dependence of the internal on the external wage structure less transparent.
but would
failure.^
While we
stress that
find
it
is
an important link between general training and turnover, we should
not differences in worker mobihty which lead to variations in firm-
sponsored training.
To
see this, suppose that differences in q are being generated
differences in workers' costs of
not
by
differ
may be
moving
=
A'(r)
skill level (i.e.
to a
new employer, A. As long
0), as in
the baseline case in Figiu-e
training. In the
=
same
vein, the presence of turnover
/'(t) everywhere, there
A
2.4
the firm
is
not sufficient for
not sufficient for training: with
is
would be no training irrespective of the value of
q.
Note on Welfare
Interestingly, the distortion of the
is
1,
do
able to extract a fraction of the rents created by imperfect mobility, but will
not invest in training. Therefore, the mere presence of mobility costs
?/(r)
as these costs
by
wage structure may actually improve
the well-known theory of the second-best at work.
and cannot
invest in their general skills, training
distortion, in this case in the labor market,
may
If
welfare.
This
workers are credit constrained
outcomes are
inefficient.
Another
induce firms to undertake some of these
investments, and improve output and welfare.
If
labor market frictions did not affect any other choices, a
to v{t)
1,
=
af{T)
+
b
with a
would increase human
eqinlibrium training f
frictions will
<
tilting
1, i.e.
the outside wage function
This
capital investments.
=
<
r*
when
7;(t)
have a number of allocative
need to be compared to the benefits
in
move from
=
costs,
v{t)
down
will also increase net
=
/(r)
as in Figure
output since
Naturally, in practice, increased
/(r).
such as lower employment. These costs
terms of better training incentives. In any case,
the implications of labor market frictions on training are worth bearing in
mind when
suggesting labor market reforms. For example, proposals for reducing union power and
removing other regulations
ical
in the
labor market, which are on the current polit-
agenda, could have unforeseen consequences regarding the
system where employers pay
2.5
German
German
apprenticeship
for the general training of their workers.
Firm Sponsored Training Without Credit Constraints
We now
discuss the impact of labor market frictions on training in the presence of
perfect capital markets.
The
trTith is
presiimably between these two extreme cases, but
our analysis in this section will give the general idea.
^Since f
<
r*, a further reduction in f
would reduce
Most important, we
welfare. Also note that
if
find that
the training differences
across countries are due to variations in the intensity of specific training, the standard theory would
no market failure.
through formal training programs.
predict the negative relation between turnover and training, but there would be
However, we find
this unlikely
because most observed training
8
is
common
contrary to
market problems are not necessary
beliefs, credit
the cost of general training. Whether they do or not
for firms to bear
once again determined by the
is
labor market imperfections and institntions which shape the wage structure.
We
also
assume that training investments by firms and workers are chosen non-
cooperatively. In particular, the worker
and the firm simultaneously choose the amount
of money they wish to spend on training, respectively, c^ and c/.
+
y{Tnc)
(1
Intuitively,
wage
The
=
such that c{Tnc)
is T-nc
is
-
+
c-w
"
Q)P[f{'^nc)
+
(1
—
-
^{Tnc)]
with probability
Pfir)
Cf, 01 Tnc
—
I
c~^{cw
+
C/).
by clioosiug
Cyj
probability
q,
he
is
order condition for the worker's contribution
first
v'{rnc)
+
Thcu
>
tlic
and
and taking
c„,
=
nothing from
its
—
(1
q){l
— j3)
—
[f{Tnc)
if
investment in the worker. The
first
is
essentially the
generically,
one of them
same
as (2).
parties will bear the full cost of training.
'T-nc
—
"^f-
-^^
contrast
if
t^
>
>
Despite the fact that training
the firm
may end up
paying
More
to
is
(3)
by choosing
c/
>
a quit, and the firm gets
is
>
<
if
c/
=
implication
precisely, let r^
general,
is:
(4)
0,
is
be the
little
or
all
level of training
all
the cost of training
and
the cost of training,
and
is
not credit constrained,
our results that
no contribution from workers) to be
be severely credit constrained.
the firm to pay for training.
economies with compressed wage structures
that one of the
Then:
(4).
and the worker
observe that the more distorted the wage structTire
the more likely
Cf
for all the costs of training. Therefore, for
firms pay for general training (with
we do not need the workers
—
c/
then the worker bears
is
=
if
t^ then the firm will bear
Tf,
c^
=
The
that satisfies (3) as equality, and r/ be the solution to
Tf
>
Inspection of equations (3) and (4) implies that
will hold as a strict inequality.
Proposition 4 Suppose
receives v{t).
order condition for the firm
(l-<?)(l-/3)[/'(T„e)-^/(r„,)]-c'(r„,)
which
and
C^
if
v[Tnc)\
Note that with probability q there
as given.
maximize
is:
<
maximizes
will
take c/ as given.
will
forced to quit,
{l-q)P[f{Tnc)-v'{rr,c)]-c'{Tnc)
Similarly, the firm
worker
of training
the worker stays with the firm and in this case his
q,
With
P)v{t).
Cyj
=
The amoimt
is (i.e.
the lower
Therefore,
siich as
It is
OTir
true,
also interesting to
is ?/
relative to /'),
model predicts that
in
Germany and Sweden, employers
should pay for general training, while in the U.S.
it
may be
cost of a range of training investments (such as vocational courses).
firm
is
paying
for training, a further distortion in the
whereas when workers are paying
wage structure
(3)
for the firm
and
makes
the
wages
will
shows that, somewhat paradoxically,
(4)
more
it
the
increases training,
for training, a distortion in the structure of
reduce training. Finally, inspection of
a larger bargaining power
who bear
Moreover, when
the workers
likely that the firm, rather
than
the worker, will finance the costs of training.
The
analysis in this subsection assTimed that contributions to training are
coop eratively,
in period
in the sense that the firm
and the worker did not write a binding contract
determining training and second-period wages.
1
It is
generally appreciated
that these types of contracts are difficult to write and enforce. Nonetheless,
tive to also analyze the case
make
longer possible to
because
where training decisions are made cooperatively.
how
predictions regarding
contract for a higher wage in period
2.
What
of interest, however,
is
0,
when
higher training because v{t)
Specific
The
no
1
and
that even in the
is
As
generally suboptimal.
is
<
who
will also benefit
from
his
/(r).^
Mechanisms and the Role of
Institutions
previous section described our simple theory of firm sponsored investment in general
training.
We
It is
the firm and the worker decide to increase training, they will create
a positive externality on the worker's future employers,
3
instriic-
the cost of training will be shared,
presence of cooperative investments, the amount of training
>
it is
always possible for the worker to pay more for training in period
it is
long as g
made non-
The key
ingredient was a compressed
wage structure such that
found that the crucial condition to ensure
this
>
/'(r)
is
v'{t), that
opportunities for the worker should improve less than his productivity
more
skills.
v{t),
is
worker,
Therefore, the shape of the outside wage function in the
of crxicial importance.
it is
Even though
an equilibrium object. In
this
is
this section
/'(r)
is,
when he
>
w'{t).
outside
acquires
skill- wage
space,
taken as given by the firm and the
we
discuss
how a range
of plausible
labor market frictions lead to a distortion in the external wage structure, v{t), inducing
firm sponsored training.
We
place special emphasis on the role of different institutional
arrangements in influencing v{t) and equilibrium training. Throughout
simplify our discussion by assuming that the worker
cannot pay
for
any of the training
^The exception
is
the
model discussed
marginal product of the worker with the
(1997) for a
more
costs, so
is
severely credit constrained,
we only study
in subsection 3.6,
new employer
10
we
and
the firm's incentives to invest
where v{t)
is
less
than /(t) but equal to the
Acemoglu
model with search
so that there are no externalities. See
detailed discussion of this type of inefficiency in the context of a
frictions.
this section,
Our aim
in skills.
each model
in this section
major ideas rather than analyze
to bring ont the
is
For this reason we keep the exposition as simple as possible.
fully.
Minimum Wages and Other Wage
3.1
Floors
common intervention in the labor market is the imposition of wage
floors, due to minimum wages and high reservation wages caused by unemployment
benefits. Minimum wages and replacement ratios are relatively low in the U.S. and the
Perhaps the most
U.K. as compared to the higher
do these
levels in
France and other European economies.
How
institiitional differences affect training?
minimum wage can never lead to more
training when labor markets are competitive (Rosen, 1972). The intuition for this result
is simple: because workers pay for training through lower wages, a minimum wage may
well
It is
known
that the imposition of a
prevent the firm from reducing wages enough during the training period.
rationale behind the introduction of "training subminima" in
wage
moving
consider a labor market with frictions, where v{t)
cost, unrelated to skill.
and of
power {P
=
1)
so that w{t)
Next consider a wage
benefits
=
=
minimum
/(r)
— A, due
to, say,
not distorted, thus
is
Also suppose that the firm has
0.
all
(2)
is
kinked at
is
wm,
a
from the
the bargaining
floor
wm
due to either minimum wages or imemployment
which increase the value of unemployment to workers (independently of
structure of wages
which
=
^(r).
skill).
then:
iu{t)
= max {wm, f{r) - A}
thus distorted at low levels of
maximize /(r) — w{t) —
to
the
important to realize that this distortion does not
It is
lead to firm-sponsored training; v{r)
itself
previous section would imply f
The
recent U.S.
is
laws.
Now
in
many
This
c{t).
We
will
have f
>
(5)
,
r.
The
firm then chooses r
as long as the firm chooses to
operate, because the condition for a positive training level, a distortion in the structure
of wages,
is
satisfied.
Hence, in the presence of labor market frictions,
will increase training (unless
they induce the firm to shut down).^°
Notice the stark contrast of these predictions to the standard
With competitive markets, a minimum wage
^°
T*
.
The
=
just below /(O)
human
is
capital model.
most detrimental to
exact level of training depends on the relative positions of the kink in the wage relation and
In particular, let r be such that /(t)
operate and choose t
f
minimum wages
T*. Finally,
if
r
>
—
t*
t.
If
r
>
r*
and /(t*) <
- A =
c{t*)
Then,
ium-
and /(r*) >
+ wm,
c{t*)
or
not to operate.
11
if
t
+ wm
<
r*
f < r* and c{t) < A, the firm will
then the firm will operate and choose
if
and
c{f)
> A,
then the firm
will
choose
the accumulation of general
a wage cut in the
>
minimum wage would
such a
=
w'(0)
capital because
0,
results
training where workers bear the costs,
regarding the impact of
is
prevents the worker from taking
down
not shut
the firm, and woiild
and those based on Becker's theory
minimum wages on
training.
At the international
is
mixed. Leighton and Mincer (1981) find negative
and positive
effects for
effects of
the
level,
minimum wages
male workers
Sicilian (1997) find negative effects for
women.
Unions
3.2
Another important institutional difference across economies
Germany and Scandinavian
tion,
our
level,
consistent with the pattern that the more heavily regulated European labor
on training, while Grossberg and
In
of general
instructive to look at the empirical evidence
it is
markets generate more firm-sponsored training than the U.S. At the micro
evidence
With
inducing the firm to invest in general training
Given the contrast between our
result
it
period to compensate the firm for the costs of training.
first
frictions, in contrast,
imply /'(O)
human
the role played by unions.
countries imions are heavily involved in
while in the U.S. they have traditionally been
has been declining. Furthermore,
structure against
is
commonly
it is
less
prominent and their importance
believed that unions compress the
more highly paid workers (Freeman and Medoff,
In this subsection
discussed above).
we turn
We
to union
wage
wage determina-
1984).
setting (instead of individual
assume that a union can
set the entire
wage
Nash bargains
wage structure w{t)
the beginning of the period, and then the firm chooses training. Hence, this model
at
is
an analogue to the standard monopoly imion (right-to-manage) model, except that we
replace the firm's labor
/(r)
>
start
The
situation.
We
assume that
v{t) so that the workers do not leave for outside
=
/(r)
— w{t) —
c{t).
with the simple case where the union can only choose one wage for
The union
first
>
firm maximizes ^{t)
training levels, w{t)
by the
decision with the training decision.
v{t) and the union sets w{t)
opportunities.
We
demand
=
w, and we
will
then see that the union cannot improve over this
will anticipate the
order condition, /'(r)
the wage does not vary with
skill
The union simply maximizes
=
behavior of the firm which can be summarized
c'{t). It is
This implies that the imion
>
0,
immediately obvious from the fact that
that the firm will choose the efficient training level r*.
the wage income of the worker (since the worker
paying for the costs of training). However,
constraint of the firm, 7t{t*)
all
it
has to
make
is
not
sure to obey the participation
otherwise the firm will prefer not to hire any workers.
will set the
wage
12
so as to extract
all
rents
and
force the firm
down
wage
to zero profits. Therefore, the optimal
The
>
firm invests in training because /'(r)
is
= f{r*) — c{t*)}'^
= 0. The training investment
w*
w;'(r)
because the union gets a fixed payment and the firm
efficient
is
the
full
is
residual claimant.
This immediately implies that the imion cannot do better by choosing the whole wage
among covered
schedule, w{t). If there were ex ante heterogeneity
would no longer choose a
union would
still
single wage. However,
workers, the union
can be shown in
it
this case that the
choose to compress the wage structure and induce the firm to invest
in training.
The
model once again contrast with the standard
predictions of oiir
wage
predict that by compressing the
would be
more
structure, imions should encourage firms to spon-
wage
In contrast, in the standard approach a distortion of the
sor training programs.
structure against
We
theory.
workers would reduce the retiirn to training and workers
skilled
The
less willing to invest.
general pattern predicted by our model
again consistent with international comparisons.
But, the micro evidence
is
once
is
mixed.
by Dimcan and Stafford (1980) and Mincer (1983) based on the PSID, Lillard
Stiidies
and Tan (1992) based on the CPS, and Barron, Fuess, and Loewenstein (1987) based
EOPP
on the
find negative effects of imion status
on
Black (1997), on the other hand, report insignificant imion
and
vey.
Barron, Berger, and
training.
effects using the
EOPP
data
find positive effects for formal training in the Small Business Administration
Lynch (1992)
UK, Booth
also finds positive effects for formal training in the
(1991) reports
more
training for union workers
NLSY. For
and Green (1993)
finds
siu'-
the
more
training for unionized workers in small establishments but not in large establishments.
Search and Monopsony
3.3
Consider the same set-up as in Section
find a
new
new
firm
if
he
quits.
With
firm and with probability
which
is
independent of
t}"^ If
determine wages. Since there
second bargain
he
will get
output.
is 0.
probability
p^j
is
—
p^,,
the worker
second period the worker has to
the worker
is
fact that there
is
is
successful
and
finds a
unemployed and receives benefit
no further period, the worker's outside option
Pfir) and
his
new
is
(3,
for the
h
is
1
— /3
of the
a special, but nonessential, feature. In
depend on whether the
rest of the
economy
establishment based or centralized. In
and induce training r*.
would hold in the case where
unemployment insurance systems.
in this
worker as above,
firm will capture a proportion
no further period
^'Interestingly, this result does not
set
in the
he finds an employer, he has to bargain with this firm to
competitive and whether bargaining
w=
—
but
Assuming the same bargaining power,
a wage W2{t)
The
1
2,
is
all cases,
unionized or
the union will
lu*
^^All our results
b
=
13
6(t)
and
6'(t)
<
/'(r), as
is
the case for most
the Appendix
same
the
The
(1
we analyze
residt.
outside option of the worker in the bargain of the
— Pw)b. The
PwP)f'{T)
v'{0).
=
This
We
the case where this economy has infinite horizon and estabhsh
first
is
period
is
v{t)
order condition for the firm's investment in training
As
c'{t).
first
= PwPfir) +
is (1
in Section 2, the condition for firm-sponsored training
equivalent to: PwPf'{0)
<
refer to this situation as search
/'(O)
which
will
be
satisfied
if p^,
induced monopsony; because
it is
<
1
/3)(1
—
/'(O)
>
P<
1.
—
is
or
costly for the
worker to change employers, the firm has some monopsony power and this enables the
The
firm to capture part of the higher output due to the worker's higher productivity.
costs of leaving the current firm, which imderlie the
First, the
twofold.
him and capture a
worker anticipates that
his future
quitting.
who
qints can suffer
of the firm, are
employers will also bargain with
certain fraction of his productivity. Thus, the
potential future employers contribute to the
Second, a worker
monopsony power
monopsony power
imemployment and
monopsony power
of
of the current employer.
this reduces the retiu^n to
Moreover, the possibility of unemployment reduces the return to leaving the
current firm especially for the more skihed workers, because skiUs are not useful
when
unemployed. This also contributes to the distortion in the wage structure and to firmsponsored training (see the Appendix and also Acemoglu 1997,
Interestingly, this
model predicts that when the labor market
in the sense that p^, the exit rate
higher,
we should observe more
model discussed
in the
in Prance.
48.2%
The same
reduce
OECD
result
is
more
lower and
"frictional"
imemployment
obtained in the dynamic
once again contrary to conventional
human
capital investments, but in line with
(1993) reports the monthly exit rates from
in the U.S.,
So the economies with lower
is
is
is
This result
frictions
broad international comparisons.
as follows:
from imemployment,
training.
Appendix.
wisdom that labor market
imemployment
for further details).
22%
in Japan,
exit rates
7.6%
in
Germany and 6.7%
once again are the ones with more
investments in training, as predicted by our model.
3.4
Skills
Asymmetric Information
may be
technically general, but outside employers
whether a worker actually possesses these
is
skills
or in
may be
what amount
the case, the outside wage will not reflect these uncredentialled
them
fully so that /'(r)
>
v'{t).
or quality.
skills,
If this
or not reflect
This has been suggested by Katz and Ziderman (1990)
and analyzed by Chang and Wang
this notion using
imable to ascertain
(1996).
Bishop (1994) finds empirical support
for
data from the National Federation of Independent Business Siirvey.
However, information advantages of the incumbent employers
14
may
lead to firm spon-
sored training even
if
the
skills
apprenticeship programs are well-known, thus r
employer
tial
still
German
are easily observable. For example, the content of
observed by outside firms, but the
is
has superior information regarding the ability of
workers.
its
We
ini-
have
analyzed this case in Acemoglu and Pischke (1998), and the following adverse selection
model
A
based on our previous work. Workers have two different
is
abilities
denoted by
r/.
=
0.
proportion p are low ability and, for simplicity, we normalize their ability to
The remaining proportion
1
—p
are high ability with
=
77
1.
The production
t]
fimction
is
/(r,7y) =r7?.
The incumbent
of period
1.
At
firm does not
this time,
know the
ability of a particular
must decide about
it
worker at the beginning
At the end
training.
the worker's type and offers a wage which can be contingent on
do not know worker
They
offer a
but observe the
ability,
original employer
whenever the outside wage
that there are other reasons for quits. Even
exogenous reasons with probabihty
To avoid
power
issues of bargaining
to low ability workers.
The
outside market
is
and
v{t),
<
=
/3
will lose
in the outside
of workers
This implies that
0.
market
of
to high
all
ensure that the outside
separate. Since
low ability workers
some high
ability
will also quit to
In equilibrium, expected productivity
take
and the
are:
,
The incumbent employer keeps
ability.
wage
wage
competitive, but as noted above, cannot distinguish high ability
advantage of the higher outside wage.
wage
the bargaining
a fraction A of these workers to tiu'nover.
who
>
all
will offer the lowest possible
it
wage equals the expected productivity
v{t)
assume
also
Therefore, a firm will offer a
0.
will therefore
qiiit,
We
their
w{T,ri), workers will separate for
workers from the low ability ones. Competition
workers
w{T,r]).
with asymmetric information, we give
In addition,
=
ability workers, w{T,r])
v{t)
if
>
Workers quit
A.
by setting
to the inciimbent firm
worker has received.
ability.
higher, v{t)
is
learns
it
Outside firms
ability.
level of training the
wage, v{t), conditional on training, but not
of period 1
A(1-p)t
.
a fraction
(1
— A)(l — p)
of workers, all of
which are high
Therefore, profits are given by:
7r(T)
=
(1
-
A)(l
-
-
p) [r
w{t,
-
1)]
cir)
In words, the firm pays the cost of training for
observed before training. After training
all
=
(1
all
workers because worker ability
-
A)(l
-p)[r-
v{t)]
-
c{t).
is
not
low ability and a proportion A of high ability
workers leave, the firm pays v{t) to the remaining workers, and makes profits equal to
T
—
?;(t)
per worker.
The
first
7r'(r)
=
order condition for training
(1
-
A)(l
-
p)
[1
15
-
v'{r)]
-
is:
c'{r)
=
0.
(6)
The
=
firm only retains highly skilled workers, so /'(r)
the necessary and sufficient condition for firm sponsored training
condition that the wage structure should be compressed.
condition
is
always
satisfied,
because v'{t)
=
—
A(l
+
[p
have
also
is ?;'(0)
<
1,
=
c'(0)
— p)] <
A(l
0,
our famihar
immediate to see that
It is
p)/
we
Since
1.
1.
this
Intuitively,
the presence of low ability workers in the second hand market implies that firms view
workers in this market as lemons, and therefore are imwilling to pay high wages. More
important, they do not increase their wage offers by
because training
is
not useful to low ability workers
much
who
for
workers with higher
r,
are the majority of those in the
second hand market.
Many
example are
of the assumptions in this
The
reasons of exposition.
crucial
assumption
is
inessential
and were only made
for
that training and ability are comple-
ments, which we captured by the multiplicative production hmction /(r,
r/)
=
To
tt].
see
the importance of complementarity between unobserved ability and training, consider
=
t
+
V\Tj
=
instead that f{r,rj)
The
outside
satisfied at
r
wage now
=
0,
rj.
pr
The
outside
wage
+ A(l-p)(l +
TTZ
p + X{l-p)
r)
;
in this case
=
A(l-p)
p + X{l-p)'
,
T
increases one for one with r, that
and the firm does not
is
=
v'{t)
1.
Therefore, (6)
invest in the training of its workers. This
to the fact that training raises the productivity of the
amount. Asymmetric information
is:
more and
less
due
able by an equal
leads to rents for the incximbent firm, but
still
is
is
it
does
not lead to a distortion of the wage structure.
In
Acemoghi and Pischke
among German
(1998),
apprentices.
We
we
present empirical evidence for adverse selection
show that apprentices who leave
their training firm
who
stay
Unlike other quitters and workers
who
because of the military draft (an exogenous separation) earn more than those
at the apprenticeship firm
and other
quitters.
stay at the training firm, military quitters are freed from the adverse selection problem,
because the reason
3.5
for their separation is
EfRciency Wages
Suppose that the firm
it
observed by the outside market.
invests in general training in the first period. In the second period,
chooses what wage to offer to the worker.
requires the firm to
e in
pay an
exerts no effort
and produces nothing.
contractible, there
as before, r
If e
a moral hazard problem which
is
The worker can
efficiency wage.
which case he produces /(r) where,
There
is
either exert effort at cost
general
human
capital.
Or he
or a variable highly correlated with e were
would be no moral hazard problem. -^^ Instead, a worker who exerts
'^It is natural that the effort level of the worker is not always observed. Also, in most firms, rather
than the output of an individual worker, only the output of a whole division is observed, and this is not
16
no
effort
We
has a probability q of getting caught.
worker are risk-neutral, and there
a limited
is
assume that both the firm and the
liability constraint, so
that the worker
cannot be paid a negative salary Finally to simplify the analysis, we assume that the
firm has
all
the bargaining power.
Since a worker caught shirking will receive
to exert effort
0,
the incentive compatibility condition
is:
ty
—
e
>
—
(1
q)w.
Therefore, the firm trying to minimize costs would choose
also a participation constraint for the worker to
is
participation constraint takes the form
output or
utility that the
w >
/(r)
pation constraints above,
where
is
is
identical to (5) in the case of
not so high as to shut
Firm
3,6
We
A >
is
can.
There
assume that the
is
the
amoimt
independent of
of
skill.
is:
in that case, this distortion will
as e/q
is
A
—
- ^\
firm will then choose r to maximize profits /(r)
wage fimction
Our
satisfied.
worker loses by changing jobs, which
w{t) =max<^ -J{r)
As
be
e/'q if it
that the optimal wage structure, which satisfies the incentive and partici-
It is clear
The
w =
Specific
— w{r) —
minimum
Observe that
this
wages, with e/q replacing
wm-
c{t).
encourage firms to invest in general training (as long
down
Human
production). So in general f will be positive.
^'^
Capital
human capital for clarity. However, it
which are much more useful in the current
analysis has so far concentrated on general
undoubtedly true that there
firm than the outside.
skills
exist skills
Becker's (1964) classic analysis discussed investment in such
and concluded that the firm should pay
for at least part of the costs.
Although
Becker's analysis once again assumed competitive markets, in the presence of purely
specific skills,
particular,
if
markets
will
not be competitive in the most usual sense of this word. In
a worker has some
skills
that can only be used in one firm, then for one of
easy to use to provide incentives to individual workers.
^''The exact conditions for training are the
same
as those given in footnote 10.
The assumption
tliat
independent of future job opportunities, and tlius of skills, is
not crucial. The result holds as long as the constraint induces a relation between wages and skills less
steeply sloped than /(r).
The model by Loewenstein and Spletzer (1998) has a similar flavor. In their model firms can commit
tlie
incentive compatibihty constraint
is
ex ante to pay a certain wage in the second period in order to reduce turnover. Wlienever this constraint
is binding for the firm, the firm has an incentive to invest in the worker's general skills.
17
the commodities, there
only one buyer and one
is
not apply. In this subsection
we
show that
will
can also support firm investment in general
Assume that output
human
specific
source of the firm-specific
is
inessential:
s, is
period that the worker spends with the firm
>
in Jovanovic, 1979), so s
these skills with
some
given as y
=
some
/(r, s)
where
s is firm
could be acquired during the
it
(j){s)
positive
The
first
example, via a learning mechanism as
(for
Alternatively, the firm chooses
0.
cost function
woiild always like to have
now
period the firm again chooses r at cost c{t).
first
skill,
from perfect competition
this deviation
skills.
in the second period
In the
capital.
so price-taking behavior does
seller,
>
such that df{T,0)/ds
amount
how much
(f)'{0)
of firm-specific skills.
to invest in
so that the firm
Both scenarios
are equivalent for the purposes of this section.
Let us also adopt Bertrand competition
More
generally, even
if
v{r)
is
only useful in the current firm.
among
outside firms so that v{t)
not equal to /(r, 0)
it
The independence
be independent of
will
of w(r) of s
=
/(r, 0).
s since s is
the crucial ingredient
is
in this case.
Assuming Nash Bargaining once more, we have
iu{t)
=
/3/(t, s)
+ (1 — P)f{T, 0). The
firm will then choose:
max7r(T,
=
s)
/(r, s)
—
w{t,
s)
—
c{t).
T
As
before, this
v'{0) or
training
if
imphes that the firm
5/(0, s)/dT
>
skills.
f
>
only
if /?
<
1
and 5/(0, s)/dT >
df{0, 0)/5r. Therefore, for firm sponsored investment in general
we need d'^f{T,s)/dTds >
and general
will invest
In fact, since c'(0)
0,
that
=
0, it is
is
a complementarity between firm-specific
necessary and sufficient for firm-sponsored
>
investments in general training that 5^/(f, s)/dTds
and
<
I.
Although plausible
counter-examples can be found, complementarity between general and specific
fairly
weak requirement. So our
firm-sponsored general training
To summarize,
if
is
firm specific
likely to exist.
skills
and general
skills raises
enabling the firm to invest in these general
In this case, specific
these rents are the
same
to invest in general
skills
skills.
If specific
in
and general
skills
do not
r as the production function.
generate rents from the current employment relationship, but
at all levels of general skill.
skills.
are complements in the pro-
productivity more than outside wages,
wage function has the same slope
skills
a
analysis suggests that under a wide set of circumstances,
duction function, increasing general
interact, the outside
skills is
The
firm has therefore no incentive
-^^
^^Related ideas have been discussed by other papers. Stevens (1994) considers skills which are neither
mean that workers are unlikely to
completely general nor completely specific and notes that this will
face a perfect outside labor market for these
skills.
18
However, she does not consider the interaction
This result also goes in the direction of suggesting that European and Japanese
economies should generate more investment in general training than their U.S. counterpart.
As these economies have lower turnover, we might expect workers
firm-specific skills, so that s will
more
to have
be higher in Europe than in the U.S. This immediately
implies that f should also be higher in Etirope. Therefore, our analysis in this subsec-
we might expect more
tion suggests that everything else being equal,
economies with low turnover, because they
above
Finally, the formulation
is
will generate
ent levels of physical capital, and physical and general
then firms with more physical capital would
Suppose there
other firms.
if
It
is
is
full
is
like to
With
human
capital
quits,
first sight, this
is
its
physical
and the worker would receive
not the case
if
However, this
is
not
example seems to contradict our general premise that
the worker, which
is
so. If capital is
some degree
stock of physical capital has
of
immobile, then the employer with a larger
monopsony power over the human
capital of
spills
over into the labor market.
Conclusion
When the wage structure is
distorted
of less skilled workers, firms
away from competitive wage structure and
may want
need to be credit constrained.
institutions.
These
results contrast
work where firms would never
regiilated labor markets
between
specific
What
and general
matters
is
for this result to hold,
skills as
workers do not
the form of labor market frictions and
with the standard theory based on Becker's seminal
invest in general skills.
may
in favor
to invest in the general skills of their employees.
Contrary to previous research, we showed that
and
human
the source of the distortion in the wage structure. In other words,
the imperfection in the capital market
4
his
the capital market
labor market imperfections are needed for firm financing of investments in general
capital.
differ-
employ workers with more human
perfect markets, the firm could just sell
new employer when the worker
At
have
capital are complements,
for this firm to invest in the workers'
marginal product on the outside market. This
imperfect.
human
firm. If firms
not perfectly mobile. This conclusion again crucially depends on
the existence of some frictions.
capital to the
than merely specific
one firm which has a higher stock of physical capital than
would be profitable
physical capital
firm-specific skills.
also useful in contexts other
above could be physical capital of the
training. For example, s
capital.
more
general training in
We also foimd
that
more
frictional
increase investment in training by distorting the
a source for firms' investments in general training.
Soskice (1995) discuss the case where general training
is
wage
Franz and
a by-product of specific training,
i.e.
the
on the cost side rather than on the output side as in our analysis above. Bishop
(1996) points out that individual skills may be general, but the particular mix of these general skills
used by any single employer could be firm-specific.
complementarity
is
19
structure and encouraging firms to invest in the
We
the
skills of their
employees.
view the presence of many firm-sponsored general training programs, such as
German
apprenticeship system, and the fact that U.S. employers send their workers
to vocational
and technical training
that the forces
we emphasize
facilities
without reducing their wages as evidence
are present. Also, the fact that training programs are
prominent in Europe and Japan, which have more regulated and
more distorted wage
structures,
is
in fine with our approach.
frictional
more
markets and
Future empirical work
should test the more micro-level implications that follow from our analysis and contrast
them with those
of the standard theory.
This paper also has implications for the interpretation of empirical results on the
returns to training
(e.g.
Lynch, 1992).
total increase in productivity
whenever employers pay
measured
in
if
The wage
returns to training only refiect the
labor markets are competitive.
for training, the true returns
may
Our work
predicts that,
exceed the returns to training
terms of the wage, which are often estimated to be quite large already.
20
A
Appendix:
5
Continuous Time Version of the
Search Model
Consider a continuous time
each worker
is
infinite
matched with a
horizon version of the model of Section
firm,
who
t
=
0.
is
All worker-firm matches
come
to
risk-neutral
after losing its
firm finds will be a
of
only possible in
is
at the rate
Also a worker, once
q.
independent of his training
worker finds a new worker at the rate pj
random draw from the pool
is
and discoimt the future
end at the exogenous rate
tmemployed, finds a new firm at the rate p^ which
and a firm
now. The productivity of a worker
/(r) in every period. For simplicity, training
Both firms and workers are
to
The worker has no funds and cannot commit
in the future in return for training
receives training r
period
r.
wage
Namely,
and the firm decides whether and how much
invest in the general skills of the worker.
to a lower
3.3.
.
The worker
level,
that the
tmemployed workers, irrespective of the
value of training. So workers with different levels of training have the
same probability
of getting a job.
Suppose
all
workers have training f and consider a worker with training
,
r,
then the
value of being employed for this worker as a function of his training level r, J^(t),
rJ^(r)
where J^ {t)
ing r.
is
=
y;(r)
is:
+ g(j^(r)-J^(r))
the present discoimted value of being unemployed for a worker of train-
This equation
Pissarides, 1990).
is
a standard dynamic programming equation (see for instance
The worker
job at the fiow probability
q,
gets w{t) every instant he
in
with the firm and loses his
is
which case he gets J^ and
loses
J^
.
In turn
we
have;
rJ^(r)=b + p^{j^{T)-j''{T))
And
for the firm, the value of
rJ^(r)
employing a worker with training r
= /(r)-t.(r)-Fg(j^-J^(r))
and the value of being imfiUed vacancy
Nash Bargaining
is:
is:
in this context implies that the present discounted values should
shared. Therefore, w{t) will be chosen so as to maximize:
VN1-/3
{j'^{r)-J^{r)Y{j^{r)^J^)
21
be
This gives a standard wage
rule:
^r) =
or substituting for rJ^'{T)
Pfir)
+
(1
,
.
=
(Pu,
+r+
r
0,
Prj""
:
w[t)
Now in period t =
- pyj'^iT) -
since the worker
is
q)
- P rJ^)
-
{Pfjr)
^
+ q + (jpyj
credit constrained
and cannot
invest in training,
the firm will maximize:
-
J'{r)
c{t)
by choosing training r and taking the training
only influences J^, which
is
not influence the choice of
(7)
level of all other workers, r, as given,
in turn independent of the vahie of r.
r.
So the
level of
For this reason, the first-order condition of
f
f does
takes the
(7)
simple form:
(l-/?)/'(f)
Since c'(0)
=
0, for all /5
<
1
and
r
=
+ g + /?pJc'(f)
(r
+ q + (5pw <
other firms are solving a similar problem,
we
c», the firm will choose f
=
have f
also
f,
>
0.
Since
all
and a unique symmetric
equilibrium.
The reason why
text.
/?
<
1 is
necessary for firm-sponsored training
However, the second condition
is
interesting.
the future needs to feature in the calculations,
g
First
<
oo
it
is
pu;
—
>
oo
is
oo, thiis
also required
this last
p^u
<
oo
which means
is
necessary.
requirement reiterates that labor market
imperfections are necessary for firms to invest in the general
it is
<
the case of perfectly competitive labor markets: the worker finds
an employer immediately. Therefore,
Moreover,
from the
reqiiires that r
that the worker should not be leaving the firm for sure. Finally,
In fact,
familiar
is
clear that as
p^
increases, there
steady state imemployment in this economy
higher unemployment
is
associated with
is
is less
equal to u
more investment
skills of their
workers.
investment in training.
=
q/{q
+ Pw),
in training.
Since,
this implies that
The reason
is
that
a higher rate of unemployment causes a more distorted wage structure by reducing the
outside option of more skilled workers.
22
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