Transcript Ec423: Labour Economics

Theory of Skill Premia
Lent Term
Lecture 2
Dr. Radha Iyengar
Last Week…
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Facts about inequality
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Grew in US, UK, not so much other places
Gap in Earnings between HS and College grads
grew
Doesn’t seem to be a simple cohort effect
Doesn’t seem to be all earnings volatility
This week…Skill Premia
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Why do returns to different skills differ?
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What happens when production
technologies change?
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How is this related to observed facts from
last week?
The set-up…
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We begin with a simple closed economy,
aggregate production framework:
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factors are paid their marginal products
the economy operates on its supply and
demand curves.
Two types of workers: H and L
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Can be high and low skilled, college and HS
grads, etc.
Workers
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Workers are imperfect substitutes:
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If workers were instead perfect substitutes,
their wages would always move together up to
multiplicative constant (reflecting relative
efficiency units)
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Perfect substitution implies relative wages,
only on the return to the single factor of skill
NOT relative supplies
Labor Supply
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At time t, there are L(t) type L and H(t)
type H workers supplying labor
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We’ll make labor supply inelastic for ease of
exposition
The production function for the aggregate
economy takes the constant elasticity of
substitution (CES) form (with ρ ≤1):
Elasticity of Substitution
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elasticity of substitution between skilled and
unskilled workers
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Skilled and unskilled workers are .gross
substitutes. when the elasticity of substitution σ
> 1 (or ρ > 0) and gross complements when σ
< 1 (or ρ < 0).
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In the CES framework, the value of σ plays a
critical role because it determines how changes in
either technology (given by the A’s) or supplies
(L’s) affects demand and wages.
3 Special Cases in CES framework
1.
σ → 0 (or ρ → ∞ ). In this case, skilled and
unskilled workers are Leontief, and output can
only be produced using skilled and unskilled
workers in fixed proportions. This is a case of
perfect complements.
2.
σ → ∞ (or ρ → 1). Skilled and unskilled workers
are perfect substitutes (and so relative supplies of
each do not affect relative wages .though chances
in aggregate supplies will affect relative wages by
affecting the price of skill overall).
3.
σ→ 1 (or ρ → 0). The production function is Cobb
Douglas, with fixed shares paid to each factor
Wage Setting
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Given competitive labor markets, the
unskilled wage is given by:
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And skilled wage is given by:
Two Labor Market Results:
1.
∂WH/ ∂(H/L) < 0, i.e. the own labor demand curve
is downward sloping.
2.
∂ WL/∂(H=L) > 0, i.e. Everything else equal, as
the fraction of skilled workers in the labor force
increases, the wages of unskilled workers should
increase.
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Hence, skilled and unskilled workers are Q-complements
a greater quantity of the one increases the marginal
product of the other.
This seems more natural if you think of the two inputs as
capital and labor; more intensive use of capital raises the
marginal productivity of labor and vice versa
Skill Premia!
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Combine two equations and we get:
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We can write this in log form for ease of
interpretation
The RELATIVE demand curve
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Taking derivatives of this:
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the relative demand curve for high versus
low skilled workers is downward sloping.
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For given skill bias, Ah/Al, an increase in
relative supplies H/L lowers relative wages
with elasticity σ
Why Does Increased H/L Decreases
Relative Wages?
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Two potential ways this happens:
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Suppose there’s only 1 good: an increase in the
relative supply of high skilled worker will cause
firms to reassign some tasks performed by low
skilled workers to high skilled, thereby lowering
the marginal productivity and hence the wages of
high skilled.
Suppose there are multiple goods: Output of the
high-skilled good will rise, increasing consumption
of this good but lowering consumers marginal
utility of consuming it and hence its price.
What happens if relative efficiency (A’s)
changes?
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What if we change the skill bias, i.e. Ah/Al
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Depends on whether σ is bigger or smaller
than 1
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Hard to measure σ but it’s though to be
bigger than 1
How could increase Ah/Al not increase
High Skilled wages?
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An intuitive way to see this is to consider a Leontif
production function where high and low skilled
workers are used in constant proportions in a
competitive market.
An increase in the supply of high skilled workers in
this setting effectively creates “excess supply: for a
given number of unskilled workers.
The extra skilled workers will either bid down wages
of other skilled workers or will become unemployed
(lowering average wages for skilled workers if zeros
are counted).
Not considered likely based on what we know about
σ
Average Wages
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Average wages should increase:
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When the skill composition of the labor
force rises, wages increase.
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Intuitively: When the wages of skilled are
below unskilled, this effectively implies that
unskilled are scarcer than skilled;
additional skilled workers effectively lower
the skill composition of the labor force
Societal Wealth
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If Ah or Al rises with σ > 1, wages should rise for
all workers, both skilled and unskilled (though
inequality may increase).
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Factor augmenting technical change always raises
societal wealth since we can get more output for a
given set of inputs.
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Keep this in mind as an explanation for observed
Trends
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male wages below the median fell substantially in real
terms in the U.S. during the 1980s
Not true in other countries
Summary from our Simple Model
In response to an increase in H=L (and
assuming the skill premium is positive):
1. The skill premium w = WH/WL falls.
2. Wages of unskilled workers rise.
3. Wages of skilled workers decrease.
4. Average wages rise.
These results can readily be generalized to a
case with capital, i.e., F(AlL;AhH;K); and
they will generally go through.
Long-term skill bias technical change
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The key result from the above is that as
H/L increases, w falls.
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But in every advanced country the supply of
educated workers has risen dramatically in the
past 6 decades but relative wages of better
educated workers have remained consistently
above those of less educated, though the
degree to which they have done so has varied
by decade.
Hence, the relative demand for skilled workers
must have risen practically everywhere.
Technology vs. Skill Supply Growth
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We observe increased relative supply of skill and
increased wages so we think technical change may
be “skill-biased” (favoring high skilled)
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Not necessary that technical change has outstripped
growth in supply of educated workers.
Rate of technical change is not always fixed
Tinbergen (1975) point:
“The two preponderant forces at work are
technological development, which made for a
relative increase in demand and hence in the
income ratio... and increased access to schooling,
which made for a relative decrease.”
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Evolution of Inequality
1.
Long term trend increases towards
greater relative demand and greater
supply of skilled workers
2.
Bursts of supply and/or technologicallyinduced demand accelerations/
decelerations that cause demand to
temporarily move out more rapidly than
supply or vice versa in some eras.
Katz-Murphy (1992) Model
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Insight: if you know (or assume) σ, can
back out the implied change in relative
demand for high versus low-skilled worker
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Let’s go back to our wage skill premium
from the CES model
Estimating changes in Relative Demand
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Get some time series data
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Estimate changes over time
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A’s vary by year, as do the supplies of skilled
and unskilled workers and the skilled/unskilled
wage ratio
Fixed σ
We observe supplies and we can estimate the
wage premium.
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Unknowns:
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Ah/AL
σ
Our hypothesis is that ∂ln(Ah/AL)/ ∂t > 0
so we estimate
Time
fixed
constant
Results
there has been a trend increase in the
relative demand for skilled workers
 the elasticity of substitution between them
σ = -1/0.709 = 1.41.
 Caveat: K-M regression has only 25 data
points, and they are highly serially
correlated.
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Is it steady or accelerating demand
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KM: Steady demand and fluctuations in
supply are drivers of inequality
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Natural question: Could this be due to
accelerating/changing demand
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Define a demand index
How to test for accelerating demand
Is there an acceleration in the rate of
change in Dt?
 Specific test: ΔD70-99> ΔD45-69
 How to estimate?
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A consistent series for wages and employment
Estimates of wagebill shares (wHH;wLL)
Estimate of wH/wL
Concerns…
One concern in implementing this
framework is that the wagebill shares may
confound changes in prices (wH/wL) with
changes in the composition labor if the
quality of high and low skill workers varies
with time.
 That is:
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Supply change
Price change
Isolating true change in supply
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Subtract of the component of wagebill
share change due to pure price changes
(estimated from a regression) and hence
calculates the effective supply change as a
residual.
AKK (2004) Results
Conclusions from AKK
1. There
is evidence of growing relative
demand for skilled workers in every decade
except the 1940s
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it is believed war-era industrialization dramatically
raised relative demand for less-skilled workers
AKK (2004): Demand Shifts
More Conclusions AKK
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Whether demand accelerated in the
1970s or 1980s relative to the prior
decades depends sensitively on the
assumed elasticity
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a demand acceleration in the 1970s may have
been masked by a simultaneous supply
acceleration.
If this inference is correct, inequality would
have grown in the 1970s had supply not
suddenly jumped.
AKK (2004) Changes in Wage Supply
Takeaways from AKK (2004)
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There is clear evidence that net demand
changes were larger over 1970 - 2000
(i.e., the most recent three decades
relative to the prior three).
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This is evidence of acceleration
depends heavily on including the 1940s.
There appears to be demand deceleration
in the 1990s.
 key fact: necessity of demand shifts, with
some evidence of their acceleration in the
1970s or 1980s.
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Theories for Explaining Inequality:
1.
Steady demand.
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One possibility motivated by the Tinbergen framework
(and partly affirmed for the 1960s - 1980s by KatzMurphy) is that for unspecified (and perhaps
exogenous) reasons, there has been a steady rise in
demand for skills throughout the century.
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Hence, movements in the wage premium reflect
changes in the trend growth of supply. when supply lags
demand, the premium rises (and vice versa).
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Simple but plausible one, and it may explain much of
the data if not all of it. Richer versions of the K-M model
(e.g., Card and Lemieux 2001) may do a better job of
explaining the data using this hypothesis than does the
original K-M paper.
Theories of Inequality II
2. Accelerating demand
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This hypothesis posits a discontinuous increase in the trend
rate of demand growth, perhaps occurring in the 1970s or
1980s, that, coupled with the slowdown in supply, caused
inequality to rise.
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This is also a reasonable hypothesis a priori: why should the
rate of movement of the relative demand curve be steady
across periods? What gives this hypothesis added
plausibility to many economists is the simultaneity of the
computer revolution with the rise in inequality in advanced
countries.
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Generally, hypotheses in this vein (accelerating demand)
will specify a variety of reasons why demand will have
accelerated, and provide evidence for these causes.
Theories of Inequality III
3. International trade.
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There was substantial growth in world trade
flows, especially in the United States.
The most rapid growth is during the 1970s, not
the 1980s.
Trade between countries with different factor
endowments will change relative prices and
will therefore raise or lower inequality among
owners of those factors
Theories of inequality IV
4. International outsourcing.
 This is subtly different from trade. Rather than opening
factor markets to trade, you simply purchase certain factorintensive inputs from overseas and turn them into final
products in your own country.
5. Institutional changes.
Declining union penetration and falling minimum wages are
a major feature of the U.S. and U.K. labor markets during
the period of inequality growth. In other countries, these
institutional changes have been far more moderate. A
number of authors have argued that these institutional
changes explain the observed changes in wage setting
rather than the forces of supply and demand.
Next 3 Weeks…
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Theories on why higher skills maybe more
productive
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Returns to Education
Education Production
Signaling Models