VI. Competing technologies

A naïve question

• What if the old technology can be used along with the new one?

• Would not that prevent the wages of any worker from falling?

• The answer is no: The two technologies compete for mobile factors

How can 2 technologies be used?

• The new technology dominates the old but is costly to learn (imperfect mobility)

• The new technology does not dominate the old

The Caselli “technological revolution” model

• The economy is in a LR steady state

• A new, superior, unbiased technology is introduced

• The first generation of workers has to pay a learning cost to use it

• The learning cost differs across workers

• More skilled = lower learning cost

• Capital can freely move between the two

The initial steady state:

The technological revolution

• New production function

• Learning cost

• Critical worker

• Allocation of labor

• Allocation of capital

The impact on the distribution of income

• We want to know how the TR affects the wages

• Two categories of workers: old tech/new tech

• Wages are given by marginal product conditions

• Because of capital mobility, wage ratio only depends on TFP ratio

The basic results

• Inequality clearly must increase

• The old tech must earn less

• In fact, they earn less than if technology 1 had not been introduced

3 possibilities:

• ROR goes down, and both wages increase

• ROR goes up, and one wage increases, the other falls

• ROR goes up even higher, and both wages fall

w

r

Figure 4.1: The determination of wages in each technology

w0w1

FPF0

FPF1

w

r

Figure 4.2: Configuration I: both wages go up

w1

FPF0

FPF1

w0wN

rN

w

r

Figure 4.3: Configuration II: wage divergence

w1

FPF0

FPF1

w0 wN

rN

w

r

Figure 4.4: Configuration III: both wages fall

w1

FPF0

FPF1

w0 wN

rN

Both wages can’t go up

• Otherwise, K/L must go up in old tech

• To compensate, it falls in new tech

• But then, ROR goes down in old tech and up in new tech

• That is incompatible with RIR equalization

Both wages can’t go down

• Otherwise, K/L must go down in technology 0

• To compensate, it must go up in technology 1

• But then, wages go up in technology 1

• That is a contradiction

Theorem

• Upon introducing the new technology, wages fall for the workers who go on using the old technology

• Wages are higher than before for the workers who use the new technology

• Thus, workers who do not “adapt” lose from technical progress

What is going on?

• More productive technology generates a greater return to capital

• Capital moves there, leaving workers in old tech with less capital per worker

• Labor movement cannot compensate for that

• Otherwise, K/L would be unchanged in both sectors, and ROR would be higher in new tech

Gainers and losers

• Old tech workers necessarily lose

• New tech workers have higher wages

• But they have to pay the training cost

• Therefore, they do not necessarily gain on net

• There are cases where all workers lose

• All gains then accrue to owners of capital

An example

• Only two learning costs

• All we need is that the marginal worker has cost eL

• It is easy to construct such an equilibrium

De-skilling technical change

• What if new technology suddenly easier to learn?

• We can show that wages fall in both technologies

• At the same time, more workers learn the higher paying new technology

What is going on?

• The equilibrium wage ratio only depends on the technological parameters both wages move in the same direction

• K/L must fall in both technologies, because resources move to the new one, which has a higher K/L

• Therefore, wages must fall in both technologies

L

K

E

L0L1

K0

K1

I

II

Figure 4.5: de-skilling technical progress moves the economy to region I

O

O’

Conclusion

• The introduction of a new technology may harm the unskilled who are at a disadvantage at learning it

• Its popularization jeopardizes the rents of those who already master it

• These effects are likely to be transitory on income distribution

Competing technologies with different factor intensities

• The economy is originally in steady state

• One can now use a new technology

• The new technology is more intensive in skilled labor

• Both technologies can co-exist if the new technology does not entirely dominate the old one

3 possibilities, depending on the economy’s factor endowment

• Old technology not used at all (H/L low) (A)

• Both technologies used simultaneously (H/L intermediate) (C)

• Old technology abandoned in favor of new one (B)

w

Figure 4.6: introducing a skill-intensive technology

FPF0

FPF1

ω

A

B

C

B’

C0

The effect of the new technology on factor prices

• If new technology is used, then the wages of the unskilled fall and those of the skilled go up– MRS more favorable to H in new technology– Workers left with old technology work with

less H per workers

• If both technologies are used, factor prices are pinned down at the intersection, independent of factor endowments

Asymmetrical TP

• TP in the skilled-intensive technology harms the low skilled

• By raising MPs, both factors move to the new technology

• New technology has a higher H/L ratio

• To maintain aggregate H/L ratio constant, H/L ratio has to fall in both technologies

• Thus, w falls and ω goes up

wFigure 4.7: technical progress in the skill-intensive technology

FPF0

FPF’1

ω

C

C’

FPF1

A reinterpretation

• Using the two technologies makes H and L more substitutable

• Asymmetric technical progress indirectly affects the MRS between H and L

• That makes it equivalent to skilled-biased technical change (FPF and isoquants are globally flatter)

L

H

Isoquant-1

Isoquant-0

A

B

E

Fig 4.8: representing the two technologies in the (L,H) plane

L

H

I1

I0

B

E

Fig 4.9: Technical progress in the skill-intensive technologyin the (L,H) plane.

A’

B’

A

I1’

I0’

VII. Supply effects and competing technologies

The standard view

• An increase in the skill premium should induce people to invest in H

• Accordingly, the relative supply of skills should go up

• That should dampen the initial increase in the skill premium

The alternative view

• A greater supply of skilled workers may lead to further SBTC

• Two potential mechanisms– The skilled-intensive technology is used more– New skilled-biased technologies are

introduced

• Let us study the first mechanism

The supply of skills in the 2-tech model

• If only one of the two technologies is used, then an increase in H/L reduces ω/w

• If both technologies are used, then an increase in H/L increases the use of the skilled-intensive tech

L

H

E

Figure 5.2: impact of human capital accumulation on the technology mix

E’

H’

H/L

Figure 5.3: the evolution of the employment share of the new technology

1

0

Effect on the distribution of income

• Factor prices are unaffected, since they do not depend on H/L

• Thus, supply response does not dampen initial rise in inequality

• But it does not worsen it either

• Can we change the model to get what we want?

Two ideas

• Factor prices are pinned down by a 2 x 2 system; if we introduce capital, they are no longer pinned down

• If greater use of skilled-intensive technology drives enough capital away from old technology, w may fall as in Caselli

• Let’s see what we get with a 3-factor, 2-tech model

The model

• 2 technologies, Old (O), New (N)• 3 factors H, K, L• Factor prices ω, r, w• Cost functions and• We only look at the regime where both

technologies are in use• = amount of factors used in old

technology• “ ^ ” = unit input requirement

Solving the model

Road map

• The preceding equations determine factor prices and the allocation of factors

• We will make assumptions on the nature of each technology

• We then derive predictions on how changes in the factor endowments H,K,L affect the distribution of wages, under these assumptions

Technological assumption #1

• N is more intensive in labor, relative to human capital, than H

Comovements between factor prices

• The vector of factor prices must be on the intersection between the two FPF

• That defines a 1-dimensional locus

• Locally, any shock will move that vector in a single direction

• That direction may be computed and its properties depends on the technological assumptions

Two pairs of alternatives

Three cases

To summarize:

• The most intensive factors are substitutes

• The intermediate factor is complement with the others

• This pattern does not depend on complementarities and substitutabilities within each technology

Example I

• Assume : capital is least used by N

• A fall in r has a much larger effect on O’s FPF than on N’s FPF

• Therefore ω falls and w goes up• O is more used: H/L goes up in both

technologies• Increased K/H in N has little compensating

effect on ω

wFigure 5.4: impact of a fall in r on wages, in the case of capital-skill substitutability

PFPFO

PFPF’N

ω

PFPFN

PFPF’O

EE’

wFigure 5.5: impact of a fall in r on wages, capital-unskilled substitutability

PFPFO

PFPF’N

ω

PFPFN

PFPF’O

E

E’

Example II

• Assume

• A fall in r has a similar effect on O’s FPF and on N’s FPF

• Therefore both ω and w go up

• Higher K does not create large imbalance between the two technologies

• Higher K benefits both factors substantially

Technological assumption #2

• The configuration of the two technologies has skilled-unskilled substitutability

An interesting special case

wω

r

FPFOFPFN

Figure 5.6: Factor price determination when each technology only uses one kind of labor

In that configuration:

• An increase in K increases both wages

• An increase in H reduces both wages

More generally:

Neutral accumulation paths

• The 2-tech property implies that for any change in H, there exists a unique change in K that leaves factor prices unchanged

• Furthermore, under A2 that is such that dK/dH > 0

• Note:– It doesn’t mean people don’t get richer– It doesn’t mean the distribution of income

does not change

Computing the neutral path

More generally

The effect on the skill premium

• If H and L are complements, H reduces the skill premium

• K increases the skill premium if K-H complements (“H in the middle”)

• It reduces the skill premium if K-H substitute (“L in the middle”)

• But what if A2 holds?

• H raises the skill premium and K reduces it iff

• That is equivalent to

Technological assumption #3

• The new technology is more capital-efficient:

The basic result:

• Under A3, ω/w goes up with H/L and down with K/L

• Going back to the special case, we get

• Works iff

Summary

• In the 2-tech 3-fact model, an increase in H may increase the returns to skills, while harming all wages

• That is because the new technology is more used and attracts capital out of the old

• But we need stringent assumptions: 2 in use, A1, A2, A3

Beaudry and Green’s empirical strategy

• Estimate an earnings function using pooled panel data for Germany and the US

• Relate coefficients to country-specific aggregate factor endowment

• Derive predictions on these relationships from the model

• Construct counter-factuals on how alternative accumulation paths affect the pattern of inequality

Individuals

• Productivity li = raw labor endowment

• Years of education ei

• Human capital hi = liei

The effect of aggregate factor endowments on the earnings

function

• These estimations yield country x year –specific intercepts and slopes:– a = ln w – b = ω/w

• The model tells us that they are related to H/L and K/L

• It provides restrictions on these relationships

Testing the 2-technology hypothesis

Testing H-L substitutability A2

Testing capital efficiency A3

Consequences

• There exists a neutral accumulation path

• This path involves a positive association between H and K

• Excess accumulation of H over K compared to this path generates– A downward shift in the wage schedule– An increase in the skill premium (it becomes

steeper)

Observation #1

• The returns to skills have gone up in the US but not in Germany

e

Ln z

United Statese

Ln z

Germany

Observation #2

• K/L and H/L have grown more in line with each other in Germany than in the US

United States

Germany

Neutral path

Conclusion

• In Germany, the inegalitarian effects of accumulation of H/L have been offset by accumulation of K/L

• In the United States, this did not take place

• Difference between the two countries explained without using institutional differences