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TECHNOLOGY, UNEMPLOYMENT AND EFFICIENCY
Daron Acemoglu
96-26
September, 1996
massachusetts
institute of
technology
50 memorial drive
Cambridge, mass. 02139
TECHNOLOGY, UNEMPLOYMENT AND EFFICIENCY
Daron Acemoglu
96-26
September, 1996
iV;.
.
_
EB21199/
Technology, Unemployment and Efficiency'
Daron Acemoglu^
September 1996
ABSTRACT
This paper analyzes technology choices and unemployment in search equilibrium. In contrast
to standard search models, the presence of technology choices
too httle investment in
inefficient;
there
equilibria.
The paper
is
where job tenure
is
too
little
job creation and there can be multiple
also shows that technological progress
is
likely to
be slower
in labor
markets
low.
1
Throughout recent
increase in wages
skills,
makes the decentralized equilibrium
Introduction
history, technological progress has
and employment, and perhaps
it is
been the main factor ensuring a steady
no coincidence that the past twenty years,
which have witnessed below average productivity growth, have also been the period of unusuhigh tmemployment.
ally
This paper
is
prepared
However, the link between technical change and the labor market
for
the Papers and Proceedings of the 1996 Congress of the European Ek;onomic As-
sociation. Financial support from the National Science Foundation
*
is
Department of Economics, Massachusetts
Grant SBR-9602116
Institute of Technology, e-mail:
is
gratefully acknowledged.
daronSmit edu.
.
not unidimensional.
major deterrent to
complementary to
Many
firms cite labor market conditions
new
their adoption of
skills (see
and
lack of adequate skills as a
when
technologies, especially
these technologies are
Northcott and Vickrey, 1993, Haskel and Martin, 1993).
Recent papers by Aghion and Howitt (1995), Mortensen and Pissarides (1995) and Saint-Paul
(1991, 1994) discuss the relation between technological progress
these papers do not include the
choices.
How
skills
skills
and unemployment. However,
of the workforce as a variable interacting with technology
influence the direction of technological change
literature, for instance
is
discussed in another recent
Acemoglu, (1994, 1996a, b), but these papers do not contain a careful
unemployment determination. The current paper proposes a simple extension of the
analysis of
standard search model of Diamond-Mortensen-Pissarides which enables a synthesis of the links
between
skills
the other.
and technological change on the one hand and unemployment and technology on
The standard
and labor market policy
attention
is
search model has been a very useful framework to analyze
(see Pissarides, 1990),
and one of
its
main implications
is
unemployment
that as long as
limited to constant returns to scale matching technologies, the efficient allocation can
be decentralized without any policy intervention
(see Hosios, 1990). I
show that
this conclusion
does not apply to an economy with endogenous technology choice, and neither the unemployment
level
nor the choice of technology
of equilibria,
and
in
is
in general efficient. In particular, there
one of the equilibria firms do not invest in
skills
can be a multiplicity
because they expect their
future workers to be unskilled.-'
In addition to normative conclusions, the framework
Ukely to discourage the adoption of
new
I
introduce implies that high turnover
technologies. This
is
an interesting finding since both
is
in
the U.K. and the U.S. there has been an increase in low tenure jobs in the past two decades and
the imphcations of this trend for technological choice have not yet been discussed.
'Multiplicity of equilibria can also arise in
Acemoglu (1994,1996a), and Redding (1996) has recently extended
these models to show the possibility of "low-skiU" trap
1
when
there are technology ladders. Instead in this paper
use the framework developed in Acemoglu (i995a) which enables the simultaneous analysis of technology and
employment. Pissarides (1992), Acemoglu (1994) and Robinson (1996) also investigate a related multiplicity of
equilibria
whereby firms do not create enough jobs when workers are
workers do not invest in
skills,
making
different
unemployment
unskilled,
levels consistent
and when unemployment
with equUibrium.
is
high
The Model
2
The Environment
There
a continuum of workers normalized to
is
and maximize the present discoimted value
infinitely lived,
rate
Each firm can decide
r.
and a larger continuum of firms.
1
to
All agents are
of their income stream with discount
be inactive at zero return or can open a vacancy at flow cost
7.
Each vacancy can only employ one worker.
Two
normalized to
ciates.
new
0.
The second technology
requires a
and the
and the investment
'firm-specific',
the machine
a worker can use these
Employment
of
equal to
As
its
in the
it
needs to acquire
new machine
of the
skills
are not
skills
with any firm that has the same machine. Further
new machine by y
-|-
a,
I
denote the flow rate of
and without
either the skills or
y.
the
is
number
of vacancies
standard search analysis,
two arguments,
is
I
and M(u,
v)
assimie that M(.,
v)
is
.)
where u
is
the
the flow rate of
exhibits constant
continuous and differentiable, and that M.,
.)
<
00.
I
^ as a measure of the tightness of the labor market (see Pissarides, 1990). Then, the
flow rate of
match
for
for
an
unfilled
vacancy will be equal to q{6) where
an unemployed worker
search models, in this economy there
or unskilled,
this
Both the adoption
formed through a matching technology M(u,
unemployed workers, v
returns to scale in
match
is
relations are
matches formed.
=
will operate
not 'firm-specific' either and can be sold to other firms.
is
the machine, productivity
number
c.
who
and never depre-
costs 6
can be made at any point in time. Note also that the
productivity of a skilled worker with the
of a
new machine which
acquisition of these skills costs
in skills
the existing technology with cost
first is
However, for the new machine to be used the worker
skills,
define
The
technologies can be used for production.
is
is
Q{9)
=
dq{0) with Q'{-)
>
0.
type of models, that the matching technology
of skilled workers in the
unemployment pool
with a vacancy
is
skilled
<
and the flow rate
In contrast to the standard
potential heterogeneity because workers are either skilled
and flrms may or may not possess the new technology.
is
q'{.)
is p,
is
random
I
assiime, as
in the sense that
if
is
standard in
the proportion
then the probability that a worker matching
also p.
Once formed, employment
relations
come
to
an end at the exogenous flow rate
s.
After
.
new match while
termination, the worker looks for a
vacancy.
The important assumption
am making
I
the job enters the state of an unfilled
here
that the probability of separation
is
is
independent from the productivity of the relation.
Analysis
The equilibrium
be characterized through a
will
V^ when
use
J° and
I
t
when
= we
the system
is
in steady state.
i
>
and an unskilled worker can be trained
J^
=
0.
the asset
may be
more involved.
+ a > w^
A
which
unemployment
viable options
unemployment
is
pool).
and
lost
vacancy
is
it
filled
The
It is
J^
;
however,
u
is
=
p and
any time.
at
s+e^
(e
)
Since at
'^here ^o
a standard Bellman equation,
vacancy with the technology
+ a — w'^
,
and replaced by the value of
is
matched with probability
is
is
to
the
be the
With probabiUty
case; recall
1
— p,
p
is
plus the expected value of the capital
unfilled vacancy.
q{9).
The
The second equation
probability that the worker
is
unskilled.
The
wiU choose whichever has higher present discounted
(as long as
firm has then three
value.
The
first is
to
gets the value of a filled vacancy with a skilled
will also incur the training cost c.^
assumed that the worker does not pay
worker
the proportion of skilled workers in the
the worker
it
states that
it
equal to the instantaneous
in this case the firm will definitely accept the
assumed
it
adopt the new
(1)
first is
accept the worker and train him, in which case
worker,
level
to
Next:
plus the per period dividend y
,
possesses the skills
y
t
briefly explain these equations.
capital gain
is
I
at time
a-w" + siV^ -J^)
+
y
the per period value of being a
loss as
is filled,
new technology
Each firm or vacancy can decide
are in steady state, the equilibrium
rJ^-j^ =
me
the job
under the assumption that the new technology becomes available
tightness of the labor market at
Let
denote the
I
V'='
technology at any time
t
equations.
in the state of imiilled vacancy. Similarly, for a firm without the
start the analysis
=
BeUman
new technology by J^ when
(net present discounted) value of a firm with the
and
series of
The second
for the cost of training,
credit-constrained and binding contracts cannot be written.
alternative
which would be the case
Acemoglu (1995a) analyzes a
is
if
to employ
workers are
similar setting allowing
the worker without the necessary
skills
the value of a filled vacancy with the
may
the firm
down
decide to turn
to utilize the
new
technology, in this case the firm will get
new machine but without a
worker,
difference
it
gets the value
worker
-
+
y;0
J^°
I
(note that
as:
_ jO)
(2)
I
(l) is
(3
that
if
the firm decides to employ a trained
have not written the recursions for
assume that wages are
equal to a proportion
is
5(l/0
between these equations and
order to save space). Next,
of a
y
Finally,
-V^ = g(0)((l-p)max(j°-K°)+pmax{j^°-T/^,o}).
rV°
The only
=
.
the worker and continue as an unfilled vacancy.
Value equations for firms without the new technology can be written
rJ°~j''
J^^
skilled worker,
set
by
J°^ and J^^
such that the wage
static bargaining
wage bargaining
of his current output (other
in
rules woiild
not change the results).
To
characterize the equiUbriima, the evolution of p (the proportion of skilled workers in the
unemployment pool) needs
to be determined.
vacancies which adopt the technology,
m
For this
I
define
as the proportion of active
(p
who
as the proportion of skilled workers
are employed
by firms without the new technology and n as the proportion of unskilled workers who are
employed by firms with the new technology. Then;
p
= s{l-u)W-n) + {l-4>)m]-peq{e)u ^
u
^^^^^ ^^^^
In words, the change in the proportion of skilled workers in the
by entry and
exit of skilled workers into the
pool comes from employed workers
{1
—u)
unemployment
at the rate s
workers are
\
—
(j)
are employed at firms without the
skilled. Finally,
„)
+
- 0)m - p]
(1
unemployment pool
pool. Entry into the
and a proportion ^
employed at firms with the new technology and a proportion
a proportion
-
1
—n
is
(3)
determined
miemployment
of these workers are
of these are skilled. Similarly,
new technology and a proportion
m and n are determined from the BeUman equations
m of these
given above by
seeing whether firms are willing to hire different types of workers.
Since there
is
an
infinite
supply of firms able to open a vacancy,
never open a loss making vacancy,
equiUbrimn and since a firm
will
workers to pay
and the quahtative
for their training,
V'-'
results are not changed.
>
V° <
is
not consistent with
is
also not possible,
V° =
thus
0.
Similarly, V'^
willing to invest in the
—
price ^
>
machine so that the firm can
e for e arbitrarily small.
Thus,
Given these no-arbitrage conditions,
when
(2)
r
I
J^ and
and
this
ensured via
V'^
-5 = V^ = 0m
is
When
is
+ c.
a
J'-'
firms wilhng to invest
V^ =
firms
at the
6.
immediately imply:
+s
s
are independent of time. However, clearly p
(1)
and
a <
vacancy creation
is
0=1
be adopted by
will
>
J'^
a
>
ai{9o)
t
=
=
the firm gets
all
+ 6 + C,
J^
qi(0o), at time
r6
and
n=
\.
if
a >
is:
+
+
until all workers are trained.
{r
J'^, incurs
if
and only
the
if:
s)c
•
is
not adopted, then the profitability of
at ^O;
and
ai{9o), then all active firms
As p
but loses
YZTp
the innovation
This implies from
J^
firms employing a worker
that
unchanged and 9 remains constant
never gets adopted. In contrast
and we have
potentially time-dependent
(2).
new technology adopted? By adopting
if
is
the tightness of the labor market depending on time in order to satisfy
0,
Thus, the technology
Note that
1, i.e.
we need new
have explicitly introduced time-dependence to emphasize that in equilibrium (due to
free-entry)
cost 6
+
5
machine to one of these firms
new
there are
and
(1)
sell its
r
where
V^ <
6 can be ruled out, but to nile out
(3) that
p
therefore, the
new technology
buy the new machine
will increase over
time until
at
it
t
=
reaches
increases, (1) implies that expected returns of unfilled
vacancies will also increase, and to satisfy the zero-profit condition 9 needs to increase imtil
reaches some higher value
rate of
imemployment
Result
1
:
If
Q >
9i.
Since the job-finding rate, 9q{9), is increasing in
will also fall after the
new technology
ai(0o), there exists an equiUbrium in
this equilibrimn, firms train all unskilled workers
workers, p, asymptotically tends to
9\
and unemployment
falls.
0,
1,
is
9,
it
the equilibrium
adopted. Therefore:
which the new technology
is
adopted. In
immediately and the proportion of trained
the tightness of the labor market increases from 9o to
The
analysis
firms that enter
that
we
up
to this point was conducted under the assumption that there are always
and want to buy the
a firm to do
Is it still profitable for
A
a >
are in a situation where
existing machines
which keeps
V^ —
the worker separates,
it
have to keep
will
=
solved under the assumption that p
unskilled) together with
obtain that the
7
=
g(l
jN
^
^
cost of
adopt the new technology. Then,
will
when
differently,
until
(from
the machine
because no other firm iimovates so
(1))
V^ —
and without
be adopted
if
and only
jr + s + qje))
^
= ^r + #))(l-/3)' +
,
be
workers are
Simple algebra yields:
6.
+ qi9)){l-P){y + a)-s^-sq{e)c
r{r + q{e) + s)
will
all
6
when
finds a worker, therefore (1) needs to
it
/fl^_
>
sell
V^ ^
^^^
if:
{r
+ s)c
-TT
^'^
«i(^o), since the coefficient in front of 5
firms believe others will not adopt the
new
is
larger in ao{9o).
technology, the effective
adoption increases. Thus:
Result 2
:
If
a G
is
adopted and
is
in the other
it is
not. In the first equilibrium,
unemployment
lower.
When
workers.
two pure strategy symmetric equiUbria. In one
{ai{9o), 00(60)), there exist
the innovation
all
firms adopt the innovation, the future workforce
As a
result,
even
if
some firm
willing to
new machine,
workforce
is
V
wiU be able
to
make high
buy the new machine, and
,
is
skilled
because firms train their
the current employment relation comes to an end, a
relation with a skilled worker
the
{r
it
(this is
/3)y
"°('°^
easy to see that ao(^o)
Expressed
—
new technology
" ^
is
technology.
coordination failure
because there are no new firms to buy the machine. Since the firm cannot
It
new
alone? In other words, can a coordination failure arise?
Suppose the firm expects that no other firm
We
Suppose instead
6.
ai but no firm contemplates adopting the
it
new
never
falls
below
6.
this
why
it
and
therefore, there will be
the value of an unfilled vacancy with
However, when no other firm innovates, the future
untrained, and a firm which adopts the
training of the imskilled workers
profits,
new productive
new technology
will recruit in the future.
The
will
have to pay for the
anticipation of these costs
reduces the profitability of the investment. Because of these considerations, no other firm wants
to
buy the machine from the current owner, and
new technology
the
result in
new
The
less profitable.
is
Acemoglu (1995a) where when
technologies
result of this
is
paper
therefore
V^
below
falls
intuition for this multiplicity
the future workforce
As a
S.
result,
adopting
an extension of the
is
untrained, the profitability of
is
reduced. However, instead of a two period model of Acemoglu (1995a), the
derived in an infinite horizon model, and the matching aspect
is
is
explicitly
modelled, firms are allowed to choose the timing of their innovation and training, and to
machine when they have no use
of firms
and
The
Is
for
it,
and there
is
the
sell
a free-entry condition to determine the nimiber
vacancies.
efficient allocation
one of these equiUbria
efficient?
To answer
this question,
I
write
surplus from adopting the technology and training the worker by
value of a trained worker
is
denoted by
T-^.'^
rS^-S^ =
rT^ =
Intuitively, the social planner
is
y
S^ and
the additional social
the additional social
Then, we have:
+ a + s{5 + T^-S^)
eq{G) (c
also affected
down
(7)
- T^)
by the search
frictions,
but
like
the decentralized
market, she can transfer the machine from a destroyed job to a new one; this explains 6 in the
equation for
S^ The
the society c
when he matches with
The
.
social planner
equation for
T^
can be explained by noting that a trained worker saves
a firm because the training costs can be avoided.
wiU adopt the new technology
.>...r* +
Result 3
:
as(0)
<
ai{e)
<
(r
if
and only
if
S^ >
6
+c
which
implies:
+ »)c-«j.
(8)
aQ{9).
This result states that both of the decentralized equilibria characterized above have too weak
^And I hold
the tightness of the market at some 6s.
the social planner would like to increase
technology, thus as(d)
I
derive
is
6,
It is
straightforward to see that
if
she adopts the technology,
thus she would generate even more surplus from adopting the
an upper bound on the
Therefore, the difference between the decentralized
cut-off level of the productivity of the
economy and the constrained optimal
new
allocation
is
new
innovation.
even larger.
new
incentives to adopt the
technology.
The
Firms are discounting the future at the rate r
end at the rate
and
s,
intuition
+s
is
partly given by the above discussion.
because their employment relation comes to an
after this point they receive
no benefit from the worker's additional
skills.
Instead, his future employer gets the higher return (see also Acemoglu, 1995b for a discussion
Also firms are discoiiraged from investing because for
of a similar result).
all /3
>
0,
part of
the additional returns will be captured by the worker. However, the qualitative results are not
affected
when
/?
=
as
it
can be seen by comparing
a-[{9)
and
oio{6) to
as{d) for
/3
= 0,
therefore,
the distortions caused to rent-sharing are not the only source of inefficiency (see Acemoglu, 1995a,
for discussion).
Moreover, as the decentralized economy invests too
to the efficient allocation,
unemployment
its
rate
is
is
efficient as
show here that no value
of
/?
long as
/3
is
the
new technology compared
too high because there
creation. This result contrasts with the standard search
and unemployment
little in
is
not enough job
models where the amount of job creation
chosen correctly to regulate the entry of ffims.
restores efficiency, thus the decentralized
I
equiUbrium does not do
a good job of internalizing the externalities that arise because of the productivity differences of
workers (see also Acemoglu, 1996a).
A
simple comparative static
The framework
also provides
Result 4
more
:
have proposed
is
not only useful in showing the potential inefficiencies, but
an interesting prediction related to the
The higher
is 5,
links
between turnover and new technologies.
the weaker are the incentives to adopt
new
noted above, ffims discount the future at the rate r +
less willing to invest.
technologies
and
also the
s,
thus
when
5
increases,
Moreover, because the social planner discounts the future at a
lower rate, an increase in s also makes the inefficiencies more severe.
to a
it
distorted are the innovation decisions.
Intuitively, as
they are
I
A high level of s
corresponds
market with high turnover and low tenure. Thus, labor markets with low tenure are not
conducive to the adoption of new technologies.
It is
also
worth noting that since
all
human and
physical capital are general, in the absence of matching and credit market imperfections, there
would be no
this
link
between
s
and innovation
in this
economy, the innovation would be adopted
This result
is
interesting in two respects:
if
first,
economy
and only
change in Japan
(e.g.
if
a >
in the competitive
r(S
is
scholars suggest that
an important factor contributing
Hashimoto, 1991). Second, the typical tenure of a
worker appears to have decreased recently in the U.S. and U.K. (see
and
analogue of
+ c)).
many commentators and
the life-time employment relation in Japanese corporations
to fast technological
(i.e.
this result suggests that this recent trend
may have
for instance Farber, 1996)
miforeseen consequences on the rate of
technological progress.
REFERENCES
3
[1]
Acemoglu, D. (1994); "Search
CEPR
[2]
in the
Labor Market, Incomplete Contracts and Growth"
Discussion Paper, No. 1026
Acemoglu, D. (1995a); "Training and Innovation
in
an Imperfect Labor Market"
MIT Work-
ing Paper.
[3]
Acemoglu, D. (1995b); "Public Policy
in a
Model
of
Long-term Unemployment" Economica
Vol 62, 161-178.
[4]
Acemoglu, D. (1996a); "A Microfoundation For Increasing Returns
in
Hrnnan Capital Accu-
mulation" Quarterly Journal of Economics., Vol 111, pp 779-804.
[5]
Acemoglu, D. (1996b);" Changes
Theory and Some Evidence"
[6]
Aghion,
P.
and
P.
in
Unemployment and Wage
MIT Working
Inequality:
An
Alternative
Paper.
Howitt (1994); "Growth and Unemployment" Review of Economic Studies
Vol 61, 477-494.
[7]
Diamond,
Political
[8]
P. (1982);
"Aggregate
Economy Vol
90,
pp
Demand Management
in a Search Equilibrium"
Journal of
881-94.
Farber, H. (1996); "The Changing Face of Job Loss in the United States, 1981-1993" Prince-
ton University, Industrial Relations Section
WP
10
360.
MIT LIBRARIES
3 9080 01428 2682
[9]
Hashimoto, M. (1991);" Training and Employment Relations in Japanese Firms"
and
[10]
J.
M. Ritzen
Haskel,
(editors)
and C. Martin
J.
Market Failure
(1993);
"Do
in D.
Stem,
in Training? Springer- Verlag, Berlin.
Shortages Reduce Productivity:
Skill
Theory and
Evidence from the U.K." Economic Journal Vol 103, 386-94.
[11]
Mortensen, D. (1982); "Property Rights and Efficiency in Mating, Racing and Related
Games" American Economic Review, LXXII,
[12]
968-979.
Mortensen D. and C. Pissarides (1995); "Growth, Job Creation and Job Destruction" LSE
Mimeo.
[13]
Northcott,
J.
and G. Vickrey
(1993);" Surveys of the Diffusion of Microelectronics
vanced Manufacturing Technology" Paper presented
in
and Ad-
MIT/NSF/OECD Workshop on
The
Productivity Impact of Information Technology Investments.
[14]
Pissarides, C. (1990); Equilibrium
Unemployment Theory Oxford,
[15]
Pissarides, C. (1992);"Loss of SkiU
During Unemployment and the Persistence of Unemploy-
ment Shocks" Quarterly Journal
[16]
Redding,
S.
Robinson,
[18]
Saint-Paul,
DELTA
[19]
J.
of Economics Vol 107, 1371-92.
(1996);"The Low-skill, Low-quality Trap: Strategic Complementarities between
Hinnan Capital and
[17]
Basil Blackwell.
R&D"
Economic Journal, Vol
A. (1995); "Unemployment and
106, 458-470.
Human
Capital Accumulation"
G. (1991): "Productivity Growth and Unemployment in
USC
OECD
mimeo.
Comitries"
Working Paper.
Saint-Paul, G. (1994); "Are the
Unemployed Unemployable?"
11
DELTA Workmg
Paper.
5232
'2