viii. supply effects and induced bias in innovation
TRANSCRIPT
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VIII. Supply effects and induced bias in innovation
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Induced Bias
• Traditionally, one assumes that TP enters the production function in some exogenous way
• What if innovators can ex-ante seek to obtain a given type of technical progress?
• That is what the old “induced bias” literature tries to model
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The traditional view
• Innovation augmenting one factor increases the return to the other factor
• Because of such “bottlenecks”, further innovation will be biased in favor of the other factor
• We eventually expect innovation to be “balanced”
• These bottlenecks imply that if one factor is more abundant, innovation will favor the other factor, to compensate
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The modern view (Acemoglu)
• There exists market size effects: profits from an innovation depend positively on its market size
• Market size is larger if factor affected by innovation is more abundant
• This effect tends to reinforce existing biases rather than compensate them
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Consequences for the distribution of wages
• If market size effects dominate bottleneck effects, then an increase in H/L triggers skilled-biased innovations
• These innovations themselves increase the skill premium,
• Which in turn induces people to accumulate more human capital…
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A simple heuristic argument
• Suppose firms could “pay” for technical progress in one dimension or another
• How much are they willing to pay?
• That gives us an idea of where TP is going to take place
• Firms willing to pay more more profits for innovators
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The logic
• Production function
• Marginal product conditions
• Cost function
• Willingness to pay per unit of output
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The equilibrium MWP for technical progress
• Diferentiating cost functions and substituting MP conditions, we get
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Interpretation
• Because of optimality, how I reduce costs is irrelevant at the margin
• Suppose, upon an increase in A, that I reduce L proportionally
• I produce the same, and costs are reduced by wLdA/A = F’1LdA
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What happens to MWP when factor endowments change?
• Assume H goes up
• The wage of human capital falls, thus reducing my savings from human capital augmenting technical progress (bottleneck effect)
• But a proportional reduction in H would affect more people, and thus be more profitable (market size effect)
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Implications for the induced bias
• Assume the bias in TP adjusts so as to equate MWP across types of TP
• Then the endogenous bias is determined by
• That formula determines the endogenous skilled bias b = B/A as a function of the factor endowment h = H/L
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Which effect dominates?
• db/dh > 0 if curvature of f not too large
• Bottlenecks are small if H and L are substitute, market size effects then dominate
• Botlleneck effects are large if complementarities between H and L strong enough
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The CES example
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Net effect on the skill premium
• While an increase in H/L induces SBTC, skill premium need not go up on net
• For skill premium to go up, the positive effect of induced technical change must be higher than the direct negative effect of a greater H/L
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The net effect on the skill premium
• To get an increase in the skill premium, we need a more than proportional response of b to h
• That implies even less complementarity
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Computing the skill premium in the CES case
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An endogenous innovation model
• Can the preceding analysis be made more rigorous by explicitly taking innovation into account?
• The answer is: yes
• And the analysis and intuition are basically similar
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The model’s ingredients
• We need a simple model of endogenous innovation
• Building on Romer, we assume innovation introduces new varieties
• These varieties enter as inputs into the production of aggregate intermediate goods
• Two categories of varieties depending on whether H or L is used
• Two different aggregate intermediate goods
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From product diversity to factor productivity:
• As in Romer, the CES aggregate for the intermediate input entails « taste for diversity »
• Hence, an increase in the number of varieties is equivalent to technical progress which increases the efficiency of the relevant factor
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The production structure
• Aggregate production function:
• l-aggregate uses l-inputs:
• Similarly for h:
• l-inputs use labor
• Similarly for h
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Computing aggregate factor productivity
• By symmetry, all goods of the same kind are produced in the same quantity
• Therefore, yl = L/Nl and yh = H/Nh
• Hence, Yl = AL, Yh = BH, Y = F(AL,BH)
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Pricing
• Individual price-setters face constant elasticity
• Using price index for intermediate aggregates, we get
• Profit maximization for the final good allows to recover wages
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Profits
• In equilibrium, labor uniformly allocated
• This allows to compute quantities, and thus profits
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Patents and innovation
• The value of a patent is given by
• In an interior BGP, Vh = Vl throughout, implying
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Profit equalization allows to compute equilibrium bias in
technology
• We get a formula quite similar to the heuristic model:
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The effects
• When a factor is in larger supply, any intermediate good which uses that factor will have a larger market (Market size effect) term in H/L
• If a factor is more abundant in efficiency units, its marginal product falls, which reduces the demand for the corresponding intermediate inputs (Bottleneck effect) term in F’1/ F’2
• If a factor is more productive, it means more intermediate goods for that factor, and lower market size term in (B/A)1-η
• If a factor is more productive, its price is higher, which boosts prices and profits for intermediate goods term in (B/A)
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The CES case
• Relative profits are equal to
• That determines a stable interior value of b provided
• That value is then given by
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When does the supply effect increase the bias?
• Clearly, db/dh > 0 iff γ > 0
• Substitutability market size effects dominate
• Complementarity bottleneck effects dominate
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When does the skill premium go up on net?
• The skill premium is given by
• It is increasing in h provided
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Discussion
• Again, more substitutability is needed for the SP• The bias must react enough to h• Furthermore, condition more likely when η is
smaller• η is smaller b more reactive to h
– The lower η, the lower the increase in N associated with a given increase in A, the smaller the profit dissipation effect associated with an increase in A
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Dynamics
• Assume a fixed supply of researchers• They can pick any kind of innovation at
any point in time• Assume a productivity spillover à la
Grossman-Helpman• At each date, all researchers work in the
most profitable kind of R & D• Unless patent values are equalized, they
are then indifferent
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Aggregate research dynamics
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The allocation of R & D
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db/dt = 0
dΔ/dt = 0
C
b
Δ
Figure 5.7: the dynamics of the technology bias
E
E
D
D
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b =B/AFigure 5.8: convergence path of the technology bias
b*
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db/dt = 0
dΔ/dt = 0
C’
b
Δ
Figure 5.9: response of the technology bias to an increase in H/L
C
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A
B
time
time
Figure 5.10: response of the skill premium to an increase in H/L
b
b
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IX. The bundling model
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The limitations of neo-classical models
• In neo-classical models, individuals are irrelevant
• They earn the sum of the income of the characteristics they bring to the market
• Where they work and whom they work with does not matter
• We now turn to models where individuals matter
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The role of unbundling
• A first mechanism by which individuals may matter is unbundling
• Unbundling means that all the characteristics of the individual must be supplied to the same employer
• We will show that the price of each characteristic then need not be equal across sectors
• One implication is that people will sort themselves into different sectors by different skills
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Back to the basic model
• Each worker has a skill s
• Skill determines h(s) and l(s)
• We order skills by comparative advantage so that h(s)/l(s) grows with s
• Workers can’t elect which characteristic they supply
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A pseudo-obvious result
• If there is a single homogeneous final good, then each worker earns an income
• Where ω and w are the economy-wide price of H and L
• In the unbundling model, that result is obvious• But is is not in the bundling model• We have to prove that each firm offers the
same return to each characteristic
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The firm’s optimization problem
• To complete the proof we need to show that these MPs are equalized across firms• Workers are paid the marginal roduct of their characteristics in the firm where they work
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Completing the proof
• In equilibrium, all firms have the same H/L ratio
• Therefore, each marginal product is equalized across firms
• Otherwise, firms with a higher H/L pay more for L and less for H
• But then they attract lower-skilled workers and cannot have a higher H/L ratio
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The 2-sector model
• Firms in different sectors sell their output at different prices
• A non unique price may be supported
• Example: sector 1 pays more for H and attracts the higher skilled workers
• It does so not because it has a lower H/L ratio, but because its production is more intensive in H
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The model
• Under unbundling, the allocation is determined by standard considerations
• The two FPF interact if both goods are produced
• Each factor price is unique
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wFigure 6.1: factor-price equalization in the two-sector model
PFPFA
ω
PFPFB
E
-L/H
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wFigure 6.2: full specialization under unbundling
PFPFA
ω
PFPFB
E
-L/H
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Can the bundling allocation be an unbundling equilibrium?
• A necessary condition is that there exist an allocation of people which matches H and L in both sectors
• Because people come to a sector with their own endowment of both h and l, an arbitrary allocation is not necessarily feasible
• A feasible allocation must be between the minimal and maximal human capital intensity curves
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L
H
Figure 6.3: the allocation of labor and human capital
LBLA
HA
HB
MM
MM’
E
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The “lens”
• It defines the set of macro allocations of H and L such that their exists a micro allocation of individuals which yields that macro allocation
• The lowest possible H/L ratio in sector A is obtained by allocating the lowest skilled people there first
• If I want to allocate more labor to A, I must move more skilled people there, and the minimum H/L ratio goes up
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The determination of MM and MM’
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Equilibrium and the lens
• Any equibrium must lie in the lens, otherwise it cannot be supported by an allocation of people
• Any point in the lens can be supported by an allocation of people
• If the unbundling equilibrium is in the lens, it is also an equilibrium with bundling– Neither firms nor workers have an incentive to
deviate
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If bundling is outside the lens:
• Factor prices can’t be equalized across sectors, otherwise one would be outside the lens
• Assume B is more H-intensive• Sector B pays more for H and less for L
than sector A• Workers below a critical skill level work in
A, workers above it work in B sorting• Equilibrium thus lies on MM
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L
H
Figure 6.4: Equilibrium when E is outside the lens
LBLA
HA
HB
MMMM’
E
E’
O
O’
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Uniqueness?
• As I move up along MM, the marginal worker’s income goes up faster in B than in A:– The marginal worker has more H, which is more
valued in B– Fewer people work in B, whose relative price goes up
• Therefore, at most 1 point where it is the same in both sectors
• If that point does not exist, corner equilibrium exists where everybody works in 1 sector
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If E is in the lens, it is the only equilibrium
• Any point F on MM has a lower H/L ratio in A than E
• Its H/L ratio is higher in B
• Thus it has a lower ωB/wB,and a higher ωA/wB,than E
• But then the least skilled want to work in B, and the most skilled in A not an equilibrium
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h(s)/l(s)
z(s)/l(s)
Sector B
Sector A
Figure 6.5: The distribution of income under full specialization
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The impact of an increase in demand for good b
• Under FPE, we get the usual prediction: ω goes up and w goes down
• Under non FBE, same prediction, but we must move along MM– The effect on wages not only depends on
technology but also on the distribution of skills– If h/l varies little across people, that puts limits
on the inegalitarian effects
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L
H
Figure 6.6: The effect of an increase in p under full specialization
MM
MM’
E’
E’’
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Triggering segregation
• An increase in the demand for B may move the economy outside the lens
• Sectoral skill segregation emerges• As B bids for workers, it tends to drive ω/w up• The least skilled of B move to A, and the most
skilled of A move to B• At some point, B is no longer able to match its
H/L target, it attracts workers with a lower H/L, and offers a higher ω/w
• An opposite phenomenon occurs in sector A
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L
H
Figure 6.7: An increase in p may trigger full specialization
MM
MM’
E
E’’
F