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WORKING PAPER
DEPARTMENT
OF ECONOMICS
Minimum Wages and On
the
Job Training
Daron Acemoglu
Jorn-Steffen Pischke
No. 99-25
October, 1999
MASSACHUSETTS
INSTITUTE OF
TECHNOLOGY
50 MEMORIAL DRIVE
CAMBRIDGE, MASS. 02142
njiASSACHOSETTS INSTITUTE
QFTECHW Ol-OGY
I
NOV 2
G 1999
LIBRARIES
WP No.:
99-25
Minimum Wages and On
the Job Training
By Daron Acemoglu & Jorn-Steffen Pischke
ABSTRACT:
Becker's theory of human capital predicts that minimum wages should reduce training
investments for affected workers, because they prevent these workers from taking wage
cuts necessary to finance training. We show that when the assumption of perfectly
competitive labor markets underlying this theory is relaxed, minimum wages can increase
training of affected workers, by inducing firms to train their unskilled employees. More
generally, a minimum wage increases training for constrained workers, while reducing it
for those taking wage cuts to finance their training. We provide new estimates on the
impact of the state and federal increases in the minimum wage between 1987 and 1992
on the training of low wage workers. We find no evidence that minimum wages reduce
training. These results are consistent with our model, but difficult to reconcile with the
standard theory of
human
capital.
Minimum Wages and
On-the-job Training
Daron Acemoglu
Jorn-Steffen Pischke
MIT
MIT
*
First Version: April 1998
This Version: June 1999
Abstract
Becker's theory of
human
capital predicts that
minimum wages
should reduce
training investments for affected workers, because they prevent these workers from
taking wage cuts necessary to finance training.
We show that when the assumption
of perfectly competitive labor markets underlying this theory
is
relaxed,
minimum
wages can increase training of affected workers, by inducing firms to train their
unskilled employees.
More
generally, a
strained workers, while reducing
training.
it
minimum wage
for
increases training for con-
those taking wage cuts to finance their
We
provide new estimates on the impact of the state and federal inminimum wage between 1987 and 1992 on the training of low wage
We find no evidence that minimum wages reduce training. These results
creases in the
workers.
are consistent with our model, but difficult to reconcile with the standard theory
of
human
capital.
Keywords:
Imperfect Labor Markets,
General
Human
JEL
Capital,
Low Wage
Workers,
Firm Sponsored Training
Classification: J24, J31, J41
thank John Browning and especially Aimee Chin for excellent research assistance, and Joe
Richard
Carson, Ken Chay, Jinyong Hahn, Lisa Lynch, and Chris Taber for useful comments.
Altonji,
The first draft of this paper was written while Pischke was a visiting scholar at the Northwestern
University /University of Chicago Joint Center for Poverty Research. He is grateful for their hospitality
and research support. Acemoglu is grateful for financial support under the National Science Foundation
We
Grant SBR-9602116.
Introduction
1
Much
on the minimum wage has focused on
of the recent debate
cations.
The theory
important adverse
human
of
effects
capital suggests that
its
employment
minimum wages
impli-
should also have
by reducing training and wage growth. In the standard human
by Becker (1964), Ben-Porath (1967), and Mincer (1972),
a large part of human capital is accumulated on the job, and workers often finance
capital theory, as developed
A
these investments through lower wages.
workplace training, as
it
The
negative impact on
human
in the
we
In this paper,
minimum wage
will therefore
reduce
prevents low wage workers from accepting the necessary wage
cuts (Rosen, 1972).
minimum wages
binding
The
early empirical literature has confirmed this prediction.
capital formation has been
an important argument against
minds of many economists and policy-makers.
revisit the
We provide new
impact of minimum wages on training.
empirical estimates that are quite different from those already in the literature, bringing
a
new
perspective to this debate.
We
some new
also provide
theoretical ideas
impact of minimum wages on training, which imply that minimum wages
the training of low paid workers.
a negative
effect of
Since the standard theory of
minimum wages on
human
training, our evidence enables
may
on the
increase
capital predicts
an evaluation of
the empirical success of the alternative theoretical approaches.
The standard theory
implications of
show that
human
minimum wages
investments.
The
capital
is
market
frictions,
intuition for this result
When
is
that
minimum wages
previously paid below the
no option but
new minimum wage.
may be more
intuition diagrammatically. It
A
binding
less profitable
relationship,
to lay off workers
who were
who
profitable to increase the productivity of workers,
them
off.
Figure
draws the relation between worker
minimum wage,
lay off the worker. However, with
A
1 illustrates this
skills, r,
is
productivity,
the rent that the
in the absence of such rents, forces the firm to
sufficiently high, the firm
worker despite the higher wages dictated by the
would
it
employment
and wages w(r). The gap between productivity and wages, A,
firm obtains.
the incentives
In contrast, in the presence of labor
are already receiving high wages, rather than laying
/(r),
shift
minimum wages make
there are no rents in the
as in a competitive labor market, the firm has
rents, it
We
from the worker to the employer, and may increase training
employ unskilled workers.
market
based on competitive labor markets. The
in noncompetitive labor markets are very different.
in the presence of labor
for training investments
to
of
minimum
also like to increase the productivity of the worker.
would
like to retain
the
wage. In this case, the firm
Without the minimum wage,
the gap between /(r) and w(t) was constant, so there was no point in incurring costs
of training. However, with a
minimum
wage, profits are
less at
r
=
than at r
=
1.
So
f(T)
f(T)-A
C(T)
Figure
if
1:
Training with a
the firm can increase
do
so.
In essence, the
its
Minimum Wage and Employment Rents
employee's
minimum wage
skills to
has
r
made
=
1 at
a moderate cost,
it
will prefer to
the firm the de facto residual claimant
of the increase in the worker's productivity, whereas without the
minimum wage,
the
worker was the residual claimant.
This reasoning suggests that a binding
more
in the skills of their employees.
As
minimum wage may
induce firms to invest
in the standard theory, however, the
some workers may have been low because they were compensating
investments in general
skills,
therefore, predicts that
and the minimum wage would prevent
minimum wages
human
their employers for
this.
Our approach,
reduce the training of workers taking wage cuts
to finance their training, while inducing further training for those
in their
wages of
capital investments. In the first part of the paper,
who were constrained
we outline this theory
in greater detail.
The broad aggregate
trends in the data do not appear in line with the standard the-
ory.
A variety of evidence,
(e.g.
DiNardo, Fortin, and Lemieux, 1996; Card and Krueger, 1995), suggests that min-
imum wages
including the spike in the wage distribution at the
are binding for
some workers. Therefore, the standard theory
minimum
predicts that
the decline in the real minimirm wage during the 1980s should have increased training
for
low wage workers. Comparing formal and informal company training
among high
school dropouts in the Training Supplements of the
The
CPS, we
be the
find this not to
case.
training incidence falls from 15 percent in 1983 to 11 percent in 1991, even though
minimum wage was
the real value in the
lower in 1991 than in 1983 (see
Acemoglu and
Pischke, 1999a).
Nevertheless, other aggregate trends
training
among low wage workers.
may have been
In our micro data work,
trends and exploit cross-state and region variations in
We use
the National Longitudinal Survey of Youth
This period encompasses a number of state
increases in the
minimum
in 1990
of within state variation in
responsible for the decline in
how
we
binding
(NLSY)
Our
empirical results
1987 to 1992.
and 1991. Our data therefore contain a
Furthermore, the
directly affected
specifications,
suggest that
it
NLSY is
large
amount
a panel of youths
contains a relatively high
by minimum wage
show almost no evidence
minimum wages. Some of our
by minimum wage increases,
are.
minimum wage increases as well as two federal
minimum wages.
wage workers
of low
minimum wages
for the period
and oversamples those from disadvantaged backgrounds, so
number
control for these aggregate
increases.
of a reduction in training in response to
which look most directly
at workers affected
minimum wages may have
increased worker
training slightly, although these positive coefficients are not statistically significant.
No
for
minimum wages on
(or small positive) effects of
whom
the
minimum
is
training investments for workers
binding suggest that the adverse effects of
on the human capital of low wage workers may be rather
contrast with the predictions of the standard theory.
an increase
in the
minimum wage
should eliminate
minimum wages
limited.
These findings
The standard theory
all
general training
implies that
among
affected
workers, as these investments have to be financed solely by the workers themselves.
even harder to reconcile with the standard theory
results are therefore
NLSY
in the
waves.
is
general, as Loewenstein
Our evidence
be more appropriate
and Spletzer (1997)
find to
if
Our
most training
be the case in
later
may
minimum
therefore suggests that models with imperfect labor markets
an analysis of training decisions and the impact of
for
wages on training investments than models based on competitive labor markets.
The
rest of the
paper
is
organized as follows.
The
following section discusses the
related literature. Section 3 presents a simple theoretical setup where, contrary to the
predictions of the standard theory,
setup
is
clearly.
special
and
is
In Section 4,
increase training investments. This
chosen to illustrate the main theoretical contribution of this paper
we
wages increase training
we
minimum wages
consider a
for
more general and
realistic
some workers, while reducing
describe our empirical strategy
and give an overview
presented in Section 6 and Section 7 concludes.
it
model where minimum
for others. In Section 5,
of the data.
Our
results are
Previous Literature
2
Previous theoretical discussions of the effect of the
minimum wage on
training are based
on the human capital model of Becker (1964).
In the models of
Rosen (1972) and
Hashimoto (1982), minimum wages reduce training investments, becaiise they prevent
workers from taking the wage cuts necessary to finance general
Our
ments.
human
capital invest-
theoretical result deviates sharply from this conventional wisdom.
We build
on our previous work, Acemoglu and Pischke (1999b), which showed that a compression in the structure of wages can induce firm-sponsored training. Here, we show that
minimum wages
overall
amount
There
is
shift training
investments from workers to firms, and
may
increase the
of training.
a small empirical literature investigating the impact of
training. Part of this literature focuses
minimum wages on
on whether minimum wage laws lead to slower
observed wage growth in micro data. Both Leighton and Mincer (1981) and Hashimoto
and concluded that minimum wage laws lead
(1982) have found this to be the case
less training.
a
In our model, the introduction of a small
shift of training
it
of the
wage
distribution,
and
More
generally, since
minimum wages
typically create a spike at the
appear to reduce age-wage profiles even when they have no
fore, it is unsatisfactory to interpret
ian (1999) find no effect of
minimum wage
sectional
wage
the
shifts
also
found
we
training.
There-
find lower
Sicil-
wage growth
minimum wage
increase
flatter profiles in California after
increase. However, they point out that the Californian profile also
is
cross the previous age-wage profile. This pattern contradicts the
consistent with the predictions of our model.
changes in the slope of wage
to look at the impact of
minimum wages on
profiles,
we
find
training directly, but
are only aware of four previous studies doing this for the US. Leighton and Min-
cer (1981) use
of
states.
difficulty of interpreting
more compelling
on
Furthermore, Card and Krueger (1995) compared cross
They
standard theory, but
it
still
after the 1988
up and does not
Given the
training, but
and
minimum wage
minimum, they would
effect
profiles in California before
with a number of comparison
cut the lower
Consistent with this view, Grossberg and
minimum wages on
workers.
when
the decline in age-earnings profiles as evidence of
reduced investment in general training.
for
could lead to
expenses from workers to firms, and reduce wage growth, even
causes an increase in training.
tail
minimum wage
to
worker reported data on the receipt of training from the Panel Study
Income Dynamic (PSID) and the NLS and
find that workers in states with lower
wages and therefore a more binding federal minimum wage receive significantly
training.
effects,
Cross state comparisons
may be confounded by
less
the presence of other state
however. For example, industrial and occupational composition of employment
varies substantially across states,
skill
and
different industries
and occupations have
different
requirements. These considerations suggest that across state comparisons are hard
to interpret. Schiller (1994) reports a similar finding using later data from the
NLSY by
comparing the training incidence of minimum wage workers with those earning higher
The evidence from
wages.
this
study
is
even harder to interpret because worker
traits
which lead to higher pay are typically also associated with more training. Grossberg and
Sicilian (1999) use
data from the Employment Opportunity Pilot Project (EOPP) and
compare minimum wage workers both
to workers earning slightly less
ameliorating the problem of worker heterogeneity somewhat.
negative effects on training for male
effects for
minimum wage workers and
slightly
more,
find insignificant
insignificant positive
women. Leighton and Mincer only analyzed men, although women make up
the majority of
Some
They
and
minimum wage
workers.
more recent study by Neumark and
of these problems are overcome in a
Wascher (1998), who use Current Population Survey (CPS) supplements to compare
the impact of
minimum wages on
training within states using comparisons of
workers in 1991 with older workers (who are
less likely to
young
be affected by the minimum
wage) and with young workers in 1983. These comparisons assume that state differences
in training levels are the
same for younger and
older workers
and remain so over long time
periods, which are stringent requirements.
They
wages on training, but these
be too large to be
group consists of
imum
all
effects
seem
to
young workers, but not
also find negative effects of
wage. Their estimates imply that formal training
California (a high
minimum wage
state)
was
that
in
than in states
this reduction in training is en-
due to workers being affected by the minimum wage. Assuming, quite generously,
minimum wages
affect all
(which comprises
30%
workers, training
is
vided by 0.30).
workers earning
is
less
lower by over 10 percentage points
It is
2.7 percent,
minimum
among affected
than 160 percent of the
of workers aged 20-24), this estimate implies that
(i.e.
3.2 percentage points di-
important to note that the average incidence of training among
workers aged 20-24 earning 160 percent of the
states
by the min-
among workers aged 20-24
3.2 percentage points lower
which were subject to the federal minimum. Suppose
tirely
Their treatment
sensible.
of these workers are affected
all
minimum
much
lower than
among
minimum
all
or less in low
workers aged 20-24
minimum wage
(for
whom
the in-
minimum
wage to low minimum wage states should have wiped out all training four times among
affected workers in these states. This siiggests that the fixed effects assumptions made
by Neumark and Washer are quite suspect.
cidence
is
10 percent). So this estimate implies that introducing California's
Minimum Wages and
3
Training: Basic
The main
wages on training.
result of this analysis
perfectly competitive labor markets,
which introduce
clusions of Becker's seminal analysis. Namely,
minimum wages can
tions,
to analyze the impact of
we use a simple two-period model
In this section,
we
Theory
that plausible deviations from
is
firm-specific rents,
find that
change the con-
with labor market imperfec-
increase investments in general training,
and
they will increase training for employees previously constrained in their
investments, while redxicing
We
model,
start with the simplest
are general,
all skills
petitive labor markets
As a
for those taking
it
model which
wage cuts
illustrates
minimum
in
most
human
cases,
capital
to finance their training.
our most original result. In this
and workers cannot finance
their
own
training.
With com-
and without minimum wages, there are no training investments.
moderate minimum wages increase training unambiguously.
result,
These simplifying assumptions are unnecessary
for
our main insights, however, and
they hide the potential adverse effects of minimum wages on training. In the next section,
consider a less restrictive model where workers are potentially heterogeneous,
we
can take wage cuts to finance training.
wages
will increase training for
wage cuts
lasts for
There
neutral.
start
<
1,
training
Without
is
two periods,
it
for those previously taking
in period 2 further, to
>
4>
1.
productivity applies equally in
lower output in the
all
because training
is
r
=
To
who supply
common
ability
all
agents are risk-
labor inelastically.
normalized to
first
period
We
simplify the discussion
(no training) and r
but with the experience of
1 in
that
no discounting, and
is
workers have
all
also receive training.
indivisible, so only
training,
we assume
There
2.
1.
We
the early career of workers. During this period a worker's productivity
1 as
and he can
is
and
a continuum of workers with density n,
productivity increases to
if
1
with the case in which
view period
6
some workers, but reduce
to finance training.
The world
is
more general environment, minimum
In this
Environment
3.1
We
and
2.
first
period and
is
1
that
(training) are possible.
period employment, the worker's
Training, in turn, increases his productivity
assume that training
all firms.
=
we assume
The
is
general, so this increase in
cost of training
equal to c
>
0.
is
incurred in terms of
As noted above,
in this section,
training investments have to be financed by the firm. This could be
non-contractible, so the firm can renege on
its
training promise even
the worker takes a wage cut to finance his training (see Acemoglu and Pischke, 1999a,
for
a discussion).
We now
impose:
Assumption
1:
—
(j)
This condition ensures
There
is
>
1
c.
that, training is socially beneficial.
a continuum
1
of firms competing to hire workers in both periods.
firm can hire at most one worker. Firm j has to incur a setup cost k3
We
equipment).
assume that
F(k) with lower support at k
has a continuous distribution
kj
<
and upper support
at
k
<
6
+9
(6
buy some
(e.g.
among
is
Each
firms given
by
defined below).
This smooth distribution enables us to generate a downward sloping demand for labor
in period
A
1.
negative value of k implies that the firm will
make
profits in the first
period even after incurring the required capital cost, for example because
it
special expertise in this area of business. However, to realize these profits,
and to produce.
hire a worker
k
— — oo),
>
Once
so that
revenue per worker
revenue
5, if
<p
if
suppose that the lower support k
minimum wages
set up, all firms
worker and
We
is 9.
never stop
have access to the
the worker was employed in the
firm and the worker.
make take
it
,
is
first
low enough
In the
We
period with this firm. Therefore, 6
or leave
<5,
it
offers to workers).
initial
(or equivalently,
Since the second-best opportunity of
employers capture the whole amount
even though workers' productivity
if
is
<5,
only paying the
higher than this. As will
the worker captures a fraction
demand
for labor.
product of labor in the
the
all
f3
<
is
become
crucial,
but
1 of this surplus.
workers will stay with their
initial
2
an alternative assumption which generates a smoothly de— — oo in that case is that the marginal
very large when very few workers are employed. This formualtion
Decreasing returns at the firm level
j'ields
2
is
the only deviation from competitive labor
Observe also that this mobility cost implies that
creasing
period,
Also, the firm obtains an additional
assume Bertrand competition among firms
the results would be unaffected
1
first
(e.g.
1
they employ an untrained
apparent shortly, the presence of rents from the employment relationship
employer.
needs to
in the first period.
technology.
is 1 if
it
5 creates a match-specific surplus to be divided between the
workers does not include
"market wage"
common
they employ a trained worker.
markets we introduce.
employment
Their second period revenue
a firm-specific productivity increase, and
firms
all
is
has some
same
first
The
is
equivalent of the assumption k
period
is
>
results.
we could have that a worker who changes a job in the second period incurs a mobility
because he has to acquire some costly firm-specific skills before becoming productive. All our
results continue to hold with this alternative interpretation. Also, in practice, workers earning close
to the minimum wage have high mobility. Our results continue to hold if a fraction s < 1 of workers
Alternatively,
cost
<5,
change jobs.
Equilibrium can
each firm
and
Minimum Wages
Equilibrium Without
3.2
is
pay up to
willing to
is
willing to
characterized by backward induction.
now be
pay
<fi
1
In the second period,
an untrained worker employed by another
for
3
Bertrand competition then ensures that
for a trained worker.
w 2 (NT) =
1,
w 2 {T) =
<f>.
Using the fact that in equilibrium
all
firm,
(1)
workers stay with their
period employer,
first
the profits that firm j makes from an untrained and trained worker can be written
The
first
is
=
(6
-
Uj(T)
=
(9
-
kj
- Wl +
fy
-c- Wl +
Substituting (1) into
—
1
more
firms have
if it
it is
+ 8 -w2 {T))
trains.
and
is
see that
is
trained.
(see
profits
is
simple:
=
-c,
a trained
exactly the increase in his
this
is
the
full
residual claimant of the
profit of the firm
is
equal
Since training costs c in the
not optimal for firm to invest in
firm-specific rents, because they
no incentive to train
is
U(T) - Tl(NT)
The reason
and the second period
independent of whether the worker
Although there are
{([>
(2)
period profits, while the second
So the worker
increase in productivity due to training,
skills.
first
in the second period,
period has to be paid by the firm,
+ 6 - w 2 (NT))
we immediately
(2),
contribution to the firm's output.
6,
(1
)
the firm loses the training costs
worker receives
to
)
bracket in each expression gives
in period 2.
that
Uj{NT)
as:
its
first
employee's
do not interact with training,
Acemoglu and Pischke, 1999b). Therefore, with
competitive labor markets, firms have no incentive to invest in their workers' general
skills,
even though training
is
socially desirable.
To complete the characterization of the equilibrium, we have to determine first period
wages. It is clear that only the n firms with the lowest capital costs will be active. So,
the firm with the
n th
lowest capital cost kn has to
Wl
A
noteworthy feature
is
zero profits. This gives:
kn
(3)
that compensation can be front-loaded or back-loaded. Front-
loading arises because firms anticipate
and are
=9+8-
make
8,
the rent they will receive in the second period,
willing to bid higher than the worker's current productivity.
compensation could be back-loaded
is
The reason why
that firms incur the capital cost only in the
3
first
Even though workers do not receive any of the firm-specific rents, there is no labor mobility in
equilibrium. Suppose this were not so, then the firm could offer e more than the market wage and
convince the worker to stay, so mobility cannot be part of an equilibrium.
8
period,
and anticipate
to
compete harder
for
We
workers in the second period.
assume
that
Assumption
+6—
6
2:
kn
<
1.
This limits front-loading and ensures that there
without training,
a parameter
i.e.
— the n
Now, denoting
w < w 2 (NT).
th
a positive experience
is
Recall that kn
x
is
premium even
not an endogenous variable, but
lowest capital cost.
employment by E, we can summarize
total
this analysis (proof in the
text):
Proposition
with kj
<
1
There
is
a unique equilibrium in which there
kn are active. All workers are employed,
wage given by
(3)
and
the second period
So despite Assumption
is
no training
This
unwilling to invest in the general
employment
is full
E,
is
n,
skill
and
wage W2(NT) given by
which ensures that training
1,
in equilibrium.
benefits of training,
E=
no training and
is
is
all
firms
receive the first period
(1).
socially beneficial, there
in line with Becker's standard theory; firms are
is
of their employees as they
and workers are assumed unable
do not receive any
of the
to "buy" training. However, there
in this decentralized economy, in particular, the level of
employment,
equal to the labor force, n.
The Impact
3.3
of
Minimum Wages on
Training
Now consider the imposition of a binding minimum wage wm > 1- Assumption 2 ensures
that w M > 9 + 6 — kn so the minimum wage is also binding in the first period. Since
,
the
demand
in this
for labor is
start
minimum wage
sloping, the
economy. The main question
minimum wage
We
downward
will
for the focus of this paper,
reduce employment
however,
is
how
the
affects training.
by writing wages
reasoning to above, (1) and
(3)
in the presence of
change
minimum wage
laws.
With a
similar
to:
= wm,
w 2 {NT) = wM
w 2 (T) = max {w M ;</>}.
^i
(4)
,
w 2 (T)
features the
"max" operator because the minimum wage may be
greater than the productivity of a trained worker,
</>.
Profits with
less
than or
and without training
now become:
= (9-kj -w M )+max[(l + 6-w M );Q]
= (0-kj-c-w M + max[(<t> + 6-max{lv M -,<l>})-,Q]
Uj(NT)
Uj(T)
where the
)
operate in the second period
suppose
First,
fact that the firm
"max" operator takes care of the
first
wM >
if
minimum wage
the
decide not to
too high.
is
so that the second period
<P,
may
wage
is
equal to the
minimum
even for skilled workers. In this case, we have
- Uj(NT) =(j)-l-c>0,
Uj(T)
which
always positive by Assumption
is
So
1.
in stark contrast to the
economy without
minimum wages, firms now prefer to train their employees. The firm has to pay the
minimum wage irrespective of whether the worker is skilled or not, so the full return to
training
is
captured by the employer.
wm <
Next, suppose that
minimum. Then,
the
Ilj(T)
so that second period
- Uj(NT) = w M minimum wage
depending on how high the
At
4>,
More
there cannot be any training.
minimum wages
period. This requires
We
max {<fi,w M },
If
+
<f>
W2(T)
kn
2.
6
c
If
wm <
when
and
all
<p,
then
all
firms with k
in both periods
<t>,
then
all
1
+
then there
c,
firms with k
there
there
is
then in the
so necessarily loses money.
down
all
we have
employment
this section (proof in the text):
to
make
in the
So
sure
second
4
is
is
<
now
training,
em-ployed workers are trained, w\
<
is
k* are active where k*
equal to
<
k** are active
is
is
no
now
k + are
active where
equal to
E=1—
w2 (NT)
= 6 + + 6 — c — 2wm <
wi
if
c
>
w = w 2 (NT) = w M and w 2 (T) =
k + = 1 + 6 + 5 — 2tw A / G (k**,kn ),
F(k +
6,
,
F{k**).
x
,
and
then we will never be in case
10
<fi,
so
).
gives "off-the-equilibrium" path wages,
no training. Also notice that
(J)
= iu 2 (iVT) = w M and
= 6 + 8 — c — w M & (k*,k n ),
trained,
where k**
E=1—
training,
= w2 (NT) =
E = 1 — F(k*).
employed workers are
All firms with k
(p.
employment
When
0,
+ 6 — c.
employment in both periods
all
4
> wm >
Ifl+c< w M <
so
3.
—
= wm,
w 2 (T) =
=
.
Employment
.
If 6
rents.
generally, in all this analysis
can now state the main result of
Proposition 2
1.
<fi
workers exceeds
is.
are not high enough to shut
wm <
for trained
This can be positive or negative
c.
importance of firm-specific
this point, notice the
second period, a firm which trains pays
that
-
1
wage
similarly for
2.
w 2 {T),
As
in the standard neoclassical model,
minimum
choose to become inactive. But moderate
will
=
0,
there
is
firm has to pay
minimum wages
market imperfections) are crucial
training. Firm-specific rents (labor
6
reduce employment in
all
because some firms (jobs) making close to zero profits before the introduction of
cases,
the
minimum wages
no training and employment
minimum wages even
in the
for unskilled
for this result.
Figure
1
workers and a binding
some
=
and r
the employer, as in case
1.
may
=
1,
so
The most
all
minimum wage
Training raises
of these rents.
in the introduction gives the basic intuition.
the wage both at r
If
second period collapses to zero. The
reduces the rents the firm receives from the employment relationship.
the worker's productivity, and therefore restores
increase
The minimum wage determines
productivity increases from training accrue to
interesting case
might be case
2.
If
the
minimum
wage
is
some
of the proceeds from the training, because the productivity of the trained worker
low enough,
it
induce the firm to sponsor training but the worker receives
minimum wage. 5
how minimum wages
exceeds the
Notice
affect
wage growth
here.
In case
1,
the
induces training, but will lead to a reduction in wage growth (from
zero), so inferring
whether minimum wages increase training by looking at the slope of
the wage profile, as in Hashimoto (1982),
first
1
minimum wage
— 9 — 8 + k n to
not possible. Since
is
minimum wages
period wages, they will typically reduce wage growth (though in case
sufficiently large,
they
may
increase
2,
if
</>
is
wage growth).
Finally, notice that the results contimie to apply
minimum
increase
if
w^
is
a wage above the legal
that the firm has to pay to the worker, due to other imperfections such as bar-
minimum creates spillover effects to wages above
the minimum, our analysis predicts that firms may also be induced to train the workers affected by these spillovers. In practice, minimum wages appear to create spillover
effects (e.g. DiNardo, Fortin and Lemieux, 1996; Lee, 1999), so we expect them to also
gaining. Therefore,
if
an increase
influence the training of low
in the
wage workers earning above the minimum.
The Effect of Minimum Wages When Workers
Can Pay For Training
4
We now
generalize the
model of the previous section
in
two crucial respects:
(1)
workers
can invest in their general training, but some of them are affected by credit constraints;
returns to training vary across workers.
(2)
5
This
is
special to the case
where the firm has to choose a discrete level of training. If the firm
it would never train the worker beyond the point where it has to
could choose training continuously,
pay above the minimum wage
in the second period (see Figure 1).
11
More
specifically, there is
with support
77,77
second period
if
A
.
a distribution of abilities across workers denoted by G(r])
worker with ability
untrained, and
if
4>rji
produces
?/;
trained.
The
6rji
in the first period,
cost of training
in the
independent of
c
is
77,
ability.
To
we
simplify the discussion,
—
also assume:
1)77
>
c.
This implies that training
is
beneficial for all workers, so
Assumption
3:
(</>
we do not have
to keep track
of whether the worker in question should get training or not.
Furthermore, we assume that workers can "buy" training from their employers, so
the contractual problems discussed in the previous section are absent.
Nevertheless,
workers do not have access to perfect credit markets, and need to achieve a certain level
of consumption in the
distribution of
7 by
wage income
4.1
<
to
A
77.
We
period.
if (7), with
of the distribution of
income, and 7
first
upper support
worker
i,
distribution of
level
and denote the
7
is
independent
7 out of
his
wage
implies that the individual has other assets, so he does not need his
meet
his
consumption obligations. 6 The
Decentralized equilibrium without
all
The
7.
7* for
worker needs to have a consumption
firms with kj
<
rest of the setup
is
unchanged.
Minimum Wages
Equilibrium Without
Once again
denote this by
minimum wages
kn are
is
straightforward to characterize.
Market wages are now conditioned on
active.
ability as well as training:
w 2 {rn,NT) = m
w2 U T) =
(5)
4>r)i.
(j]
Writing profits with and without firm-sponsored training as before, we see once
again that Hj(T)
— Uj(NT) = — c.
employees'
But now, there can be worker-financed
skills.
Assumption
cut.
3, all
workers
Therefore, worker
i
who can
Firms therefore have no incentive to invest
afford
gets training
Orji
This inequality ensures that the
afford to
pay
for his
own
More
will prefer to get training
and only
+5-
first
training.
if
it
training.
kn
>
c
Summarizing
6
specifically,
by
by taking a wage
if
+ 7*.
period wage
in their
is
(6)
high enough that the worker can
this result (proof in the text):
This amounts to lexigographic peferences, whereby the worker first tries to meet his minimum
consumption level, and then maximizes the sum of consumption in both periods. Introducing a concave
utility function for the worker in both periods gives similar results, as it creates a desire for smooth
consumption, but complicates the analysis substantially, so we have opted for this simpler formulation.
12
Proposition 3 There
is
a unique equilibrium in which
wages in the second period are given by
receive the first-period
whom
for
wage
w\{r]i)
and
(5),
= dm + 8 —
(6) holds receive the first-period
all
all
firms with
workers for
<
kj
whom
kn are active,
(6) does not hold
k n and do not obtain training.
wage Wifa)
= 6m +
8
—
kn
—
Workers
and obtain
c
training.
So
in this competitive equilibrium there
is
investment in training. All training
the Becker-type, financed by workers taking a wage cut in the
why
reason
the equilibrium
not first-best
is
is
of
The only
period.
first
is
because some of the workers are credit
constrained and cannot invest in training even though doing so would increase total
output.
also possible to obtain a relatively simple expression for the incidence of training.
It is
Because of Assumption
3, all
workers
who can
afford
it
We
will invest in training.
can
write the incidence of training as
T=
[" H{6n
+ 8-k n -
c)dG{n).
Jr)
Only workers
for
whom
relative to first period
wages which depend on
The Impact
4.2
Now consider
wm > Also
r\.
holds obtain training, and this depends on the size of 7
(6)
of
a binding
their ability n.
Minimum Wages on
minimum
wage,
i.e.
wM
Training
such that
to reduce the cases to be studied, suppose that
wm >
wA <
,j
&V
+
<fin
+
8
—
kn and
8
—
c,
so that
second period employment does not collapse. Similar reasoning to above immediately
gives second period
wages
as:
w 2 {m,NT) = max{w A/ ,77;}
w 2 (Vi,T) =
(7)
ma.x{w M ,(j)m}
minimum wage on investment in skills.
Some of the workers previously financing their own training are now unable to do so.
For example, consider worker % such that 7* < Om + 8 — kn — c < w^j that is worker i was
financing his training by taking a wage cut, to a level now below the minimum. Clearly,
Let us start with the adverse effect of the
,
the
minimum wage
some workers.
7
This
training
is
If
8
=
prevents
this.
7
So a binding minimum wage reduces training
—so that we are in competitive labor markets —
,
this
is
for
the only
without a training subminimura. In our model, as in the standard Becker model, introducing
subminima
increases training.
13
impact of the
minimum wage on
minimum wage
the
eliminates
In addition, however, the
training; since all training
all
training
among
general in this economy,
is
affected workers.
minimum wage induces
firms to train their low skill workers
> Orj, + 6 — kn — c, that
minimum wage. It is then
as in the previous section. Consider a worker with y,
who
could not afford to buy training before the
the analysis in the previous subsection, that
Similarly, even
invest in training.
wM >
if
when w A! <
4>r)
wM > ^ +
c,
a worker
from
clear,
^i, then the firm would
if
u
is
prefer to
the firm prefers to
provide training. Therefore, as in the previous section, labor market rents and
minimum
wages induce employers to invest in general training of some workers.
formally, as in the previous section, a worker receives firm-sponsored training
More
if
wm >
(since
>
<jn\i
r}i
+ c,
if
Vi
the trained worker's wage
Alternatively, the worker will obtain training
minimum
wage. This happens
the
is
c
is
(
at the
when he
+8-
new equilibrium
k*
minimum,
(8) is still satisfied).
finances
himself, despite the
it
- c> ma,x{w M 7J
(9)
,
cutoff capital cost.
These observations provide some insight into the
effects of
minimum wages on
train-
induce firms to train their workers, but prevent workers'
Minimum wages
ing.
8)
if
9rji
where k*
+
own
To understand the whole picture, however, we need to charthe equilibrium fully, which is a little more involved than before. We have
investment in training.
acterize
to determine
rium
level of
first
period wages for workers of different
employment when a minimum wage
is
abilities,
and
find the equilib-
binding. However, since
wages are not central to our focus, we only give these in Appendix
1,
first
period
and only determine
equilibrium employment here.
The key
such that
observation
all kj
<
that there exists, once again, a cutoff level of capital cost,
is
k* will
be
Furthermore, given the additive relation between
active.
firm and worker heterogeneity, firm
profit,
II,-,
from hiring any worker
to hire (otherwise,
his period 1 wage).
rji
all
firms would
So
let
i,
j,
if
so that each firm
want to
make
active, has to
hire the
is
exactly the
indifferent
more
profitable worker, pushing
up
us write the profit that a firm makes from a worker of talent
IT,-
(77O
= max {II,
{ Vi
,
NT)
,
II,
fa T) }
,
,
where
=
total
about which worker
as:
Uj{r)i,NT)
same
{erii
-w
1 {rii
,NT)-kj +
)
14
{'qi
+ 8-max{w M ,r
li
}),
Uj{rii,
=
T)
after substituting (7).
77,
-
(6r)i
AT)
101(77,-,
not receiving training, and
ing training. These
for all
first
-
kj
denotes the
+
c)
{<j)t)i
<
k* should
To
is
make
,
period wage for a worker receiv-
first
period wages have to adjust to ensure that Hjfa)
is
—
profits equal to k*
characterize the equilibrium,
Clearly
kj.
we need
make
n j* (t?*) =
where
kj*
=
k*,
(077*
-
77*,
- wM -
k*
and we have used the
Uj
=
k*
— kj
zero profits, so a firm with
101(77,,
.)
> wm by
to determine k*. Since the
binding, the marginal worker has to be employed at the
the ability of the marginal worker as
=
the equilibrium cutoff capital cost. This ex-
pression follows by noting that, the firm with k* will
kj
+ 8- max {w M 0^})
period wage for a worker with ability
first
T) denotes the
101(77,,
hired in equilibrium, where k*
i
-
twifa, T)
minimum.
8
law.
minimum wage
Hence, defining
we must have
c)
+
+ 8 - max {w AI: &]*}) =
(^77*
worker at the
fact that a
0,
minimum wage
in the
second period necessarily receives training. Hence:
k*
The number
=
(6
+ 0)77* + 8 — c — w M — max {it; a/, (pn*}
of workers employed,
of active firms,
i.e.
to the firms with k
[1
where k*
is
as given
by
(10).
while the right hand side
by the
(77*,
fact that
those with
i.e.
G
and
<
has to be equal to the number
77*,
Hence:
k*.
- Gtf)] n =
Notice that the
F(k*)
left
(11)
hand
side
is
strictly decreasing in
77*,
boundary conditions implied
is
increasing. Together with the
F
are distribution functions, this ensures a unique solution
k*).
We
can now summarize the results (proof in the
Proposition 4 There
k* is given by (10)
The
and
is
(11).
_
F(k*)
Workers with
G(w M -
77*
This would imply
r\i
c)
-
??,
>
f)
=
[w^j
level
G(n*)
+
f
who has
+ c + k* —
is
F{k*) where
[1
now:
-
G(77( 7 ))]
dHfr)
lower talent but low 7, so that he can pay
/9. However, 77 is unambiguously greater
6}
obtained below, confirming that the marginal worker has to be at the
15
E=
satisfying (8) or (9) receive training.
among employed workers
Alternatively, the marginal worker could be one
for his training.
text):
a unique equilibrium with employment
incidence of training
rpMW
than
>
77
(10)
.
minimum wage.
where
is
17(7)
= max {tuyi//</>;
explained by noting
[max{w M j} —
,
that,
8
+
who have
workers
k*
+ c] j9} The second
.
terra in brackets
high enough ability such that
(8)
does
not hold could potentially finance their training, but in that case, they need to have
sufficient
funds in the
credit constraints.
first
period,
Therefore,
i.e.
low enough
minimum wages
7, so that
they are not affected by
increase training for workers
who were
previously unable to finance their training, and have second period wages close to the
minimum. They reduce
who were financing their own training, and
above the minimum so that it is not in the interest
training for workers
have second period wage sufficiently
of their employers to provide
As
them with
training.
MW
the above discussion suggests T
could be smaller than or greater than T, so in
this
more general model, minimum wages could increase
still
employed. More
or reduce training
own
T
those
they will increase training for some workers, especially
specifically,
those at low wages affected by credit constraints, and reduce
cuts to finance their
among
training.
it
for those
taking wage
This discussion also suggests that we expect
T MW
minimum wages to increase training), when most workers
are credit constrained, and when there are many workers with abilities between 77* and
wm — c, for whom minimum wages lead to firm-sponsored training.
Finally, we have so far compared an economy without minimum wages to one with
a binding minimum wage. The results of comparing two economies with different levels
of minimum wages are similar. The only difference is that in a model with a binding
but low minimum wage, some workers with low values of 7^ are already prevented from
paying for their own training. So increasing an already binding, but relatively low,
minimum wage is perhaps more likely to increase training than introducing one in an
economy without minimum wages. Whether this happens is an empirical question, and
we will now provide some new evidence on this.
to be greater than
(i.e.
Empirical Strategy and Data
5
minimum wage was unchanged between 1981 and 1990, but various states
imposed their own minima above the federal level during the late 1980s. While minimum
The
federal
wages were rather uniform across states before 1987 and after 1991, there was substantial
dispersion between these dates.
statutory
minimum wages
We use
on
in the
We
US
will exploit this variation.
Table
1
displays the
states over this period.
two complementary approaches to identifying the impact of minimum wages
training.
The
first
one, which
we
find
most compelling, looks
at the training of
minimum wage.
The second approach looks at the relation between training and a measure of how binding
workers
who
are directly affected
by an increase
16
in the state or federal
minimum wage
the
This latter approach
across regions.
is
most
is
closely related to
the empirical work in the previous literature, and therefore serves as a check on the
robustness of our results.
Empirical Specification
5.1
The most
direct
way
to look at workers
is
minimum wage on training outcomes
by changes in the minimum wage. In
to estimate the impact of the
who
are actually affected
order to illustrate the approach, consider the following regression equation
= amw
rirt
where rTit
is
like
and individual
t.
lt
t
effects,
i
(12)
irt
in region r at time
and x it are other individual
d
t,
t
,
vr
One measure
to the
for
mw
minimum wage
Schiller (1994)
this strategy
minimum wage
binds for individual
i
mw
in region r at
would be whether the actual wage of an individual
irt
for the region
and Grossberg and
and
characteristics
education, age, gender, and information about the job an individual holds.
a measure of whether the
is
+ j3'x + d + v r + & + e
a measure of training for individual
are time, region,
fj,i
irt
is
irt
time
close
and time period. This has been the approach of
Sicilian (1999) using cross-sectional variation.
But.
has the problem that other, possibly unobserved, person characteristics
which are correlated with the individual's wage
tend be correlated with training
will also
receipt.
We
therefore difference eq. (12) to obtain
Arirt = aAmw irt + P'Ax + Ad + Ae irt
it
Changes
in training should
now be
t
(13)
.
related to changes in whether a worker
is
affected
by
minimum wage. As a measure of Amw irt we use a dummy variable which indicates
that the minimum wage increased from one year to the next, and the worker earned
below the new minimum wage in the base year. This measure captures workers who are
directly affected by a change in the minimum wage, similar to Card's (1992) analysis of
employment effects. The measure relies purely on the variation of the minimum wage
and base period wages, but not changes in individual wages, which may be correlated
with when a worker received training. Our analysis will focus on individuals who do
the
not move between states because moving would also confound AmiVi rt with behavioral
effects.
Therefore, differencing has eliminated the region effect in eq. (13).
Although we
wage most
on
eq.
feel
directly,
that this analysis of eq.
(13) exploits variation of the
hence gives the most reliable
(12) to study the
impact of the
level of
17
results, previous studies
the
minimum wage on
minimum
have relied
training.
To
make our
more comparable
results
will in this case
We
or region.
t,
measure how binding the minimum wage
w™. What matters
The same
and
regions,
which a given
effects in different regions
wage
level of the
wT
therefore just parameterizes the
An
level.
time
minimum wage
wage regions than
minimum wage
in high
median wage
wage
For this purpose, we
is
a measure of the location
of older workers) over the
whole
minimum wage itself, and
and w™/w r measures how high the
wage
distribution,
wage
distribution. Notice that
level,
we
are not using
and might create a
training incidence were also cyclical.
obvious choice for the regions are states, since
minimum wages
However, the wage distribution also varies within
vary at the state
states, so that the relative
minimum wage measure can be defined for smaller regions. Apart from states, we
two other measures. One partitions states into SMSAs and non-SMSA parts as
This
region definition.
between large
SMSAs
wT
is
New York
we
Appendix
City)
rural areas in a state (like upstate
When we
2.
The second
wages of male workers age 35-54
if
use states or these smaller regions,
states,
if
i.e.
is
should be more affected by a given
tend to earn
less
wr
uses the average of the
the respondent
the respondent
is
more dispersion
regional measures
federal
we
1
we show
wage by only 0.055
in
in this
male, and of the median
minimum wage than men because
the relative
measure (which
use below) than in the
minimum wage
median
female. This measure exploits the
minimum wages
male medians by state and year over the sample period.
substantially
oiir
than men.
In the right hand panel of Table
is
New
"region" definition distinguishes between the
in the state
wages of female workers age 35-54
women
and
distinguish 136 regions. Details on the construction
male and female wage distribution within
women
our
the average of the median wages of male workers age 35-54 in each
year between 1987 and 1992.
fact that
use
us exploit the often substantial variation in wage levels
In total,
of these are available in
for
lets
(like
York) in the analysis.
measure
is.
allowed to have different
is
which would move with the business cycle at the regional
if
in region r at
should not be affected by the
relative to the region's
spurious correlation
a particular state
in
the
depending on their average wages.
sample period. This measure
w rt
in low
,
is
is
would not be captured by w™. Therefore, we prefer
distribution in region r (the
minimum wage
how binding
minimum wage measures w™/w r where w r
consider relative
of the
is
more workers
affects
this source of variation
specifications in
however,
for the theory,
minimum
federal
directly, the variable
by using simply the actual minimum wage
start
undertake analysis
also
Rather than indicating affected workers
of the levels equation.
mwirt
we
to these previous studies,
New
is still
minimum wage
increases between 1989
It is
using the
apparent that there
coarser than the other
itself.
and 1991 raised the
For example, the
relative
minimum
Jersey but by 0.085 in Arkansas, both states without a state
18
minimum wage above the federal
minimum wage measure leverages
level in 1989.
This illustrates
the increase in the federal
how
the scaling of the
minimum wage across
states
with different wage distributions.
There are a number of practical problems
and
(12)
most training
to
all
For example, training
(13).
is
in
implementing the estimation of equations
not easily defined at a point in time. Because
a short period of time, we will define rrit as referring
spells only last for
incidents of training within a single year. Thus, Trit will be
received any training during the year,
and
1
the individual
if
otherwise. In the differenced equation (13),
the dependent variable takes on the values
-1, 0,
and
1.
We
will
estimate the models
and the inclusion
as linear probability models, facilitating differencing
of fixed effects in
the levels version.
Looking at a time period as long as a year has
may change
its
drawbacks. The
within a year. In order to minimize the impact of
this,
minimum wage
we look
at periods of
minimum wage
12 months starting in April and ending in March. Both federal
increases
minimum wage increases also took
effect on April 1, but many did not. Whenever the minimum wage changed during the
year, we use an employment weighted average of the minimum wage in effect during the
in 1990
and 1991 went into
Some
effect April 1.
state
year.
The
covariance matrix of the error term in eq.
average structure at the individual
Huber estimator, which
covariance estimator
the
minimum wage
is
is
level.
robust to arbitrary cluster effects at the individual
is
variable, only varies at the region
composed
of
an individual
,
level while
is
There
is
dard errors for this error structure.
both an individual
level
component
Aj,
level
we use
indi-
=
A
2
+ v rt +£r
it,
a region*time component
uncorrected across individuals, regions, and time
we
are estimating a
no straightforward way to calculate consistent stan-
We
extend the standard Huber estimator to allow
component and a region*time component
This estimator seems to perform well in practice in samples of our
results of
This
therefore overstate the precision of
Notice that the error E rit will be heteroskedastic, since
linear probability model.
for
may
and year
Suppose the error term has the form e rit
v rU and a component £rit which
periods.
level.
consistent in this case but not efficient. In (12), the key regressor,
the estimates (Moulton, 1986).
the error
order moving
first
We therefore estimate standard errors with the
vidual level data. Conventional standard errors
i.e.
have a
(13) will
some small Monte Carlo experiments
19
in
Appendix
3.
in the error term.
size.
We
report the
The Data
5.2
Our data on
The NLSY
training
is
come from the National Longitudinal Survey
a panel of youths aged 14 to 21 in 1979.
because
siiitable for this project
it
above the
minimum wage
interviewed in the
set of questions
work
likely to
Card and Krueger,
We
1995).
from 1987 to 1992, years of
it
is
particularly
oversamples those
in jobs at or slightly
will follow the cohorts
significant changes in state
and
NLSY
asked a consistent
about on-the-job training during the previous year.
The information
minimum
federal
NLSY
(see
Youth (NLSY).
This dataset
samples young workers, and
from disadvantaged backgrounds, who are more
of
wages. During the 1988 to 1992 surveys, the
about the training includes length and type of the program,
costs of the training
were paid
for
and whether the
site,
by the employer or someone
else.
The
explicit
first set
of
training questions in 1988 refer to a longer time frame than the questions in subsequent
years, because
no similar data were collected
in 1987.
In 1993, the
module on training
in
the survey was expanded substantially and the survey switched from paper and pencil to
computer assisted interviewing.
We use some data from the
information on training during the April 1992 to
1993 survey to complement
March 1993
year.
There were some
other minor additions to the training questions before 1993 as well.
The sequence
"I
of questions
would now
like to
on training begins with a
lead-in stating
ask you about other types of schooling and training you
may have had, excluding regular schooling we have already talked about.
Some sources of occupational training programs include government training
programs, business schools, apprenticeship programs, vocational or technical
institutes,
correspondence courses, company or military training, seminars,
and adult education courses."
This suggests that respondents will mostly report relatively formal training programs
and neglect other sources of informal on-the-job
training,
a suspicion which has been
substantiated by Loewenstein and Spletzer (1999) using the more detailed training data
in the
is
NLSY starting in
1993. While this
may be
a drawback, this limitation of the data
pervasive in this literature.
We
are only interested in training programs which take place in firms, or are spon-
sored directly by the employer, not in courses taken by individuals outside work on
their
own
initiative or
government sponsored training programs.
the following forms of training as "employer related training"
:
We
therefore classify
any training
the respondent gives as venue an apprenticeship program; formal
company
for
which
training; or
seminars or training programs at work run by someone other than the employer; or
20
if
the respondent classifies the training as on-the-job training or work experience; or
the employer paid for the training (even though
we do not
interpret the answer to this
We
question as the employer necessarily bearing the investment costs).
a training programs as employer related
ment program.
9
if
if
do not
classify
the training was partly paid for by a govern-
For each training program we record the start date as reported on the
1988 to 1993 surveys.
date
If this
and 1993, we assign the training
falls
within an April to
March period between 1987
We
to this particular year.
treat observations with a
10
missing start date as missing.
We
do not use any information on the job or employer
in the estimation directly.
However, training often takes place when individuals start new jobs and
increases
may
affect turnover
turnover in some fashion.
and
Hence,
hiring.
it
minimum wage
seems important to control
for
We include a dummy variable for whether a respondent started
any new job within a particular year from information
in the
work history module of
the data.
We limit
likely to
our sample to workers
weighted by the
in the analysis, but
NLSY
it
DC
all
a group most
of blacks, Hispanics
The
results are
Individuals living in the District
had a plethora
minimum wage rules,
minimum wage. Our basic
of different
who report a wage at the interview for the current
and who were employed for at least one month during the
workers
for the past year,
according to the information in the work history module.
to those with valid
less,
the military subsample.
hard to define a sensible overall measure of the
sample includes
and
we drop
sampling weights throughout.
Columbia are excluded, because
making
12 years of education or
We use the oversamples
be affected by the minimum wage.
and poor whites
of
who have
wage information. For the
who move between states.
addition, we use the 1987 to 1993
11
We
(13)
we
year
sample
also restrict the
analysis using eq.
year
also include
individuals
In
calculate the
relative
to
do
median wage
for
this
files
even for smaller areas within states.
For example, each region-year
is
cells
are that small,
The most common government program, JTPA,
by minimum wage
The NLSY
We
cell
has
and the
274.
involves
wage
subsidies
up
to 50 percent
if
trainees
program
is
unlikely
are placed with private sector employers. Hence, the incidence of training under this
10
CPS.
rotation groups are large enough
on older male workers, but few
median number of observations
to be affacted
of the
workers age 35 to 54 from this data source to construct the
minimum wage measure. The CPS outgoing
at least 27 observations
9
outgoing rotation group
legislation.
also provides information
on the length of training.
training directly, because of the frequency of missing values but
We
we checked
do not use the duration of
that our results are robust
to excluding very short training spells.
n The NLSY
CPS wage may
refers to this
wage measure
refer to a prior
job
if
as the
CPS wage
the respondent
21
is
because of the
CPS
style question.
not working at the time of the interview.
The
Empirical Results
6
Table 2 reports means of some demographic indicators
NLSY.
least
samples from the
for the three
All samples include respondents with 12 years of schooling or less working in at
Since young adults
one month during the year.
still
obtain additional schooling in
samples changes over time. The non-mover sample
this age range, the
the unrestricted sample.
About 20
from
differs little
to 25 percent of each sample report having started
a new job during the calendar year. While this includes secondary and temporary jobs,
the
number matches
who
age group
CPS. This
same
relatively closely the fraction of low education workers in the
month
report tenure of 12
or less
on
their current job in the
relatively high rate of job starts reflects the large turnover
January 1991
among young, low
skilled workers.
to
The average nominal hourly wage in
almost $10 in 1992. While a number
less,
as
shown
the basic sample rises from about $7.50 in 1987
of sample
members earn the minimum wage
in the last row, the majority of respondents earn far
wage. These samples therefore include
many workers whose wage
by the minimum. These higher wage workers
differenced analysis.
When we
effectively
is
above the
members
minimum
not directly affected
form our control group in the
look at the impact of the level of the
the other hand, most of the sample
minimum
are not directly affected
wage, on
by the minimum
wage, a problem which has also affected previous studies. In order to address this
we
also use
a low wage sample, defined as workers employed at a wage which
percent of the federal
minimum
sample. These low wage workers include more
school dropouts
is
The
or less in the previous year.
the basic descriptive statistics for this sample, which
last
women and
blacks.
The number
and do not grow substantially over the sample period, due to the sample
spillovers resulting
much more
from
it.
likely to
of high
much
lower
selection.
row
We
Since a larger fraction of these workers are directly affected
find larger negative
sample.
Table 3 reports sample means for some of the key variables in our regressions.
first
150
be actually subject to the minirmim wage or
by the minimum wage, according to standard theory we should
effects in this
is
size of the basic
only slightly higher. Average wages in this sample are
think of this group as
issiie
two columns give
about a third the
is
which
of the table reports the incidence of training,
only exception
is
1987, where the
measured incidence
due to the fact that the training questions were
first
is
much
is
around 10 percent.
lower.
This
is
The
The
presumably
asked on the 1988 survey so that
the questions referring to 1987 had a longer recall period than for later years. There
also a small
spells of 1
or
drop in 1991, possibly due to the recession.
day or
less,
If
we exclude very short
the incidence drops to about 7 to 8 percent.
22
is
training
Our measure of the minimum wage in a region
minimum wage.
In Table
3,
we
the higher of the state and the federal
report the average
minimum wage
minimum wage was
1987, the average
had state minima above the
further to 3.51 in 1989,
when only
3.36,
of 3.35.
in the California state
due to new minimum wage laws
Oregon, Washington, and Pennsylvania.
minimum, and
levels.
increases
among them
deviation across respondents
reaches a high of 29 cents in this year, indicating a substantial
minimum wage
to 3.44
It rises
in other states,
The standard
In
New England
Alaska, and the
minimum wage
federal
mainly reflecting the increase
in 1988,
state
in a year across all
These averages are weighted by the residence of our sample population.
regions.
states
is
amount
of variation in
This variation drops substantially in 1990 and 1991, when
the two federal increases raise the minima in those states which had not taken action
before.
The averages
wages of 3.80 and
of 3.87
and 4.26 are now only
New
4.25. In 1992,
Jersey raises
slightly
its
above the federal minimum
minimum wage
to 5.05, increasing
the spread again.
For our analysis of equation (13),
by the minimum wage. The
minimum wage
report a
first
initial
four different measures for workers affected
one includes
in a year prior to a
wage below the
we use
all
who earned
workers
minimum wage
increase.
minimum. The top panel
less
This includes workers
of Table 3
sample were affected by minimum wage increases
due to the increase
in the California
slightly
more workers, but a
wage.
The
large fraction of workers (7
minimum wage
in the base year. It
these workers should be considered affected or not.
universal during the time period
mostly measurement error.
workers. Excluding
An
Lee (1999),
for
we
state increases in 1989 affect
The second measure
is
is
excludes
not completely clear whether
Minimum wage
coverage was fairly
the
first
measure which includes these
fraction of affected workers about in half in each year.
minimum may
also affect the
and our model then predicts that
example, finds large spillover
during our sample period, and
mostly
consider, so that these reports prestimably reflect
We therefore prefer
them cuts the
increase in the
spillover effects,
12
in 1988,
and 9 percent, respectively)
only affected by the federal increases in 1990 and 1991.
workers below the
who
shows that about
1.4 percent of the
minimum
than the new
we
wages of higher wage workers via
their training should
effects
we
affected.
from the minimum wage changes
report similar results below in Table
investigate whether spillovers affect our results,
be
5.
also included workers
In order to
who
initially
minimum in the affected group. We choose alternatively 150
This yields about two to four
percent and 130 percent of the new minimum wage.
times as many affected workers as our original measure. The bottom panel of Table 3
reports the relative minimum wage measures, i.e. the minimum wage divided by the
earned above the new
12
It is also
possible that respondents receiving tips do not include these in the
23
wage measure.
median
state, regional, or state/gender
the federal
and 1991.
Regression results for the
differenced version of the
first
Apart from the minimum wage
any linear
a
effects of age),
full set
model are displayed
on these covariates are quite
more
of time
dummies and
variables for the change in high
new
This
few workers
who
effect is imprecisely
ifications
we
mum
the
is
able to pick
on the variable
coefficients
effect of raising
estimated because there are
up the expected variation
for affected
minimum wage on
likely to receive training
and
These estimates are sensible and demonstrate
estimated quite precisely.
that the training variable
The
coefficients
acquire a high school degree or equivalent during the sample period.
Workers starting a new job are 3 percentage points more
this effect is
The
job.
High school graduates are 7 percentage points
sensible.
likely to receive training.
in Table
the regressions include a constant (capturing
effect,
school graduation status and for whether the worker took a
(1),
measures
Results Using Affected Workers
6.1
4.
in these
minimum wages and
over time reflect again the increases in various state
increases in 1990
The changes
for older workers.
in the data.
workers are directly interpretable as the
the incidence of training.
The
four different spec-
correspond to four different definitions of the "affected" variable. In column
define
all
as affected.
workers whose wage in the previous year
The
is
below the current mini-
minimum wage
point. The effect is
point estimate indicates that being affected by a
increase raises the probability of receiving training by
1
percentage
not significant, however, and a 95 percent confidence interval includes negative effects
as large as 1.8 percentage points.
The
the previous
minimum
as discussed above,
refer to
column
specification in
it
in the
is
(1)
reporting wages below
base year as affected. While we prefer this specification,
possible that
some
of the
wages below the
initial
minimum
uncovered workers. Therefore we exclude these workers from the affected group
The
in the second column.
results are not very different.
specifications allows spillovers of the
wages.
who were
counts workers
If
we
redefine the affected group as workers
150 or 130 percent of the
zero effects of
minimum wage on
new minimum wage
minimum wages on
training,
in
Neither of the previous
workers with slightly higher
whose previous wage was within
columns
(3)
and
but these specifications
(4),
we
may
find basically
count too
many
workers as affected.
The
training question that
we use
includes very short training programs, and
important to ensure that our results are not sensitive to eliminating these short
With
this purpose,
we
it is
spells.
also repeated these regressions excluding training spells lasting
24
a single day or
from 0.004
We obtain
less.
for the
measure
slightly smaller coefficients for affected workers, ranging
column
in
the measure in column
(2) to -0.013 for
(4),
while
the standard errors were basically unchanged.
Overall, the results contrast sharply with the predictions of the standard theory.
The standard model
affected
is
predicts that
by a minimum wage
affected
general training should be eliminated for workers
increase.
The average
incidence of training in the sample
may not be the right baseline, since it includes higher wage
not affected by the minimum wage. Average training incidence for workers
by a minimum wage increase in the following year is 5.2 percent for the measure
about 10 percent, but
workers
all
this
of affected workers used in
column
(1).
The 95 percent
confidence interval
is
consistent
with declines in training as large as 1.8 percentage points. This means we can reject
minimum wage
the
eliminates
more than a
that.
third of the training in this group. Similar
conclusions are obtained for the other measures of affected workers.
Since according to the standard theory, an increase in the
eliminate
all
general training
with the standard theory
if
among
affected workers, our results could only
most training
(1997) find in later waves of the
NLSY
63 percent of
be consistent
But Loewenstein and Spletzer
is specific.
another 14 percent of training programs, most of the
They
minimum wage should
all
training to be general,
skills
in
are reported to be general.
We
find similar results with other datasets as well.
and
can therefore reject the
minimum wages should wipe out all
However, we cannot rule out that minimum wages simply
strongest implication of the standard theory that
training for affected workers.
reduce training for affected workers, without completely eliminating
results indicate a substantially smaller effect of
estimates in the previous literature.
Results Using
6.2
While the
results in
our methodology
minimum wages on
effects of
somewhat from the previous
this section also includes workers
sample
differs little
who move from
minimum wages on
effect
it is
For example, as we
minimum wages reduce
existing
amount
many
In this section
literature.
The sample we use
we
in
state to state between interviews, but
workers not directly affected by the
natural to worry about whether
on the earnings of workers
13
training,
from the non-mover sample.
Recall that this sample contains
wage, so
training than the
Minimum Wage Changes
present alternative results based on the regression equation (12).
this
Nevertheless, our
13
Table 4 indicate no adverse
differs
it.
will
have a significant
in this sample, since in the absence of such a finding,
discussed in Section
training
minimum wages
minimum
2,
among workers
Neumark and Wascher's (1998) estimates imply that
close to the minimum wage by much more than the
of training.
25
we may expect no
effect
minimum wages on
on training incidence
training,
we
Before turning to the impact of
sample on the real value of the minimum wage and a
in this
dummies. The
feature of the results
first
are affected by changes in the
have an
minimum wage on
therefore look at the effect of the
Table 5 displays quantile regression estimates of the real wage of workers
actual wages.
effect
full set
of year
and
state
that low quantiles of the wage distribution
is
minimum wage, which shows
that
minimum wages do
on the wages of low paid workers. So according to the standard theory,
on
there should be a negative effect
A
either.
training.
minimum wage raises wages of the 10 th percentile worker
which may seem small. The second column in the table repli-
one dollar increase in the
in the
NLSY
by 37
cents,
cates these results with a comparable sample using the
with similar
results,
CPS
outgoing rotation groups,
showing that these results are not particular to the NLSY. There
why the coefficients even at the low quantiles should be less
certainly much measurement error in the wage reports of workers,
are various reasons to expect
than one.
There
is
biasing these coefficients down.
Furthermore, Table 2 revealed that even workers at the
10" percentile will typically earn above the old
1
may
they
not receive the
full
increase
when
the
minimum wage already, and therefore
minimum wage goes up. Nevertheless,
t/l
the results in Table 5 show that workers as high as the 30 percentile of the wage dis-
tribution
also
be
may be
affected
by minimum wage changes, and therefore
their training
may
affected.
Table 5 also shows that there are
many
workers in this sample
by minimum wages. This means that our estimates of training
biased towards zero.
in the lower
less
effects will
tend to be
than 150 percent of the federal
in the previous year, corresponding roughly to the
percentile of the original sample.
actually affected
are not affected
This motivates our strategy to compare our basic results to those
wage sample using only workers earning
minimum wage
who
workers up to the 30 th
This sample more closely approximates the workers
by the minimum wage or by
spillovers resulting
from the minimum.
If
the results in the larger sample are biased towards zero, then the more restrictive sample
should lead to more extreme estimates.
Table 6 presents our regression results for the incidence of training on the
wage and
relative
minimum wage
and without time and region
measures.
14
If
effects
present four sets of regressions with
fixed effects, as well as
individual instead of region fixed effects.
mies
We
for blacks, Hispanics, females,
14
minimum
one specification which includes
Other covariates in the regressions are dum-
high school graduates, and whether the individual
makes it less likely that the individual will be trained in the future, the individual
model may be problematic. However, in our sample, training is positively correlated over time.
training this year
26
started a
new job during
the year, and a linear variable for age. 15
demographic covariates are again
Contrary to the typical finding
in this low
new
more
in the literature,
individual effects are controlled
If
is
no region or time
and
positive
to have
may
more
simply
industrial
mean
and time
higher
receive less training,
column
wage increased by 81 cents
reflects that states
differ, for
we
in real terms
from 1989 to 1991.
We
column
mation, which
is
first
Rows
3
if
we
The
This increase led to about
One
reason for this
minimum wage
To
will
is
that the
minimum wage
have very different
exploit this information,
inforeffects
we next turn
measures.
results
where we divide the minimum wage by
The
specification
minimum wage measure
in
a moderate negative
In row 5 below, where
we
coefficient.
results, this coefficient is
which exploits primarily
column
(2)
which are much
now
even significant. This specification
But the
closer to zero, indicate again that the
wage measure was picking up across region
results in
use more detailed regions
compares most closely to the approach of Leighton and Mincer (1981).
(4) or (5),
Un-
2.
and are consistent with both
the cross region variation in the
columns
minimum
federal
look at the low wage sample in row
the median wage of older males in the state.
in
control for state
two rows does not exploit a relevant part of the
and 4 of the table report
and obtain more precise
when we
16
that a given level of the
minimum wage
terms of their
find similar results including individual fixed
depending on how high wages are in a region.
to the relative
in
(5).
positive effects.
are using in the
or
a small negative effect on training.
fortunately, these results are very imprecisely estimated
variable
example
in general, this
This latter specification, which we prefer, suggests that
(4).
more negative
and
when
strongest
is
minimum wage measure
with higher minimum wages tend
minimum wage measures below
effects instead of state effects in
substantial negative
men
In fact, the positive result in column (2) vanishes
structure.
0.6 percentage points less of training.
are
training as
and workers starting
surprisingly, this latter effect
that high and low wage states
minimum wages have
The estimates
much
Because these states tend to have higher wages
at the relative
effects in
receive as
for.
This
and occupational
when we look
women
effects are included, the effect of the
significant.
training.
Not
training.
on the
coefficients
Minorities receive significantly less training.
sensible.
wage group. High school dropouts
jobs receive
The
results
minimum
differences in training incidence.
We
feel
15
Curvature of the age profile is empirically unimporant for the small age range in the sample,
we do not include higher order terms.
16
In the specification with individual fixed effects, only the region*time clusters remain in the error
term. The standard Huber estimator allowing for these clusters is consistent. Our standard errors in
therefore
column
(5) are therefore
the most reliable.
Interestingly, the standard errors
variable do not differ substantially from those in
column
27
(4).
on the minimum wage
that the estimates including time and region or individual effects are most reliable.
Some
of the time variation of our training
measure
is
likely
due to the change
in the
survey questions and cyclical variations. Differences in training incidence across regions
may
and occupational compositions. The negative
reflect differences in industrial
of the
minimum wage
wage regions tend
to have
which are the most
training.
column
in
more
reliable,
(2) is therefore likely to reflect
training.
The
effects of
and region
effects,
minimum wages on
17
In order to interpret the magnitudes of the estimates
this relative
relative
the fact that higher
results including time
do not indicate any negative
effect
and confidence
intervals using
measure of the minimum wage, return to the bottom panel of Table
minimum wages
To gauge the impact
3.
The
increased by about 5 to 6 percentage points from 1989 to 1991.
of the federal increases,
more
it is
only for the states that were subject to the federal
useful to calculate the
minimum
in 1989.
minimum wage measures by
the federal increases raised the relative
means
For these states,
0.07 using the male
and by 0.08 using the state/gender medians. This means that
state or region medians,
a 95 percent confidence interval for the estimates in column
(4)
using state medians for
the unrestricted sample excludes negative changes in training of 2.9 percentage points
or larger in response to the federal increases. It
the findings by
Neumark and Wascher
that the California state
increase between 1989
points
among young workers age
as our sample.
We
instructive to
compare
this result to
(1998), for example. Their point estimates imply
minimum wage
and 1991)
is
(which was similar in magnitude to the federal
led to a decline in formal training of 3.2 percentage
20-24, a group with a similar average training incidence
can reject a decrease of this size
for
our sample.
Looking at the low wage sample, we obtain a virtually identical point estimate when
we
include time and state effects.
point estimate
is
When we include individual instead of state effects,
actually positive now.
Thus, the results with the low wage sample do
not indicate that the estimates for the basic sample were attenuated.
are unchanged
of the
when we look
median wage.
than the
states.
at the
minimum wage measure
In rows 5 and
We
6,
These conclusions
scaled by alternative values
we use the median wage
for 136 regions smaller
find small positive point estimates for the basic sample,
slightly larger estimates in the
low wage sample.
To the degree
is
positive, rather
Our theory
predicts that
more
precise than the state results, however.
minimum wages reduce employment, but our samples focus on employed
When we use a sample of respondents including non- workers,
workers. This might bias our estimates up.
we
actually find slightly
minimum
than negative. The within estimates using these
smaller regions turn out not to be any
17
and
that these results
indicate attenuation in the basic sample, they suggest that the actual effect of
wages on training
the
more postive
results,
however.
28
The
wage
two rows
last
Table 7 present results scaling the
results for the basic
Controlling for time
However, this result
less
if
we
precise,
and state
effects,
we now
not replicated
is
because there
more
is
The
variation in the measure
For the low wage sample, the results are a bit different.
exploiting gender differences.
earned
the median
sample are again rather similar to the previous measures.
now somewhat more
In addition,
minimum wage by
workers in the same state and of the same gender as the respondent. The
for older
results are
in
find a negative effect for
when we
wage sample
tighten the low
than 130 percent of the federal
is
wages.
control for individual effects instead.
further to include only workers
minimum wage
much more
in the previous year,
We
a coefficient of 0.097 (with a standard error of 0.294).
estimate for the low wage sample
minimum
likely
we
who
find
conclude that the negative
an indication of the sampling
variation of these estimates rather than evidence that the estimates for the basic sample
are attenuated.
Concluding Remarks
7
Standard theory of
pact of
minimum
human
capital
makes an unambiguous prediction regarding the im-
wages: training should decline for affected workers, because workers
finance the provision of the general
minimum wages
prevent
this.
We
component of training by taking lower wages, and
show that
this conclusion is not robust. In labor
markets where employers obtain rents from the employment relationship, the theory
has quite different implications regarding the impact of
While minimum wages reduce training
also
for
some workers
encourage firm-sponsored training and increase
minimum wages on
training.
as in the standard theory, they
human
workers. Therefore, our model predicts offsetting effects of
capital investments for other
minimum wages on
training,
minimum wages increasing training investments.
In the second part of the paper, we provided some new empirical evidence on the impact of minimum wages on training. Focusing on workers actually affected by minimum
wage changes we find no evidence that minimum wages reduce training. In addition,
we can reject negative estimates of the magnitude previously found in the literature.
and
is
even consistent with
This result
is
not an artefact of our methodology, since we find comparable results us-
ing specifications which are
negative estimates
states.
more
when we simply
similar to previous studies.
regress training
real
obtain the most
minimum wage
within
However, these estimates are also the most imprecise, and therefore the least
informative.
When we
rely
on
relative
minimum wage
the differential impact of the changes in the federal
effects
on the
We
on training.
We
measures, thus better exploiting
minimum
wage,
we
find
no negative
probe these results by comparing estimates from a larger base-
29
line
sample to those from a smaller sample of low wage workers.
resembles what other researchers have used, in that
by the minimum wage.
minimum wage on
If
includes
many
baseline sample
workers unaffected
these unaffected workers simply obscure the impact of the
training,
low wage workers, but this
it
The
is
we should
find systematically
more negative
effects using
not the case, once again suggesting that binding
minimum
wages do not reduce training.
A drawback of oirr
a
much
analysis
is
that
we
only focus on rather formal training.
larger part of on-the-job learning in low
plausible that formal
and informal training are
not shed any direct light on the receipt of
more extensive questions on informal
a period with
little
aging so that fewer
less
wage jobs
is
more
Possibly
informal.
positively related, but our analysis does
formal training.
training starting in 1993.
The NLSY introduced
Unfortunately, this
minimum wage changes, and the NLSY sample
workers receive the minimum in the 1990s.
dispersion in
30
It is
is
is
also
Appendix
8
Wages With Worker
First Period
1:
Heterogeneity
First, take
a
wM >
satisfying
ii l
In contrast,
we could have
worker
in the second period
if
=
k*
Then, n,-^)
=
IT/
—
w^
i is
if
r)i
if (8)
and
(9)
G
(rji
Some
of the
level
wage
—
-
+
8-w M
-
T)
=
6r}i
+8-
k*
-
c}
(14)
.
binding.
that
the
is
k*
i
—
c}
.
takes a
wage cut
in the first
k*
- c> w M
.
do not hold, then,
= max{w M ,(l + 6)7], + 8 first
k*}
,
period wages for given
k*.
Construction of Regions
2:
minimum wage measures used
by a regional reference wage.
in this
An NLSY
paper scale the state minimum wage
respondent's reference wage
in his/her geographic region for 35-54 year old
CPS Outgoing
is
kj solves for
minimum wage is binding
but does not bind when he is trained.
c, (jrqi),
not trained,
which completes the characterization of
Appendix
k*
= max {wm, 6r]i + 8 —
Wi(r)i,NT)
9
=
so:
wi(r]i,
Finally,
Ylj
then by construction, worker
satisfies (9),
period to obtain training,
6)ii l
=
kj solves for
wi(i]i,T)
Next,
IIf(?7j)
when the minimum wage
period wages
first
then
=ma,x{w AI ,(<p +
Wi{r]i,T)
So (14) gives
frfr,
Rotation Groups.
is
the median
male workers calculated from the
This appendix explains
how
the regions were con-
structed.
To account
states,
for the fact that there is significant variation in
average wages within
and to allow the minimum wage measure to have greater within-state
we used information on an NLSY respondent's
Because of sample
MSAs. For
all
sizes,
other areas
an individual resided
The
CMSAs
following
list
in
CMS A/MSA of residence,
we used msa_code only
(i.e.,
an
smaller
MSA
variation,
("msa_code").
for individuals residing in the large
and non-MSAs), we used data on whether
("msa_status").
contains the 35
defined by the 1990
MS As
many
MSAs we
FIPS Guidelines
31
classified as large.
(plus the St. Louis,
We
MO
included the 20
CMSA,
while
we
CMSA
do not distinguish the Providence, RI
added 15
MSAs
from other metropolitan parts of RI) and
with large populations.
GA
Atlanta,
Baltimore,
MD
Boston-Lawrence-Salem,
MA-NH CMSA
NY CMSA
Buffalo-Niagara Falls,
CMSA
Cincinnati-Hamilton, OH-KY CMSA
Cleveland-Akron-Lorraine, OH CMSA
Columbus, OH
Dallas-Fort Worth, TX CMSA
Denver-Boulder, CO CMSA
Detroit-Ann Arbor, MI CMSA
Hartford-New Britain-Middletown, CT CMSA
Houston, TX CMSA
Chicago-Gary Lake County, IL-IN
Indianapolis,
IN
Kansas
KS
City,
CA CMSA
Miami-Ft. Lauderdale, FL CMSA
Milwaukee-Racine, WI CMSA
Los Angeles- Anaheim-Riverside,
Minneapolis-St. Paul,
MN
New Orleans, LA
New York-New Jersey-Long
Island,
NY-NJ-CT CMSA
Norfolk-Virginia Beach-Newport News,
FL
Orlando,
Philadelphia- Wilmington-Trenton,
Phoenix
VA
,
PA-DE-NJ
AZ
Pittsburgh-Beaver Valley,
Portland- Vancouver,
PA CMSA
OR CMSA
CA
St. Louis, MO CMSA
San Antonio, TX
San Diego, CA
Sacramento,
San Francisco-Oakland-San
Seattle-Tacoma,
Jose,
CA CMSA
WA CMSA
Tampa-St. Petersburg-Clearwater,
Washington, DC,
FL
DC-MD-VA
32
CMSA
The
full set
of regions consists of state-msa_code level regions for the above 35
and state-msa_status
how
living in Massachusetts illustrates
lived in the
Boston
The example
level regions for all other areas.
CMSA,
the reference wage
is
chosen.
If
of an individual
If
the individual
the reference wage would be the median wage for 35-54
year old male workers living in the Massachusetts part of the Boston
median").
MSAs
CMSA
"MSA
CMSA,
(the
the individual lived in a metropolitan area other than the Boston
the reference wage would be the median wage for 35-54 year old male workers living in
Massachusetts metropolitan areas other than the Boston
in a non-metropolitan area, the reference
CMSA.
If
the individual lived
wage would be the median wage
old male workers living in Massachusetts non-metropolitan areas
for 35-54 year
("non-MSA median").
NLSY and CPS sometimes suppress the specific
smaller MSAs and/or smaller states. In the CPS
For confidentiality reasons, both the
MSA
of residence for individuals in
data, there were five states in which msa_status
Nevada, Rhode Island, Utah and Wyoming.
as
non-MSA, with the
We classified
CMSA.
Reno MSA.
In
Rhode
New London MSA. In Utah, they are
Finally, no MSAs in Wyoming are identified.
fringes of
MSAs
an
In Nevada, they are from the non-
Island, they are
of the
classified as living in
these suppressed observations
following rationale. In Maryland, the suppressed observations are
from the Maryland part of the Philadelphia
central city part of the
was sometimes suppressed: Maryland,
from the Rhode Island part
from the Utah part of the Flagstaff MSA.
For
all five states,
MSA or the information was
an individual was either
suppressed,
observations from
i.e.
were grouped with the non-MSA observations to ensure confidentiality.
Thus, classifying
all
the individuals living in areas with suppressed codes as
non-MSA
seems the most sensible choice.
In addition, there are
MSAs
which straddle
different states
MSA in a particular state is not identified if the part is
the Indiana part of the Cincinnati
MSA,
and sometimes part of an
too small. This was the case
the Maryland part of the Philadelphia
for:
CMSA,
the North Carolina part of the Norfolk
MSA
CMSA
groups these areas with other metropolitan ar-
eas,
and Minneapolis MSA. The
and thus
NLSY.
MSA
land's
CPS
and the Wisconsin part
of the Chicago
appropriate to use the state-MSA median for these observations in the
it is
Finally, in
Maryland, the Cumberland,
are not separately identified.
non-MSA median
is
really a
MD-WV MSA
and the Hagerstown,
MD
Here we assign the non-MSA median since Mary-
median excluding the Baltimore and Washington,
D.C. MSAs.
In the
NLSY
was suppressed
data, there were two complications. First, as in the
for certain individuals.
We dropped
of 21,680 observations from the Basic Sample).
the
New England
states whereas the
CPS
uses
33
CPS, msa_status
the suppressed observations (62 out
NECMAs for
CMSA/MSAs. The NLSY switched to
Second, the
NLSY
uses
NECMA codes for 1987 by using information
on state and county of residence. We then mapped NECMA codes into MSA codes.
Specifically, individuals living in the Boston NECMA or Hartford NECMA were classified
as living in the Boston CMSA and Hartford CMSA, respectively. Also, individuals living
in any NECMA were classified as living in an MSA.
NECMA codes in
we constructed the
1988;
NLSY
All together, the unrestricted
regions
sample contains 21,618 observations from 136
and 753 region-year
categories.
Of the 136
level regions, 45 to
state-MSA
level regions
msa.code
regions, 44 correspond to state-
and 47 to state-non-MSA
regions.
These regions form a partition of the country. The median number of observations in
each region-year
Chicago
of
CMSA in
all cells
the
cell in
is
274 and the range
fall
27
(for
the Indiana part of the
1990). Less than 10 percent
than 5 percent of the
less
NLSY
into those cells.
Appendix
We assume that
is
CMSA in
1991) to 2261 (the Los Angeles
have fewer than a 100 observations and
observations
10
CPS
Estimation of the Standard Errors
3:
=
the error term has the form e tj
+ Vj + ^j
Xi
and j denotes region*time. Let x^ be a vector of right-hand
where
i
denotes individual
side variables,
Xil
Xi
£•
=
il
*U
J
the matrix of right-hand side variables for individual
the Xi's.
To simultaneously adjust
i,
X the stacked matrix of
and
and region*time
for individual
effects,
all
we use the
covariance matrix
v=
(x'x)- l x'nx(x'xy
l
where
X'SIX
=
2_J X'i£i£'iXi
+ X, >
i^k
i
In order to get an idea
how
„
£ij£kj%ij%ki-
j
this covariance estimator
conducted a small Monte Carlo experiment.
performs in our sample, we
For this experiment
we generated samples
with the same number of observations, individuals, regions, and time periods as in our
unrestricted sample according to the design
y
*.
= OA + O.lxuj + O.lXij + O.lxai +
f
Vij
\
i
ifp<y*-
iip>y*j
34
Xi
+
Vj+tij
where p and each of the
~A
r
x's are
In regression
(0, 0.1).
drawn from a uniform
and
(0,1) distribution
^
A,, Vj,
we computed the OLS estimate of y on the three x's and
matrix above. In regression 2, we estimated the regression
1,
constructed the covariance
of y on the x's also including region
and time
fixed effects.
We replicated
each regression
10000 times with the following results:
Regression
regressor
standard deviation of /?
mean of estimated standard error
x Uj
%2j
^32
Elij
X 2j
X3
0.0116
0.0320
0.0126
0.0116
0.0355
0.0124
0.0116
0.0314
0.0124
0.0115
0.0304
0.0122
No
No
Year Effects
Region Effects
Regression
1
x 2j
,
Yes
Yes
indicates that the covariance estimator does a
sampling variation for
for
Regression 2
1
all
regressors.
However, in regression
which only varies at the region*time
wage measure,
is
good job
level, i.e.
understated by about 15 percent.
2,
in estimating the
the sampling variation
the analogue to our
Of
minimum
course, these results are only
suggestive.
In our design, Vj contributes a third to the total variance of the error term.
The
would change
results
as
we change
the relative variances of this error component.
35
i
References
[1]
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[2]
Acemoglu, Daron and Jorn-Steffen Pischke (1999b) "The structure of wages and
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Gary (1964) Human
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Becker,
[4]
Ben-Porath,
Yoram
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Chicago:
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human
(1967) "The production of
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107, 539-572.
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life
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Card, David (1992) "Using regional variation in wages to measure the
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capital.
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the
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Hashimoto, Masanori (1982) "Minimum wage
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Loewenstein,
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Mincer, Jacob (1974) Schooling, Experience, and Earnings.
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37
Table
Minimum Wage and
Statutory
Relative
1
Minimum by
State
and Year
Minimum
Minimum Wage
IVage/Avg.
Median Wt ige Age 35- 54
1990
1991
1992
1992
1987
1988
1989
4.25
4.25
0.308
0.306
0.305
0.344
0.383
0.381
4.75
4.75
0.215
0.214
0.213
0.237
0.260
0.259
3.80
4.25
4.25
0.262
0.261
0.260
0.293
0.326
0.325
3.35
3.80
4.25
4.25
0.342
0.341
0.339
0.382
0.426
0.424
3.35/4.25
4.25
4.25
4.25
4.25
0.234
0.279
0.294
0.292
0.291
0.290
3.35
3.35
3.35
3.80
4.25
4.25
0.245
0.244
0.243
0.274
0.305
0.304
3.37/3.75
3.75/4.25
4.25
4.25
4.27
4.27
0.236
0.265
0.279
0.277
0.277
0.276
Delaware
3.35
3.35
3.35
3.80
4.25
4.25
0.242
0.241
0.240
0.270
0.301
0.300
Florida
3.35
3.35
3.35
3.80
4.25
4.25
0.304
0.303
0.302
0.340
0.378
0.377
Georgia
Hawaii
3.35
3.35
3.35
3.80
4.25
4.25
0.290
0.288
0.287
0.324
0.360
0.359
3.35/3.85
3.85
3.85
3.85
4.25
4.75/5.25
0.251
0.276
0.275
0.273
0.300
0.343
Idaho
3.35
3.35
3.35
3.80
4.25
4.25
0.296
0.294
0.293
0.330
0.368
0.366
Illinois
3.35
3.35
3.35
3.80
4.25
4.25
0.239
0.238
0.237
0.268
0.298
0.297
Indiana
3.35
3.35
3.35
3.80
4.25
4.25
0.281
0.280
0.279
0.314
0.350
0.348
Iowa
Kansas
Kentucky
3.35
3.35
3.35/3.85
3.85/4.25
4.25/4.65
4.65
0.285
0.283
0.293
0.330
0.363
0.386
3.35
3.35
3.35
3.80
4.25
4.25
0.270
0.269
0.267
0.301
0.335
0.334
3.35
3.35
3.35
3.80
4.25
4.25
0.291
0.290
0.288
0.325
0.362
0.361
Louisiana
3.35
3.35
3.35
3.80
4.25
4.25
0.289
0.288
0.286
0.323
0.359
0.358
Maryland
3.35
3.35
3.35
3.80
4.25
4.25
0.235
0.234
0.233
0.262
0.292
0.291
3.55/3.65
3.65/3.75
3.75
3.80
4.25
4.25
0.250
0.256
0.256
0.258
0.287
0.286
3.35
3.35
3.35
3.80
4.25
4.25
0.231
0.230
0.229
0.258
0.287
0.286
Minnesota
3.35/3.55
3.55/3.85
3.85/3.95
3.95/4.25'
4.25
4.25
0.256
0.272
0.288
0.292
0.312
0.311
Mississippi
3.35
3.35
3.35
3.80
4.25
4.25
0.340
0.339
0.337
0.380
0.423
0.422
Missouri
3.35
3.35
3.35
3.80
4.25
4.25
0.279
0.278
0.277
0.312
0.348
0.346
Montana
3.35
3.35
3.35
3.80
4.25
4.25
0.292
0.290
0.289
0.326
0.363
0.361
Nebraska
3.35
3.35
3.35
3.80
4.25
4.25
0.303
0.302
0.300
0.338
0.377
0.375
Nevada
3.35
3.35
3.35
3.80
4.25
4.25
0.266
0.265
0.264
0.297
0.331
0.330
New Hampshire
New Jersey
New Mexico
New York
3.45/3.55
3.55/3.65
3.65/3.75
3.75/3.85
4.25
4.25
0.257
0.263
0.269
0.277
0.308
0.307
3.35
3.35
3.35
3.80
4.25
5.05
0.216
0.216
0.214
0.242
0.269
0.319
3.35
3.35
3.35
3.80
4.25
4.25
0.284
0.283
0.281
0.317
0.353
0.352
3.35
3.35
3.35
3.80
4.25
4.25
0.238
0.237
0.236
0.266
0.296
0.295
North Carolina
North Dakota
Ohio
3.35
3.35
3.35
3.80
4.25
4.25
0.315
0.313
0.312
0.352
0.391
0.390
3.35
3.35
3.35
3.80
4.25
4.25
0.291
0.290
0.288
0.325
0.361
0.360
3.35
3.35
3.35
3.80
4.25
4.25
0.260
0.259
0.258
0.291
0.324
0.322
Oklahoma
3.35
3.35
3.35
3.80
4.25
4.25
0.282
0.281
0.279
0.315
0.350
0.349
Oregon
3.35
3.35
3.35/4.25
4.25/4.75
4.75
4.75
0.262
0.261
0.287
0.336
0.364
0.363
1990
1991
3.35
3.80
3.85
4.30
3.35
3.35
3.35
3.35
California
3.35
Colorado
1987
1988
1989
Alabama
3.35
3.35
Alaska
3.85
3.85
Arizona
3.35
Arkansas
Slate
Connecticut
Massachusetts
Michigan
2
3.35
3.35/3.70
3.70
3.80
4.25
4.25
0.269
0.273
0.294
0.300
0.334
0.333
3.55/3.65
3.65/4.00
4.00/4.25
4.25
4.45
4.45
0.281
0.302
0.321
0.324
0.338
0.337
South Carolina
3.35
3.35
3.35
3.80
4.25
4.25
0.305
0.304
0.302
0.341
0.379
0.378
South Dakota
Tennessee
3.35
3.35
3.35
3.80
4.25
4.25
0.337
0.336
0.334
0.377
0.420
0.418
3.35
3.35
3.35
3.80
4.25
4.25
0.331
0.329
0.328
0.370
0.411
0.410
Texas
3.35
3.35
3.35
3.80
4.25
4.25
0.280
0.279
0.278
0.313
0.348
0.347
Utah
3.35
3.35
3.35
3.80
4.25
4.25
0.259
0.258
0.256
0.289
0.322
0.320
Vermont
3.45/3.55
3.55/3.65
3.65/3.75
3.85
4.25
4.25
0.306
0.313
0.320
0.324
0.361
0.360
Virginia
3.35
3.35
3.35
3.80
4.25
4.25
0.252
0.251
0.249
0.281
0.313
0.312
Washington
West Virginia
Wisconsin
3.35
3.35/3.85
3.85/4.25
4.25
4.25
4.25
0.236
0.244
0.277
0.294
0.293
0.292
3.35
3.35
3.35
3.80
4.25
4.25
0.294
0.293
0.292
0.329
0.366
0.365
3.35
3.35
3.35/3.65
3.80
4.25
4.25
0.270
0.269
0.286
0.302
0.336
0.335
Wyoming
3.35
3.35
3.35
3.80
4.25
4.25
0.263
0.262
0.261
0.294
0.327
0.326
Pennsylvania
Rhode
1
2
Island
Minnesota: Only large employers covered by the new 1991 minimum wage.
Oregon: Minimum wage changed from 3.35 to 3.85 and then 4.25 during the year.
minimum wages in each state and year. Years begin in April
minima are shown if the state minimum changed during the April to
minimum wage divided by the average median wage for male workers 35-54
Notes: Left hand panel of the table shows the higher of the state or federal
of the year shown
March
period.
until
The
March of the following
right
year. Multiple
hand panel of the table shows the
years old in the state during the 1987 to 1992 period.
38
Table 2
Sample Means of Demographics
(Standard Deviations in Parentheses)
Variable
1988
1992
Unre stricted
Sample
1987
1992
Female
0.434
0.428
0.432
Black
0.134
0.132
Hispanic
0.067
Non-move) Sample
•
Low Wage Sample
1987
1992
0.427
0.527
0.602
0.128
0.133
0.169
0.203
0.067
0.064
0.067
0.061
0.073
27.2
31.2
26.2
31.2
25.8
31.1
Less than High School
0.187
0.171
0.192
0.173
0.262
0.240
New Job
0.273
0.216
0.268
0.220
0.338
0.323
8.16
9.71
7.58
9.70
5.12
5.91
(5.36)
(6.54)
(5.51)
(6.52)
(2.57)
(2.82)
Age
Nominal Hourly Wage
Real Hourly
Wage
(1982-84$)
Fraction Earning
Minimum or Less
Number of Observations
7.30
8.52
6.81
8.51
4.60
5.18
(4.79)
(5.73)
(4.95)
(5.72)
(2.30)
(2.47)
0.042
0.058
0.068
0.059
0.155
0.162
3872
3094
3979
3136
1673
1048
NLSY.
Unrestricted sample consists of individual-year observations that have high
one month of the year and in both the prior and current year have non-missing
wage data. Non-mover sample excludes from the unrestricted sample individuals who have moved to a new state since the
previous year. Low wage sample imposes on the unrestricted sample the restriction that the "CPS wage" in the previous
year is less than or equal to 150% of the federal minimum wage. Year refers to April to March (of following calendar
year). New job refers to the start of any new job during the year. Hourly wage is the "CPS wage" for workers employed at
a "CPS job" only. NLSY data include black, Hispanic and poor white oversamples. The poor white oversamples were
discontinued in the 1991 survey year, accounting for the lower number of observations in 1992. Statistics are weighted by
Notes: Unbalanced panel from the
school education or
the
NLSY
less,
work
in at least
sampling weights.
39
Table 3
Sample Means of Key Variables
(Standard Deviations
1987
Variable
in
Parentheses)
1988
1989
1990
1991
1992
0.099
0.106
0.094
0.103
Non-mover Sample
0.099
Training Incidence
Nominal Minimum Wage
Minimum wage
in prior year is
increased and
wage
3.51
3.87
4.26
4.28
(0.29)
(0.16)
(0.05)
(0.15)
0.014
0.020
0.069
0.091
0.001
0.007
0.008
0.034
0.050
0.034
0.062
0.085
0.263
0.293
0.011
0.041
0.058
0.166
0.204
0.007
3872
3793
3187
3122
3094
0.100
0.107
0.094
0.102
below the current
minimum wage
Minimum increased and wage in prior
year is below the current minimum
and above prior year minimum
Minimum wage increased and wage
in prior year is
3.44
(0.21)
below 150
% of the
minimum wage
Minimum wage increased and wage
in prior year is below 130% of the
current minimum wage
Number of Observations
current
Unrestricted Sample
0.064
Training Incidence
Nominal Minimum Wage
Minimum Wage
0.099
3.36
3.44
3.51
3.87
4.26
4.29
(0.06)
(0.21)
(0.29)
(0.16)
(0.05)
(0.15)
3.02
3.08
3.12
3.42
3.75
3.76
(1982-84$)
(0.05)
(0.19)
(0.26)
(0.14)
(0.05)
(0.13)
Minimum Wage/Median Wage (men
0.267
0.271
0.276
0.301
0.331
0.332
(0.030)
(0.027)
(0.028)
(0.031)
(0.038)
(0.037)
0.272
0.277
0.282
0.307
0.338
0.340
(0.043)
(0.041)
(0.042)
(0.045)
(0.053)
(0.051)
0.324
0.330
0.336
0.366
0.402
0.404
(0.077)
(0.076)
(0.078)
(0.086)
(0.097)
(0.097)
0.068
0.044
0.050
0.047
0.072
0.059
3979
4043
3958
3295
3207
3136
Real
35-54, states)
Minimum Wage/Median Wage (men
35-54, regions)
Minimum Wage/Median Wage
54, state
(35-
and gender)
Fraction Earning
Minimum
or Less
Number of Observations
Notes: See Table 2 for a description of the sample composition. Training incidence refers to employment related training.
refers to the higher of the state or federal minimum applicable to an NLSY respondent. Median wage for
35-54 year old workers are calculated from the CPS Outgoing Rotation Groups. The poor white oversamples were
Minimum wage
discontinued
in the
weighted by the
1991 survey year, accounting for the lower number of observations
NLSY
sampling weights.
40
in
1990 to 1992.
Statistics are
Table 4
The
Effect of
Minimum Wage
Increases on Affected
Independent Variable
Minimum wage
increased and
the current
wage
increased and
in prior year is
prior year
wage
below
minimum
Change
in
in
high school graduation status
new job
status
(3)
(4)
—
—
0.016
—
(0.019)
—
—
(0.008)
—
—
—
in prior year is
% of the current minimum wage
Minimum wage increased and wage in prior year is
below 130% of the current minimum wage
Change
(2)
0.010
(0.014)
in prior year is
minimum and above
Minimum wage
below 150
wage
minimum wage
increased and
below the current
Minimum
(1)
Workers
—
0.005
-0.002
(0.010)
0.070
0.070
0.070
0.070
(0.053)
(0.054)
(0.054)
(0.054)
0.032
0.032
0.032
0.032
(0.008)
(0.008)
(0.008)
(0.008)
Non-mover sample, consisting of all workers with a high school education or less, who do not move between states
from one year to the next. Dependent variable is the change in training incidence between two consecutive years. All
regressions also include a constant and year dummies. Regressions are weighted by NSLY sampling weights. Standard
Notes:
errors are adjusted for the presence
error.
Sample
size
is
of individual effects
in the error
17074.
41
term, and therefore robust to the
MA structure of the
Table 5
Quantile Regressions for Real Wage on Real
Minimum Wage
Unrestricted Sample
Quantile
NLSY
CPS
0.10
0.376
0241
(0.087)
(0.024)
[0.084]
0.20
0.156
0.137
(0.105)
(0.011)
[0.109]
0.30
0.146
0.052
(0.163)
(0.016)
[0.121]
0.40
0.049
0.032
(0.158)
(0.045)
[0.102]
0.50
0.137
0.000
(0.178)
(0.025)
[0.111]
0.60
0.029
0.130
(0.173)
(0.053)
[0.113]
0.70
-0.120
0.030
(0.247)
(0.043)
[0.135]
0.80
0.296
0.011
(0.446)
(0.044)
[0.198]
0.90
0.312
0.157
(0.593)
(0.143)
[0.282]
Year Effects
Yes
Yes
State Effects
Yes
Yes
Notes: Samples include respondents with a high school degree or
regressions are weighted
by the
NLSY sampling weights.
less.
Dependent variable
Standard errors
in
is
the real hourly wage.
error term. Bootstrapped standard errors using state*year blocks are in brackets (100 replications).
is
21618
in
the
NLSY, and
1 1
9464
in the
CPS.
42
NLSY
parentheses are not adjusted for clusters in the
Number of observations
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