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LABOR MARKET IMPERFECTIONS AND
THICK MARKET EXTERNALITIES FROM INNOVATION
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LABOR MARKET IMPERFECTIONS AND
THICK MARKET EXTERNALITIES FROM INNOVATION
Daron Acemoglu
No.
93-14
Oct.
1993
r»—MWIT^.^.. -
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93-14
LABOR MARKET IMPERFECTIONS AND
THICK MARKET EXTERNALITIES FROM INNOVATION
Daron Acemoglu
Department of Economics, E52-371
Massachusetts Institute of Tectinology
Cambridge,
02139
MA
First Version: June 1992
Current Version: October 1993
JEL Classification: 031, E24
Keywords: Search, Innovation, Training, Thick Market
Externalities
Abstract
When labor market imperfections are important, workers (and firms) do not receive their
marginal product. This is shown to imply that the adoption of an innovation that increases
the non-firm specific marginal productivity of a worker creates a positive externality on other
firms. The presence of this externality can lead to a multiplicity of equilibria whereby in the
inferior equilibrium innovation is not profitable because the workforce is untrained (unskilled).
This mechanism illustrates how labor market conditions influence investment and innovation
activity thus offering new links between unemployment and growth. These links also imply that
when the entry decisions of firms are endogenized a further thick market externality is created
since entry, by reducing unemployment, makes investment and further entry more profitable.
Finally when firms are allowed to choose the timing of their innovation, free-rider effects are
introduced and the Pareto preferred equilibrium disappears.
full
am grateful to Abhijit Banerjee, Charlie Bean, Oliver Hart, Michael Kremer, Chris Pissarides,
Kevin Roberts and Andrew Scott for useful comments. I also thank seminar participants at
Boston College, LSE, Northwestern, MIT, Princeton, Royal Economic Society Conference,
University College London, University of Sussex and Yale where a previous version of this
paper was presented under the title, "Labor Market Imperfections, Innovation Incentives and the
I
Dynamics of Innovation
Activity". All remaining errors are mine.
1)
Introduction
Innovations and investment in
new technology
among
the major channels
activities are often
thought as a major
are likely to be
of growth in the economy and cyclical changes in these
When
driving force of economic fluctuations (e.g. Schumpeter (1939)).
invest or to innovate depend
on the actions of other firms
which expectations become
equilibria in
in the
self-fulfilling is possible
a firm's incentives to
economy, a
multiplicity of
and economies with similar
fundamentals can exhibit vastly different growth and cyclical behavior.
Two
mechanisms
that introduce strategic complementarities/thick
market externalities
in
investment decisions have been extensively studied in the literature. First, in monopolistically
competitive markets, the
demand
for a firm's product
other firms implying that a given firm
do
so.
These aggregate demand
is
more
may depend on
likely to
externalities
produce (or
the production level of
invest),
when
other firms
have been investigated by Shleifer (1986),
Blanchard and Kiyotaki (1987), Murphy, Shleifer and Vishny (1989). Second, productivity of
individual investment
may be
increasing in the
amount of aggregate investment,
for instance
because productive information spreads between firms. This type of technological externality has
been analyzed
It is
in different contexts
by Romer (1986), Durlauf (1991,1993), Acemoglu (1993).
also possible to classify the search externality
as the thick market externalities in
returns
embedded
model of Diamond (1982)
Diamond's economy
is
in this category,
generated by the social increasing
in the search technology.
With the possible exception of Diamond's contribution, labor market
interactions are not
central to this literature. This paper argues that interactions in the labor market can be a source
of an important additional externality. Most innovations are associated not only with an increase
in the productivity
of physical capital but also in the human capital of workers.
becomes important
to determine
the increased
human
who would
It
therefore
benefit from the future revenue stream provided by
capital of workers. Additionally, the propensity to innovate is obviously
a key ingredient in economic growth and the influence of the organization of labor markets on
growth
is
an important theoretical and practical concern that has attracted very
little
attention
(although the implications of growth on the equilibrium rate of unemployment have recently been
studied by
Aghion and Howitt (1992) and Bean and Pissarides (1992)).
In this paper
we
analyze investment in
new technology
workers. This complementarity between physical and
nature but
forms.
We
it
human
that requires the training of
capital can
can also be interpreted as the workers learning to adapt to
will additionally
assume
that there
1
be technological
new
in
organizational
always exists a positive probability
that the
employment
a
new
relation will
come
to an
end and either the worker or the firm will have
to look for
partner (see micro evidence suggesting the presence of high uncertainty for jobs, e.g.
Leonard (1987), Davis and Haltiwanger (1990,1992), Blanchard and Diamond (1989,1990)).
Despite such large reallocations and uncertainty concerning the future of the employment
relation,
complete markets in particular competitive labor and perfect credit markets, ensure
property rights on the increased revenue stream due to the higher
efficiently distributed, leading to first-best innovation
require the worker to
make a payment
human
capital of
that
workers are
and training decisions. Efficiency would
to the innovating firm equal to the present value of the
increase in his future earnings, which, in the presence of complete markets, coincides with
present value of the social benefit from training (Becker (1975)).
frictions are important, for instance
not receive his
full
due
marginal product
to costly search, the
worker
in his future relationships
this result arises despite the fact that the firm
labor market
will anticipate that he
and therefore
and underinvestment.
less than first-best subsidy, leading to undertraining
emphasize that
However when
may
will
pay the firm
It is
important to
and the worker are allowed
to write
complete contracts and the worker has access to unconstrained borrowing opportunities. This
mechanism not only leads
to less than optimal training
and innovation incentives, but also
introduces a strategic complementarity between the innovation decisions of different firms: whilst
an individual firm faces higher private costs due to a lower training subsidy from
it
from high human
also anticipates being able to extract higher surplus
bargains
in the
if it
possesses the
new
economy, the higher
is
differently, the higher is the
the
more
profitable
This
is
a
it
new
the profitability of
number of firms
becomes
that
for each firm to
market and
It is
in the
the proportion of trained workers
physical capital to an individual firm. Put
adopt the innovation and train their workers,
do
so.
is
strong enough to lead to multiple Pareto-ranked equilibria. In the
is
low because the workforce has
a direct result of low innovation incentives.
unemployment
in future
caused neither by technological externalities nor by interactions
Pareto-dominated equilibrium, innovation
capital,
new
is
workers
source of externality affecting innovation and training incentives, distinct
from those outlined above.
in the product
technology. Thus the higher
capital
workers,
its
economy
We
also
show
insufficient
that
the
human
higher
is
(or in the relevant sector), the lower is the marginal profitability
of innovation which implies that high unemployment will be associated with slower growth.
Consequently, more serious imperfections in the labor market can lead to slower growth via two
channels:
first
by creating a larger wedge between
social
and private productivity and second
by increasing unemployment. In search models, unemployment
is
usually decreasing in the
number of firms
that enter the market.
unemployment, implies
profits decreasing in the level of
is
The mechanism
created by the entry decisions of firms; as
which makes
identified in this paper,
that another novel strategic interaction
more firms
enter,
investment and further entry become more profitable. Finally,
unemployment
when we allow
is
reduced and
firms to choose
the timing of their innovation activity, additional free-rider effects are introduced in the
innovation decisions and destroy the favorable equilibrium, thus intensifying the inefficiency.
The plan of
the paper
is
as follows.
The next
section explains the basic externality in a
two-period model and discusses the empirical relevance of the mechanism that
this paper. Section 3 considers the
is
proposed
in
continuous time infinite horizon analogue of this model.
Section 4 closes the model of section 3 and discusses the links between unemployment and
growth. Section 5 illustrates the free-rider effects by allowing firms to choose the timing of their
innovation and finally section 6 concludes, while the appendix contains
2)
Search in the Labor Market and Thick Market Externalities
a)
A
all
the proofs.
Two-Period Example
Consider a two-period economy consisting of a continuum of firms and workers with
that there is full
risk-neutral, the discount rate is set equal to zero
and the product
1
employment. All agents are
market
and
is
Workers and firms are matched one
one so
equal measure normalized to
.
to
competitive. Each firm can initially produce y units of the single good of this
at the start
the output of
of the
its
first
period
it
has an option to invest in a
new technology
economy
that will increase
production process to y -I- a in both periods. However, workers in this economy
do not possess the necessary human
capital to
work with
this
new technology and hence
they
need to be trained in order for the new technology to be productive. Note that the increase
the output of the firm
is
in
independent of the number of firms that adopt the innovation. This
assumption rules out both technological and aggregate demand externalities as the revenue of the
firm
this
is
independent of the number of firms investing in the
new mechanism
enables us to emphasize the
The
installation
suggesting that
of
this
new investments
argument does not depend on
cost for each
worker
is c,
innovation opportunity
be trained
technology
is
suggested in this paper.
assumed
to cost 6.
is
which we only use
assumed
to
only available at the
in either period.
technology. Although restrictive,
Although there
is
evidence
are often bulky (e.g. Cooper and Haltiwanger (1993)), our
this aspect
which
is
new
The human
be
to simplify the analysis.
The
less than the incremental output; a.
start
of the
capital that the
first
training
While the
period, an untrained worker can
worker acquires
will in general
have firm-
specific
and non-firm-specific components. The firm-specific part of
our concern
in this
paper as
assume
that
some
would be able
to
human
work with an
we assume
analysis,
be written between the firm and the worker
new technology
part of this
human
capital is not
will not lead to the effects discussed in the introduction as long
it
as comprehensive contracts can
Since the adoption of a
this
human
Crucial to our mechanism
is
economy
is
considered,
Becker (1975)).
it
plausible to
is
worker who can run a new machine
capital is general: a
identical
that all the
across the
(e.g.
machine owned by a different firm. To simplify the
capital that the
worker acquires
the inability of workers and firms to
general.
is
make
their relationship
continue as long as they desire; unavoidable separations are possible. Empirical evidence
suggests separations and job destruction to be an integral part of the labor market (e.g. Leonard
Diamond
(1987), Davis and Haltiwanger (1990,1992), Blanchard and
Krueger (1991)). For instance Blanchard and Diamond (1989) report
workers move jobs per month and Leonard (1987) shows
reallocation, as
model
much
this situation
as
4.5% of
by assuming
Haltiwanger (1990,1992))
all
end of the
at the
another region, sector or firm'.
To
first
may have
to the
example as simple as possible we assume
this to
by stochastic events. In general there
market
in the
is
that there are
no new
is
arrivals.
second period, labor will be traded
in a
Walrasian market and
However we are not interested
such a move can be made sufficiently
he
this equals the
(it is
assumed
that
trained or not, implying that competitive bidding will allocate
'
that
this
competitive and workers have access
the "right" workers to the "right" firms as trained workers are
worker learns over time
and
will also
second period, but again to keep
saving the firm makes by hiring a trained rather than an untrained worker
know whether a worker
to
happen with
fact that firms
a trained worker will receive an amount c more than an untrained worker, since
firms
move
have a predetermined length, but instead the
where the labor market
to perfect capital markets. In the
we assume
two assumptions capture the
actual duration of the relationship is determined
We
period and as a result disappear (shut-down)
to leave this firm for instance die or
their relationship will
First consider the case
absence of sectoral
in the
shocks (as evidenced by Davis and
simplify the analysis
probability d for each worker as well. These
be new workers and firms who come
even
that close seven million
workers are separated from their jobs every month.
that firms face idiosyncratic
with probability d. Similarly workers
workers cannot make sure
that
(1990), Blinder and
is
in voluntary quits
more valuable
for firms that have
caused by a better wage offer because
unattractive for the
worker by an
exit fee.
Yet
if the
not happy with this firm or that his talents will be put to
better use in another sector or firm, an exit fee will not solve the problem, see footnote 3.
adopted the innovation). In the
first
period, workers realize that if they are alive, they will
obtain an additional c in the second period.
Thus each worker would be
willing to subsidize their
firm for the increase in the present value of his future earnings by partly paying for his training,
for instance
by taking a wage below
from the perfect
capital markets
worker's earnings
is
and posting a bond. The increase
in the present value of the
equal to (l-d)c as with probability d he will not be in the market.
other side of the market, if
by a-c, next period
by borrowing
his marginal product in the first period or
(as
it
it
invests, the firm will increase
will
revenue by a,
its
On
the
period and
this
have to pay a higher wage to get a trained worker or hire an
untrained worker and pay for his training). But this second period return will only accrue to the
firm if it
when
is
the
not destroyed. Thus
sum of
its
present value
is
(l-d)(a-c).
It
be profitable
will
the increased revenue this period, the expected value of higher revenue next
period and the subsidy paid by the worker exceed the current cost which
investment
is
to invest only
profitable iff
(2-d)a>5+c,
is
5+c. Thus
also the optimal decision rule for this
economy.
Therefore despite the uncertainty concerning the future of the employment relation, the
competitive markets allocate resources efficiently because after separation both parties obtain
their full marginal product.
Let us
now
turn to a labor market with matching frictions. In the second period workers
without a firm and firms without a worker will search for partners and get matched together.
However
frictions
Further as
we
imply
that after the initial
match neither party can costlessly change partners.
are considering a two-period model,
it is
not possible to turn
look for a better partner, thus a trained worker will accept a job
use of his
skills.
This
is
however not
crucial to our
in
down a match and
which he cannot make best
argument (see below). This imperfect
mobility creates a surplus between these pairs and ex post bargaining over this surplus will
determine wages. For simplicity
whole surplus and wages are
let
set to
us assume that the match-specific surplus
a proportion
/3
of
this.
is
equal to the
Also to demonstrate that
rather than capital market imperfections that drive our results,
we assume
that
it is
labor
workers have
access to a perfect capital market and enforceable contracts between the matched pair can be
written.
These two assumptions also imply
of property rights between
that a simple reallocation
the firm and the worker cannot solve the problem.
This economy
is
is
analyzed backwards starting from the second period. If a trained worker
matched with a firm who adopted the innovation
y-l-Q!.
Thus, the wage paid to a trained worker
untrained worker
is
is
in the first period, the total surplus will
w'=fi(y+a).
On
the other hand,
matched with a firm possessing the new technology, the
be
when an
total surplus is
y
firm does not train the worker.
if the
The assumption
that firms
and workers can write complete
contracts implies that the firm should get the marginal return to
w"=6y
untrained worker receives
Finally if the firm did not innovate in the
the
wage
w°=By.
that
Now
it
pays to
assume
not, the proportion
that a proportion
worker
will
still
As matching
(1-d).
is
same result
if
period, then the total surplus
w"=B(y +a-c)).
is
equal to y and
trained or not,
is
income of a trained worker
be
is
alive. Conditional
is
given by
of the firms are expected to innovate. Since no new
not conditional upon whether the firm has the
new technology
on
this,
in the
</>.
who possesses
second period^ conditional on being alive
now
he will stay with the firm with probability
the
new
64)
is just
he will be
technology. Thus his expected income
The expected
is [(l-d)+d<^]fi(y-l-a)-l-d(l-</>)By.
income of an untrained worker on the other hand
Let us
or
second period. With probability (1-d)
completely random (see discussion below), with probability
separated but matched with a firm
in the
<i>
training decision; thus the
of firms looking for a match in the second period will also be
calculate the expected
the
first
the
worker, irrespective of whether he
its
firms arrive and firm death
we get exactly
(incidentally,
its
Thus
By.
the expected increase in the
present value of the worker's earnings
SB=(l-d)(l-d+d0)Ba,
is
the subsidy (bribe) that the worker
On
willing to pay to the firm in order to receive training.
the other side of the market, the firm will receive the full marginal benefit of
innovation, a, in the
wages
is
(see footnote 2)
first
and
period.
it
However,
may have
in the
second period
it
will
to incur the training cost again if a
have
to
pay higher
new worker who
is
untrained arrives. Thus the expected present value of the increase in the firm's expected revenue
in the
second period, AR,
is
AR=(l-d)[(l-d-l-d0)(l-B)a+d(l-0)(a-c)]
where the
first
term on the right-hand side
with a trained worker.
The second term
which has probability
d(l-<^) since
their
workers
in the first period
is
is its
the profit that the firm
net profit
a proportion
<A
when matched with an
if
the
l-</)
^
is
greater than the cost,
together
untrained worker,
of newly unemployed workers will
sum of
the incremental return in the
period, a; the increase in the expected return in the second period,
paid by the worker, SB,
it is
of firms adopted the innovation and trained
and hence a proportion
be untrained. Innovation will thus be beneficial
makes when
AR; and
first
the training subsidy
8+c. Collecting terms we obtain the following
The assumption that even if the worker stays with the firm, he receives w' is a convenient
normalization as the worker pays the expected value of this increased salary back to the firm
form of a training/innovation subsidy.
in
condition for innovation to be profitable
(2-d)a>8+c^d(l-d)(l-<f))c
Inspection of (1) leads to a
(i)
There are insufficient incentives
by "innovate
(given
the
worker
Some
all
number of
iff
(1)
interesting observations;
outcome
to innovate relative to the competitive/first-best
(2-d)a^5+c"). The underlying reason
to capture all the future benefits created
by
this
is
the inability of the firm and
innovation and training decision.
of the future benefits accrue to \ht future employer of the worker. Underpinning
this
and
the results of this paper are the following three assumptions: (a) the innovation in question
necessitates upgrading the worker's general
human
capital
which increases
his future as well as
current productivity; (b) there exists a positive probability that the worker will not be together
with the same firm in the future;
(c)
labor market frictions prevent the competitive allocation of
workers, thus imply that workers expect to receive less than their marginal product. The crucial
ingredient here
is
the randomness of matching. This implies that
we
cannot make sure that the
may
"right" workers end-up with the "right" firms. Naturally in practice, trained workers
to accept a job in
which
their skills are not being put to use.
However,
this
refuse
would not change
our results as when trained workers meet a firm without the new technology, they will continue
and incur a search cost and therefore they will be receiving
to search
product because of the search
with the
new technology and
cost.
As a
result
less than their fi^ll
marginal
workers will care about the proportion of firms
similarly firms will care about the
human
capital of the pool of
workers. (Although the main externality analyzed here remains, a number of different issues
arise
when we allow workers
It is
in this
to
change partners and model search costs
employer (such as an
is
certainly not
one between the worker and
first-best
its
current
exit fee), because all the spill-overs within this relationship are being taken
care of by the existing training subsidy, SB^.
By
the return to the worker, but rather, that of the
^ It
what arrangements would restore
instructive at this stage to contemplate
economy. The required subsidy
explicitly).
its
training decision the firm
is
not increasing
worker's^ure employer. Therefore, a payment
can also be noted that if the worker did not die but just moved to another sector, region
or firm because of
some exogenous reason
learned that the match specific surplus
specifying an exit fee can be written.
is
(e.g.
he
is
no longer productive with
this firm or
small in a Jovanovic (1979) type setting), a contract
However
it
can easily be seen that this will not change
The value of the exit fee needs to be subtracted from the subsidy, SB and added to AR
and these two will exactiy cancel out. The crucial point here is that the quit is not because of
anything.
a high wage offer but because
it is
optimal (or unavoidable) for the worker to move.
from the future employer of the worker
to his current
employer
is
Since such a
required"*.
subsidy cannot be easily implemented by the market, decentralized equilibrium will often
where the
to internalize this externality. Transfer markets for sportsmen provide an instance
market implements such a scheme; the new team has to make a payment
player.
The
a match between a firm with the
The
However
two separate job
as long as the probability of
new technology and a worker with high human
on the abundance of these types, the
(ii)
to the old club of the
crucial ingredient for such an arrangement is the existence of
markets, one for trained and one for untrained workers*.
effects suggested in this paper will
to the actual cost,
The
5+c. However, with
because the firm anticipates that
can also see that
.
it
depends
capital
be present.
decision rule summarized in (1) can be interpreted as "invest iff the benefit
than the effective cost of innovation"
is
effective cost in a competitive labor market
frictions,
may have
we have
fail
greater
is
equal
the additional term, d(l-d)( 1-0)0
of training
to incur the cost
in the future.
this externality leads to natural multiplier effects since, as
one firm
Here we
invests,
it
reduces the effective costs to other firms and they become more willing to invest. Thus a shock
that
makes investment more productive
for a group of firms will also increase the profitability
of investment for, and innovation activity by, other firms.
(iii)
since the effective cost of innovation
Incentives to innovate are increasing in
As more
in this variable.
firms innovate, the pool of trained workers grows and
it
is
decreasing
becomes more
profitable for each firm to innovate. Therefore the interactions in the labor market create thick
market
(iv)
externalities.
Although the source of the externality
is that
workers (and firms) do not receive
their full
marginal products, the bargaining power, 6, does not affect the effective cost of training. This
is
because of our special set-up. In our model a trained worker loses (l-15)a when he meets a
firm with the
new
new technology
"*
technology, however this
extracts
when
it
is
exactly equal to the
the future employer of the worker distinguishes this effect
(1984) where bargaining only over wages
may
lead
investment
it
less
them and
from the one discussed by Grout
to
investment increases the quasi-rents obtained by the workers.
wage
that the firm with the
meets a trained worker. However, the worker also receives
The fact that the externality is not between the worker and
solved if binding
amount
the firm but between
underinvestment because higher
However such a problem can be
contracts can be written or workers can subsidize the firm for the
undertakes.
Our
externality
does not require these restrictions on
bilateral
contracting opportunities.
Saint-Paul (1993) and Burdett and Smith (1993) discuss returns to education
of such market segmentation.
*
8
in the presence
than his marginal product because with a positive probability he ends-up with a firm
make good use of
bargaining power enters the decision rule, but
if
cannot
worker and the firm face different probabilities of death,
his skill. If the
becomes more important
who
effect is of second-order.
its
However, bargaining
workers have to make their human capital decisions before meeting
a firm.
We can now
summarize the main
result
of our discussion;
Proposition 0:
If 6-l-c<(2-d)a<5-l-c-l-d(l-d)c, there exist
economy; one
in
which
the other in which
all
firms adopt the innovation in period
no innovation nor
Returning to
(ii)
two pure strategy symmetric Nash
above, the intuition of our result can be given as follows;
from which
anticipates that the workforce,
line with
is
the
workers and
train their
training take place.
firms do not invest, the effective cost of training
This
and
1
equilibria in this
view
that
certain
investment because their workforce
for protecting infant industries;
is
its
come,
will
be low human
developed countries do not
attract
untrained and unskilled (a similar argument
for a discussion
other
prohibitively high for the firm as
is
future workers
less
when
is
it
capital.
sufficient
also used
see Johnson (1971) or Corden (1974)).
However, as firms who adopt the innovation would often
find
it
profitable to train their
new
workers, the general level of training in the workforce will be endogenous and in order to
analyze this problem fully
we
need a dynamic model which
Finally, since the equilibrium in
welfare can be improved in this
which the innovation
economy by
subsidies
may vary between
For
shows
new
Pareto inferior,
many
countries and our
that the
need for training
in
some firms who would
not adopt
require to be targeted for such subsidies.
by a monopolist, the monopolist may try
a discount in order to entice firms into adopting the innovation. It is often observed that
*
to offer
< 1)
is
instance, industries with high d or a high degree of
heterogeneity (which would imply that there will always exist
the innovation, thus
in the next section.
not adopted
common
that justifies these but also
sectors.
is
develop
subsidizing training or the adoption of the
innovation*. Training and re-training subsidies are quite
model suggests a mechanism
we
Alternatively, if the innovation is being supplied
softwares offer discounts at early stages which
is
consistent with such a story.
However,
such action by a monopolist will not in general eliminate the externalities in our model.
b) Empirical Relevance
Since this paper
to ask
assume
whether
this
new
proposing a
is
mechanism
is
externality affecting investment decisions,
empirically plausible and relevant. First
that there are mobility costs in labor markets, in particular for high
workers spend a long time without a job after a separation
(e.g.,
infinite
Most
capital.
Devine and Kiefer (1991) or
in
changing jobs.
in hiring activities (Barron et al (1985)). Further, the
empirical literature on job reallocation and gross worker flows
uncertainty surrounding the future of
plausible to
is
human
Topel and Ward (1992)) and there also exist adjustment and transactions costs
Firms also spend considerable resources
it
we have
employment
is
indicative of significant
As a rough measure, we can
relations.
use an
horizon version of equation (1) with discounting which would imply that the effective
cost of innovation
is
higher by
^
—
^
when
other firms do not invest, where
R
is
the real
R+d
annual interest rate (which
is
the relevant discount rate since capital markets are perfect). Given
monthly separation rates are as high 4.5% (see Leonard (1987), Blanchard and Diamond
that
(1990)) or annual separations run close to
50%
US
a year in
manufacturing
(OECD
(1986)), a
conservative estimate of d would be around .20, also bearing in mind that trained workers have
lower turnover than untrained ones (Mincer (1988)). taking, the annual
4%,
this
would imply
workers, which
is
that the cost
is
66%
higher
when
b
other firms do not train their
an economically significant magnitude.
Our mechanism
instance that workers
stay despite the
of training
real interest rate to
is
also consistent with a
who
number of findings
switch jobs in general experience slower
moving premium (Mincer (1988)) and
that
training fully (Bishop (1991)). Both of these are predicted
in the training literature.
wage growth
who
than those
workers do not pay for
For
their general
by our model as workers receive
less
than their marginal product once they change jobs. However, these findings can also be
explained by interpreting
all
training as a combination of general and firm-specific training,
hence cannot be used to conclusively endorse our mechanism.
An
alternative line of attack is to investigate whether there exist cases in
which training
costs played a crucial role in adoption decisions and whether thick market externalities
important in this process. With this aim in mind,
innovations.
we turn
Fichman and Kemerer (1993) discuss
Methodologies),
4GLs
to the adoption of software engineering
three
of them were
innovations;
(Production Fourth Generation Languages),
Database Management Systems). Of these innovations only the
all
initially
were
thought to be very promising.
SMs
last
and
SMs
(Structured
RDBs
(Relational
one was adopted although
in particular
were hailed as "a
revolution in software engineering" and had the capacity to bring "significant reduction in
10
systems maintenance costs" (Fichman and Kemerer (1993)). However, very few companies put
them
to
to practice
and they were soon abandoned. The only
be high training
costs.
Although the benefits appear
(as discussed in Section 5)
may have been
the key.
significant disadvantage of
to
be potentially large, free-rider
other explanations can also be offered to account for the failure of
However
seems
effects
Very few companies ended-up adopting
innovation which would have increased the effective cost to those few
that are often put
SMs
who went
this
ahead. Yet
SMs; two obvious candidates
forward are network-externalities' and learning from others' experience.
there are no obvious reasons
significant since standardization does not
why
technological network externalities should be
seem
to
be as much an issue as
in
communication
systems. Also since initial expectations were very high and the physical investment required was
not very expensive (though the training costs were high), waiting to learn from others'
experience
may
not be a very good explanation either. Turning to 4GLs, these were expected
to bring "ten-to-one
improvements
in
programming productivity" compared
to
COBOL and other
3GLs. Additionally these new techniques did not have compatibility problems when switching
from 3GLs and the actual training costs were not high. Again, the two conventional explanations
do not appear
satisfactory.
There was no need for networking; different companies used different
programming languages before
the arrival of
4GLs and
as the set-up and actual training costs
were low, waiting should not have been an important
versions of
4GLs
arrive
the other hand,
However, many
different
arrived in the market and each different language required additional training,
thus the effective cost of training
who would
deterrent.
was much higher than
from companies
RDBs
that
that
the actual cost because
new employees
adopted other languages would have to be re-trained.
had a very similar background to 4GLs and
adopted and became the dominant technology. This
is
SMs were
despite the fact that
RDBs
On
very quickly
required very
expensive software and training, thus the response of the whole industry seems to be the key
here.
All three stories are consistent with our theory, while not easily explained by the
alternatives.
It is
also possible to obtain historical examples.
An
attractive
one for our purpose
is
the
QWERTY keyboard discussed by David (1985). This is obviously an inferior technology adopted
' It
can be argued that our externality
is
a form of network externality, as coordination
also a key issue in our mechanism. Although this
is
mechanism is explicitiy
derived from microfoundations and interactions in the labor market. With network externalities,
we refer to those technological in nature (such as standardization in communication). For an
analysis of network externalities, Katz and Shapiro (1986).
11
is
partiy true, our
at the
time to slow
down
typists so as not to
jam
the typewriters. Also, there
about the success of alternative keyboards and no need to standardize since
the final output.
However,
QWERTY
if
it is
obviously requires
3)
is
no need
to
low, the effective cost would
is relatively
only a few companies changed their keyboards.
Thus a number of
suggesting that
uncertainty
mattered was
all that
has survived to the present. Although there
standardize the output and the actual cost of training
be very high
was no
different pieces of empirical evidence accord well with our story,
empirically relevant and plausible while
much more
its
exact quantitative importance
careful empirical investigation.
The Basic Dynamic Model
Consider a dynamic analogue of the economy of the
last section.
This economy consists
of a continuum of risk-neutral and profit-maximizing firms with measure F, and a continuum
of workers with measure
F
is
small relative to
produces goods worth
Each firm
At the firm
y-l-b.
is
assumed
to
For simplicity and
in contrast to the
it
not an assumption that changes our results, but
it
do not have
to follow the time path
will therefore
employ a large number of workers
level, there are constant returns to scale
workers have no bargaining power (fi=0). As
that
is
1).
1.
(thus
and each worker
previous section,
we assume
can be seen from the previous section,
this
we
simplifies the analysis considerably as
of wages for trained and untrained workers. Each worker
be paid a wage rate equal
to the opportunity cost
of time which
is
assumed
be
to
constant and equal to b. This also implies that the firm will pay for training as the worker
is
receiving none of the benefits.
We
denote the number of workers that a firm employs at time
random shocks
to
workers and firms,
t
by
n(t).
we assume a constant exogenous probability
Instead of
of involuntary
separation for each pair such that at every instant sn(t) workers leave the firm and join the
unemployment pool. The firm receives X applicants from
is
constant in this section,
X too
is
constant.
We
assume
the unemployed.
that
As unemployment
new workers can
start
production
as soon as they arrive thus the firm does not lose any output in the turnover process.
employment of each firm follows
The
the law of motion
n'{t)=X-sn{t)
12
(2)
where
The firm
n'(t) is derivative
of
n(t)
y >0 and workers accept
all
job offers as they always receive the same wage
the
employment
economy
from a point of steady
state.
We
at
At time t=0 we are
a steady
in
install the
a cost c per worker.
demand
externalities
the applicants* since
all
rate. In steady state
n(t)=n=X/s. In what follows our
how
will later discuss
state
with n(t)=n
available. This innovation will raise the product per
but the firm needs to
accepts
both the number of
number of workers per firm can be endogenized.
firms in the market and the
at
be constant
level of a typical firm will
will start
becomes
with respect to time.
As
new technology
= X/s,
worker by a for
a cost 5 and
at
an innovation opportunity
all
future periods,
to train the existing
workforce
no technological or aggregate
in the previous section, there are
and the incremental revenue per firm as a
result
of
this innovation is
independent of the number of firms.
To proceed
it
with the analysis,
innovates and by V(t)
when
it
let
the value of the firm at time
all
be denoted by
J(t)
when
does not. Each period, (1-s) proportion of the workforce from
the previous period remains with the firm and
technology
t
workers are the same, V(t)
X new workers
arrive. Since without the
given by the following asset value equation
is
(3)
rV(t) -V'(t) =(1 -s)n(t)y + Xy
where
is
r is the discount rate
(remember
already subtracted). However,
no change
in the return to
Two
issues arise
that output
per worker
is
y+b
when n'(t)=0 and n(t)=n, we
a firm without the
when we analyze
new
will
so that the
will determine
what
it
from innovation.
returns
will
First, returns will
We
further
assume
be time
to
choose a
do when untrained workers apply. The firm
—
that
is
the general skill
(i.e.
naturally accept all applicants irrespective of their level of training (as there
cost to doing so).
bill n(t)b
technology. Therefore V=ny/r.
workforce will be changing endogenously). Second, the firm needs
which
strategy
wage
have V'(t)=0 as there
varying as the number of trained unemployed workers will not be constant
level of the
new
>c
where c
is
is
will
no opportunity
the cost of training a newly
r+s
arriving untrained
profitable, see
workers.
*
this.
Lemma
However
in section 5
worker (when
and
there
is
assumption
makes
it
is
like to
not satisfied, innovation will never be
profitable to train all
another aspect to waiting;
until then firms are
The firm would
These
3.1). This
this
when
newly arriving untrained
to innovate? This
we
will consider
only allowed to adopt the innovation immediately after
expand as much as possible, however labor market
it
frictions prevent
frictions also allow firms with different productivity levels to coexist despite firm-
level constant returns.
13
becomes available and once they carry out the investment, they
The
The
cost of adopting the innovation is 8.
train its existing
On
workforce.
a
quit, thus
untrained workers, the firm also receives
who
total initial cost is
5+nc
as the firm has to
(a+y)
the revenue side, the firm receives a net return equal to
from each worker who has not
the cost c for those
will train the workers.
total
of
As
(l-s)n(t).
X(y+a) from workers
it is
profitable to train the
arriving this period but incurs
are untrained. In order to monitor changes in future training costs,
define q(t) as the proportion of untrained workers in the unemployment pool. Thus q(t)
measure of the general
skill level
of the economy. However,
because employed workers
q(t) only,
innovation will train
all their
the workers of firms
who
also
workers, thus
did not innovate.
firm that did not innovate by m(t)'.
X=ns which
may
we
it
is
be trained or untrained. Firms
skill
that
composition of
starts
from a point of steady
state, therefore
(4)
-/ '(0 =n{a ^y) -/wc(l -q(t))
Intuitively, a firm that has
adopted the innovation will always train
costs will vary depending
on the training
from unemployment; by
the firm has to incur nsc(l-q(t)).
level of the
new workers.
workers,
all its
therefore in steady state the revenue of such a firm will always be equal to n(a+y).
will arrive
in a
enables us to rewrite the value of an innovating firm as:
rJ(t)
its
adopt the
denote the proportion of trained workers
The economy
one
not sufficient to keep track of
only need to determine the
We
is
we
However,
In steady state ns workers
definition a proportion (l-q(t)) of these will
be untrained and
As new workers only come from unemployment,
m(t) does not
enter (4) directly but influences the evolution of q(t).
In other words, q(t) and m(t) will vary over time.
on the proportion of firms
unemployed worker
that adopt the innovation,
finds a job,
p and
will
The law of motion of q(t)
<^,
will
and on the probability
be given by (see the derivation of equation
depend
that an
(5) in the
appendix)'";
(5)
qXt)=p(<f>(t)^(l-<l>it))m(t)-qit))
'
This
is
again related to our assumption that there does not exist market segmentation
depending on skill
use of their skills.
'°
m(t) and
level, thus trained
</)(t)
will
is
constant in
who
cannot make best
become more important in section 5. Since in this section it is assumed
it becomes available, <^(t) is constant over time
be adopted as soon as
symmetric equilibria.
that innovation can only
and m(t)
workers can be matched with firms
14
In steady state, entry into and exit from
workers
who
join the
unemployment pool,
innovation and are therefore trained.
unemployment occur
come from
0(t)
trained
Of
the
firms that have adopted the
A proportion (l-<^(t)) come from firms that did not innovate
and a proportion m(t) of those are trained. Also a proportion
unemployment are
at the rate p.
which explains the
term.
last
It is
q(t)
who
of the workers
useful to note that
p
exit
assumed
is
equal across trained and untrained workers. Relaxing this assumption would not change our
but would complicate the mathematics considerably.
results,
Finally, the law of motion of m(t)
is
given as follows;
«^
m'{t)=s{q{t)-m{t))
At each
They
instant,
workers arrive
at the rate s
and a proportion
q(t)
of those are trained.
also leave the firm at the rate s and a proportion m(t) of those are trained.
profitable for a firm to invest if the net present value of investing
the net return of investment,
of motion of J(t),
equilibria,
Lemma
we
q(t)
is
and m(t)
only check
<i>{i)
greater than V(0).
To determine
jointly. Since in this section
=l
we
is
this
positive; i.e. if J(0)-5-nc,
we
need to solve the law
3.1:
when
all
all
the
other firms in the
innovation
if
economy
lemmas, the proof of
The terms
+
that constitute ao
Lemma
c^
be
is n.
—
+/r
,
it is
profitable to
n
are doing so.
3.1
is in
the appendix.
r(5/n+c)
intuitively explained;
is
the flow cost of
no workers leave. However, the firm also considers rsc/(p+r), a "tax" imposed
on the firm by workers who leave. Innovation
larger
be
and 0(t)=O.
p+r
As with
will
are only interested in symmetric
For values of the productivity of the new technology, «>«(,=
invest
It
The
latter effect is
for each worker, 6
is
due
is
more
likely, the
lower
is c, 5, s
and
to the fact that, although the training cost has to
the fixed cost of innovation and once the innovation
is
adopted
r
and the
be incurred
all
workers
have higher productivity. This builds a type of scale economies into the innovation process.
will
The parameters
cost,
s
and p enter the decision rule because, although they do not influence the actual
(6+nc), they are crucial for the effective cost of innovation.
Now consider how incentives to innovate differ when other firms do not invest. The "tax"
imposed on the innovating firms
will
be higher because the pool of untrained workers
15
is larger.
Lemma
3.2:
For values of the productivity of the new technology, a^a.^sc+
—
rS
+rc
,
optimal not to
it is
n
invest
when no
other firm invests.
As ao<ai, we can
Proposition
in
which
The
result
all
that
ao<a<a,,
there exist
of
two pure
same
effective cost of innovation dep>ends
the effective cost.
is
On
Symmetric Nash
Equilibria,
is
we
obtained in the previous
on the average quality of the human
the other hand, the
of this human capital and the more willing
section,
strategy
as the result
the workers the firm expects to receive in the future.
higher
this section:
firms adopt the innovation and the other in which no firm invests.
intuition of this proposition is the
The
section.
main
1:
For values of a such
one
establish the
The lower
more firms
is this
average quality, the
invest, the higher is the quality
each individual firm to innovate. As
this interaction also leads to multiplier effects in
capital of
in the
previous
response to changes in costs or
productivity.
In what follows
we
will
sometimes refer
to the equilibria
of Proposition
1
as "good" and
"bad" or equilibria supported by favorable or unfavorable conjectures. These names are
appropriate since there
is
a clear Pareto ranking between these equilibria. Also the "good"
equilibrium can be thought of as having a higher growth rate because an
economy
in the
"good"
equilibrium undertakes more investment than one in the "bad" equilibrium". In particular
suppose that
a
is
drawn from a
probability of investment in the
is
distribution
H(a) with support
good equilibrium
is
[0,
0o=l-H(ao), and
a^.
It
follows that the
in the "bad" equilibrium,
6i = l-H(ai). The probability of investment can be thought as a measure of the economy's
growth potential implying
Not only
is
that the
"good" equilibrium has higher growth potential since
eo> 9,.
there a multiplicity of equilibria under plausible circumstances (and without
nonlinearities and/or externalities in technology), but also the multiplicity of equilibria illustrates
"
If generalized with repeated arrivals
of innovations, the "good" equilibrium would have
However repeated arrivals introduce mathematical difficulties as when the
second innovation arrives, the economy is out of the steady state. Naturally with one innovation
a higher growth
opportunity, as
when
rate.
we have here,
the growth effect will be negligible.
firms differ in their adoption costs, but the expressions
available
upon
request).
16
We also obtain
similar results
become more involved
(details are
a phenomenon that
capital are
is
thought to be important by
complements
in
many economists;
as physical and
most production processes, a predominantly low
can be thought to deter investment. However
this intuition is not true
when
the skill levels are traded). Proposition
a result and formalizes
the innovation
However,
invest.
4)
it
is
1
skill level
human
capital
this intuition; in the
that they anticipate their future
workers
to
all
to such
firm adopts
be predominantly untrained.
may have endogenously
also asserts that this state
why no
"bad" equilibrium the reason
is
and
of the workforce (as long as
shows how labor market imperfections can lead
Thus the "bad" equilibrium can be seen
arisen because firms
do not
as an "underskilling" trap.
Closing the Model
So
variables,
p and X have been
far F, n,
some new
the labor force
a steady
is
is
insights about the interaction of labor markets
U
state,
normalized to
will
1, this
be constant. The
we endogenize
treated as exogenously given. If
also is the
rate at
unemployment
these
and the innovation process
can be obtained. Let us denote the measure of unemployed workers in
p,
workforce
the labor market
competitive because workers will always be paid the marginal product of their
firms will have no reason to care about the general
skilled
human
this
rate.
economy by U. Since
As we
are dealing with
which an unemployed worker finds employment,
defined as equal to the flow into employment over the stock of unemployment, thus
p=XF/U
will
be constant
too.
The following
results
can then be stated;
Proposition 2:
The value of a firm
that innovates, J(t), is decreasing in the
unemployment
rate
of the economy.
Proposition 3:
The
probability
unemployment
of innovation
in
the
favorable
equilibrium,
Gq,
is
decreasing
in
the
rate.
Proofs of these two propositions can be found in the appendix.
\
The mechanism
that leads to this result is that the
17
unemployed workers are by
definition
Therefore,
untrained".
innovation.
to that
The end
the higher
result,
unemployment, the higher
is
the effective cost of
is
a negative relationship between unemployment and growth,
similar
is
of Pissarides (1990) and Aghion and Howitt (1992) where higher growth leads to lower
unemployment through higher job
growth.
An autonomous
creation. But here, the causation runs
increase in
unemployment
not in the above mentioned ones. This
is in line
from unemployment
growth
will lead to slower
Habakkuk's (1962) famous
in
to
our model but
thesis that tight labor
markets lead to faster growth, which receives some casual empirical support. However,
Habakkuk's
contrast to
interpretation that
most technologies are labor saving and
in tight labor markets are the driving force leading to innovations
with what
we know
our theory maintains that innovations are complementary
wages
which seems not accord well
MacLeod
about the nature of most inventions (see
that high
in
(1988),
to labor, but
we
Mokyr
(1990)),
obtain this result
because tight labor markets provide more incentives for workers and firms to invest.
More
generally, p, the probability that a worker finds a job, will be a function of the
number of firms
as well as the
of search equilibrium models
number of unemployed workers
(e.g. Pissarides (1990)),
firm and the unemployment rate in this economy.
we
Using the insight
in the market.
can endogenize both the size of each
However we
determination of unemployment and innovation incentives so
are most interested in the
we
will
adopt a number of
simplifying assumptions and keep the size of each firm constant. Since out of a population of
1,
nF workers
are employed, the
unemployment
economy, U,
rate in this
given by
is
en
u=i-nF
This also implies that as an additional firm becomes active, unemployment
We
will also
assume
that there is a fixed cost
is
reduced by
n.
of entry for each firm, k(F). This cost
is
a function of the number of firms in the market which will enable us to capture congestion
effects.
These
effects arise in search
"crowded" and the probability
profits
that
models because as more firms enter, the market becomes
a given vacancy will be
from opening a new vacancy. Our desire
the analysis
makes
congestion effects.
this unattractive for us. Instead
As more
and McAfee (1987)).
of firms,
'^
reducing expected
keep the firm size constant
we assume
that k'(F)
firms enter the cost of opening a
new
>
in
order simplify
to incorporate these
firm increases (e.g. Howitt
We also assume that the market cannot support more than a certain
F**** thus lim^_^o.ax k(F)=<x)
It
to
filled falls, thus
.
Also like Pissarides (1985,1990)
can easily be seen that even
institution that could offer
them
if
training they
we
will
number
make
use of
unemployed workers had access to an educational
would be willing to pay less for it than employed
workers and the qualitative results would remain unchanged.
18
a zero profit condition in order to close the model. However Pissarides assumes
exists profit opportunities in the market, thus the
number of vacancies
is
some date and make
for firms to decide whether to enter or not at
new technology
the productivity of the
obtain
some of
become
it
variable that
makes more sense
the initial investment but if
higher than anticipated, these firms will be able to
the rent.
We thus assume that all
will
is
jump
a
instantaneously adjusts to satisfy a zero profit condition. For our purpose,
that there never
available at t=0.
for the fact that
it
will
know
entry takes place at t=-T. Firms
The
productivity of this innovation
once the productivity of the new technology
is
not
know which
revealed.
We
new technology
known ex
We will be looking
be drawn from a distribution H(a).
Expectations Equilibrium of this economy, thus firms
is
a
that
ante except
for the Rational
equilibrium will be played
will
show
that
even once
we
condition on firms' conjectures about which equilibrium will be played, there will exist an
more firms
additional strategic complementarity: as
The zero
-'^{
r
The
becomes more
profitable.
form of
profit condition will take the
k(F) =-^ +e
enter, entry
r"'^(/(0,a,F) -5 -nc
-^)dH{a)}
(8)
r
•'"Xn
right-hand side of this equation can be explained as follows: the firm receives the
flow ny from t=-T to
0. Thereafter
continues to receive ny.
The
it
can refuse to adopt the innovation
in
which case
present value of this profit flow, evaluated at t=-T,
Alternatively if the productivity increment, a,
is
is
it
ny/r.
greater the cut-off productivity level, a^, the
firm will adopt the innovation, obtaining J(0,a,F), incurring the innovation and training cost
6-l-nc,
a,
and losing the flow income of the old technology. As
we need
to take expectations conditional
that although
worker
is
on a>a(,(F) which
is
not
know
the realization of
what integration does. Note
n does not depend on the number of firms, the probability that an unemployed
matched with a firm,
p, does
the flow profits, J(0,a,F) depend on
First, in (8) there
conditional
we do
F
and via
this,
the cut-off level of productivity, q!,(F) and
too.
can be two different cut-off points for the adoption of
upon a given number of firms
(i.e.
believe they are in the "bad" equilibrium, the
"good" versus "bad" equilibrium).
number of firms
by
19
in the
this innovation
When
all
firms
market will be determined
Jsc*—*rc
r
P\F)^r
r
where p depends upon F through equations
The LHS
increasing by assumption.
falls,
p increases and
which
is
profitability
is
Note
is
is
that all these equilibria are conditional
may
firms enter. Alternatively firms
These curves can thus
is
everywhere
unemployment
enter,
we
irb(F)
obtain
more than once
intersect
greater than Xb(0), there will exist an equilibrium
two additional
active but
more firms
of innovation increases. Differentiating
also an everywhere increasing function.
which no firm
The RHS of this equation
(5).
also increasing since as
as Figure 1 illustrates. In particular, if k(0)
in
and
(4)
y
equilibria with positive activity
may
also exist.
upon the "bad" equilibrium being played once the
expect to be in the favorable equilibrium, in which case the
equilibrium condition becomes
;t(^.S.e-'7"r . (!!i^-^-S-nc-!Si)M(.).^^(F)
*
^—^"=
r
We can
•'
,^
p(F)*r
n
p(F)+r
r
see that similar effects are present here as well but there
is
also the added effect that the
cut-off productivity level is a function of the
number of
strengthens the strategic complementarity that
created by entry decisions.
In general, the
firms enter, X, the
number of firms
number of
of each firm will shrink. This
is
economy,
in this
applicants per firm will
is
n, will also
fall
the effect of congestion
active firms. This effect further
we tried
incentives through the scale economies discussed earlier.
In this context
way,
it
is
it
it
relationship
Also note
will also reduce innovation
Even when we model
the congestion
cannot be analytically determined which effect will dominate.
instructive to return to the relationship
to slower growth.
state equilibrium size
to capture with k(F).
unemployment. As emphasized above, higher unemployment leads
and hence
depend on F and as more
and the steady
that if further entry reduces the equilibrium size of firms,
effect explicitly in this
(11)
r
to
between investment and
lower investment incentives
Yet Aghion and Howitt (1992) detect an inverse 'U' shaped
between growth and unemployment
(i.e.
a low level of unemployment can be
associated with a low as well as a high level of growth) in a cross-country regression using
OECD
data,
while Bean and Pissarides (1992) question the existence of any well-defined
relationship. This lack of negative relationship
between unemployment and long-run growth
20
in
'
the data poses a potential challenge to one of the predictions of our model.
first
be remembered
unemployment
due
(e.g.
should
it
growth and unemployment are both endogenously determined and while
that
unemployment may lead
high
However,
slower growth,
to
high
growth
may
also
lead
Aghion and Howitt (1992)), thus
to the creative destruction effects of
raw correlations may not be too informative. Further, the endogeneity of entry decisions
model serves
to
muddy
i.e.
s,
and
5, c, H(q!)
will lead to different levels of activity in their economies.
unemployment
their
As
matching technology,
activity, i.e. F, increases,
but each firm also becomes smaller, thus leading to lower investment
falls
incentives through the scale economies.
with low growth.
On
Hence a low
F
the other hand as
level of
increases and
unemployment can be associated
unemployment
falls,
probability from unemployment) rises thus increasing the incentives to innovate
for i=b,g).
of technical progress
model
active
p (the
(i.e.
is
may
from
that
technical progress (or growth). In contrast in our
influences
that the
of Aghion and Howitt. In their model, the form
lead to higher (or lower) unemployment.
number of firms which
exit
7r|'(F)>0
High growth can therefore be associated with low unemployment. Yet, note
causality in our case is very different
their
our
in
the waters via the level of activity and the size of firms in the market.
Countries will differ in their fundamentals,
which
high
to
Thus
the driving force of
model the "driving force"
unemployment and through
incentives of the firms (and the growth rate of the economy).
It
is
the
is
the investment
this,
often argued that the
organization of the labor market will have implications for the growth performance of an
economy (going back
at least to
Habakkuk (1962) and perhaps
mechanism
just identified, running
which such
effects will operate.
different
look
from unemployment
to growth, provides a route through
This analysis also generates certain testable implications
from Aghion and Howitt (1992)'s inverse U-shaped
at the relationship
The
as far back as Marx).
relationship. In particular, if
we
between unemployment and growth, using sectoral data and controlling
for sector/region specific variables (such as average firm size, training costs, general skill level
of the workforce
etc), there
should be a clear inverse relationship. However,
control for these variables, the relationship
Finally,
when our model
innovation activity
An improvement in
shift
is
is
may no
move from
closed, an interesting complementarity between invention and
obtained due to the multiplier effects discussed in the previous sections.
the invention performance of the
statics (i.e.
point
A
not
longer be negative.
economy can be captured by a right-wards
of H(a), the distribution function of the innovation's productivity.
comparative
when we do
we do
Now
consider local
not shift from one equilibrium to another, thus in Figure
to point B), F, the
number of
21
active firms, will increase and
1
we
unemployment
the cut-off level for innovation will
to
fall.
This complementarity implies that a shock which leads
growth when drawn from a favorable distribution may not lead to growth when drawn from
a less favorable distribution
incremental productivity, a, can be greater than the
(i.e.,
new
cut-
off level, a^, but below the old cut-off level, a^)- Therefore in economies with better innovation
prospects, mediocre investment opportunities will be exploited while the
economies
that face
same
not true for
is
an unfavorable distribution for new technologies. This mechanism would
further agglomerate initial technological differences between economies.
5)
Timing of Innovation Activity and Free-Rider Effects
In this section the basic model of section 3
to
choose the timing of their adoption after they receive the opportunity rather than being faced
with a
"now or never"
decision as in the previous sections.
firms are maintained. Since firms have a timing decision,
to adopt the innovation. If the
answer
we
adopted. With this aim in mind,
becomes available
at
The assumptions
that the training
and the marginal productivity of innovation, a, are equal across
cost, c, the innovation cost, 5,
all
modified in one respect. Firms are allowed
is
is
t=oo,
this
we
ask when
it
will
be profitable
corresponds to the innovation never being
write the payoff to adopting at time
t
an innovation that
time t=0;
W{t) =(1 -e
-"
)^ +e -"
[J(t)
(12)
-S -(1 -m{t))nc]
r
Intuitively for the first
is
the first term in (12).
workers.
As a
(l-m(t))nc and
It
t
periods the firm gets the return of a firm that has not innovated which
At time
it
receives
J(t).
be optimal
in the case
where W'(0)
opportunity
is
If
the firm incurs the innovation cost 6 but also has to train the
proportion m(t) of the workers are already trained,
will obviously
Lemma
t
is
Discounting
to innovate at
this to
t
only
only incurs the cost
time t=0, the second term in (12)
if
positive, waiting will
W'(t)=0
(or
when W'(0)<0).
be profitable
at
t=0 when
is
obtained.
In particular
the innovation
received.
5.1:
a<a.=sc+
—
n
it is
it
not profitable for a firm to invest alone.
22
+rc
(13)
The
intuition of this
that the effective cost
Lemma is
an extension of our results in sections 2 and
of innovation
lower when more firms
is
their
train
We know
3.
workers.
By
implication, the first firm to innovate will face a high effective cost as no other firm has yet
innovated. Therefore,
order to reduce
its
all
other things being equal, the firm would prefer to wait for others
effective costs.
However, by waiting the firm
revenue which obviously has a cost.
will
If
dominate and the firm will prefer
same
as condition in
firm will find
when
it
is
do not want
it
to
move
first
is
3.2 that each
However
is
profitable because
reduced. Yet, by the same reasoning those
first.
us that if
1 tells
a>ao,
will
be when (13)
there will exist
is satisfied.
two symmetric
Without
equilibria.
possibility of waiting, there exist other possibilities: all firms can adopt the innovation
t=0 or
together at
first
the
would bear a disproportionate share of the burden, thus they do not want
the option to wait. Proposition
go
is
will prefer to wait for others.
can view firms as trying to free-ride on others. Waiting
Next we can ask what the form of the equilibrium
With the
Also note that (13)
we know from Lemma
go alone and they
to
its
(13) is satisfied, the first effect
believes other firms will not be investing.
as other firms invest the effective cost of training
firms that adopt
i.e. if
(13) does not hold,
profitable to invest even if
we
not too high,
delaying the increase in
to wait for others to innovate'^.
Lemma 3.2; when
(13) is satisfied, firms
Alternatively
a
is
in
and the
even when
all
a only a proportion of firms, indifferent between adopting
rest follows slowly.
However, Proposition 4 shows
other firms adopt the innovation,
it
will
when a > ao) and
when
(13)
delaying,
is satisfied,
be profitable to wait, thus free- riding on
the training costs. This implies that the favorable equilibrium in
disappears (even
that
now and
which the innovation
the ineffficiency of the previous sections
is
is
adopted
intensified (proof
of Proposition 4 in the appendix).
Proposition 4:
When
and
firms can delay adoption the innovation
all
firms innovate together
The
first to
when
(13)
is
is
never adopted in equilibrium
if
(13)
is satisfied
not satisfied.
intuition is given in terms of the free-rider effects.
Firms would not
like to
be the
innovate because the others would free-ride on the costs of training the workforce. But
"
For instance, in
may gain a competitive edge, e.g. Fudenberg
In practice there will naturally exist other considerations.
markets, the firm that innovates
first
Judd (1985) and Tirole (1990) for a review of the
23
literature.
oligopolistic
et al
(1983),
when
all
other firms invest, each firm would
still
and wait for the training
like to free-ride
move
of the workforce to increase sufficiently. As a result no firm wants to
effectively blocks the innovation.
effects
Thus the
and increases the inefficiency
in the
flexibility to
level
which
first
choose the timing creates free-rider
model by destroying the favorable equilibrium. This
can also be interpreted as creating inertia in the economy in response to new technologies as no
one wants
to
move which
is in
some
respects similar to
(though Mokyr's concept
to technological progress"
what Mokyr (1990) dubs as "resistance
much
is
richer as
it
includes creative
destruction effects).
6)
Conclusion
The determination of investment and innovation
and economists have been analyzing the
market imperfections give
that labor
equilibria
and free-rider
effects.
incentives
is
an important research area
effects of externalities in this process. This paper
rise to
such externalities which
The model we consider can
explain
may
how
shows
lead to multiple
skill
shortages can
endogenously arise making future investments less likely and also suggests some new linkages
between unemployment and growth.
A
major shortcoming of our analysis
ignored. Although
change our
results,
it
was informally argued
it
of future research that
will
be instructive
may be
is that
the
wage determination process was
that effects through
to analyze this
wage determination would
problem
fruitful is to empirically test
largely
in
some of
more
detail.
not
Another area
the results implied
by
this
model, in particular those relating to the link between unemployment and innovation incentives.
Although our model predicts
in contrast to
low unemployment can be associated with high or low growth,
Aghion and Howitt (1992)
as the size of firms), lower
tested
that
it
implies that if
unemployment
on aggregate data but on
we
control for
all
other factors (such
will lead to higher growth. This cannot
sectoral or regional data,
it
be easily
should be possible to investigate
whether, controlling for the size of firms and skill-level of the workforce as well as fixed
effects, the level
of unemployment affects investment and productivity growth adversely.
24
Appendix
Derivation of Equation
(5):
Let Q(t) be the number of trained workers in the unemployment pool and M(t) the number of
Then
trained workers in a firm that has not innovated yet.
(Al)
Q'(t)=nsF<i>(t)^M{t)sF(\-<l>{t))-pQ{t)
At each
instant ns
workers join the unemployment pool from each firm.
<^(t)F firms
have
adopted the innovation thus their workers are trained. (l-0(t))F have not adopted the innovation
yet and only sM(t) trained workers
quits the
unemployment pool
become unemployed from
at the rate
p and thus pQ(t)
pool. Divide both sides of this equation by
p=nsF/U. This
Proof of
trained workers exit the
U which is constant;
unemployment
write M(t)=nm(t) and note that
gives us (5).
Lemma
3.1:
We
are considering the case where 0(t) =
The
steady state value of q(t)
variable, q, and
these firms. Also each worker
is
equal to
l.
Thus our system reduces
1, that
of J(t)
one non-predetermined variable,
J. If
is
to
two variables q and
n(Qr+y)/r. There
is
one predetermined
the rational expectations path
is
unique,
one
initial
condition should enable us to determine the time path of both variables and there
one
initial
condition given by q(0)=0.
A
J.
is
unique rational expectations equilibrium path exists as
the roots of the problem are equal to r and -p from equations (4) and (5).
The
solution takes the
form of
p+r
^^^>
r
q{t)=Ae-P'^l
where
A
is
a constant which
we
determine from the
initial
condition
q(0)=0
as
A=-l.
It
then
follows that
Jity-n^e-P'^'^^^^
p+r
r
and
25
(A3)
my'^k'^^y) -n£L
p^r
r
Innovation
a>ao.
is
profitable if J(0)-6-nc is greater than V(0),
which gives us the condition
QED
Proof of
Lemma
3.2:
In this case unemployed workers are always untrained.
will
(A4)
be no change
As
there is a continuum of firms, there
of trained workers in the unemployment pool and thus the
in the proportion
return to investing is
rJ
The
if
a>a,.
is strictly
increasing in p.
p
Proof of Proposition
increasing in
Proof of
again given by
V
above, thus
it is
profitable to invest
2:
that innovates,
constant population,
is
is
QED
The value of a firm
00
^^^^
=n{y-^a) -nsc -nac
from not innovating
return
Proof of Proposition
which
'
Lemma
is
when
As we
all
other firms invest,
J(t), is
given by (A3),
are in steady state with a constant
defined as equal to nsF/U. Thus p
is
given
is
number of firms and
decreasing in U.
QED
3:
p and hence decreasing
in
U.
QED
5.1:
Differentiating (12) with respect to time
WXt) =e
Substituting
from
(4),
e"
We
we
-"
[ny -rJ{t) ^J'{t)
^rS^mc -mcm{t) +ncm
^^"^
'(/)]
get
W(t) = -na +nsc +nrc +r8 -nscq(t) -nrcm{t) +ncm
are considering a firm that will innovate alone which implies that
m'(t)=0. Substituting these in
26
^^°'
'{t)
m(0)=q(0)=0,
thus
^^^^
e" W'(t) = -na+nsc*nac+nrc+r8
This
is
positive if (13) is satisfied and the firm prefers to wait.
Proof of Proposition
Suppose (13)
at
time
t?
QED
4:
is satisfied.
Can we have an equilibrium
This can only be an equilibrium
if
in
which
<^(t)
firms adopt the innovation
W'(t)<0. However, from (A8), W'(t)>0
irrespective of the value of 0(t) as long as m(t)=q(t)=0. Therefore at
argument
at all
t,
t=0 and by
a similar
every firm would prefer to wait further and in equilibrium, the innovation will
not adopted. If (13)
is
not satisfied,
innovation immediately at t=0.
W'(0)<0 and
QED
27
all
firms find
it
profitable to adopt the
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