1. VI. Competing technologies

2. 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

3. 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

4. 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

5. The initial steady state:

6. The technological revolution
New production function
Learning cost
Critical worker
Allocation of labor
Allocation of capital

7. 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

9. 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

10. 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

11. r
FPF1
FPF0 w0 w1 w
Figure 4.1: The determination of wages in each technology

12. rN r
FPF1
FPF0 w1 wN w0 w
Figure 4.2: Configuration I: both wages go up

13. r rN
FPF1
FPF0 w0 wN w1 w
Figure 4.3: Configuration II: wage divergence

14. r
FPF1 rN
FPF0 w0 w1 wN w
Figure 4.4: Configuration III: both wages fall

15. 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

16. 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

17. 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

18. 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

19. 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

20. 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

21. 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

22. 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

23. K O’ K1 II E K0 I O L L0 L1
Figure 4.5: de-skilling technical progress moves the economy to region I

24. 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

25. 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

26. 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)

27. ω A C B’
FPF1 C0 B
FPF0 w
Figure 4.6: introducing a skill-intensive technology

28. 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

29. 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

30. ω C’ C
FPF’1
FPF1
FPF0 w
Figure 4.7: technical progress in the skill-intensive technology

31. 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)

32. H A
Isoquant-1 E B
Isoquant-0 L
Fig 4.8: representing the two technologies in the (L,H) plane

33. I0’ H A I1 A’ E
I1’ B B’ I0 L
Fig 4.9: Technical progress in the skill-intensive technology
in the (L,H) plane.

34. VII. Supply effects and competing technologies

35. 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

36. 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

37. 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

38. H’ H E E’ L
Figure 5.2: impact of human capital accumulation on the technology mix

39. 1
H/L
Figure 5.3: the evolution of the employment share of the new technology

40. 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?

41. 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

42. 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

43. Solving the model

44. 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

45. Technological assumption #1
N is more intensive in labor, relative to human capital, than H

46. 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

48. Two pairs of alternatives

49. Three cases

50. 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

51. 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

52. ω E’ E
PFPF’N
PFPFN
PFPF’O
PFPFO w
Figure 5.4: impact of a fall in r on wages, in the case of
capital-skill substitutability

53. ω E’
PFPF’N E
PFPFN
PFPF’O
PFPFO w
Figure 5.5: impact of a fall in r on wages, capital-unskilled substitutability

54. 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

55. Technological assumption #2
The configuration of the two technologies has skilled-unskilled substitutability

56. An interesting special case

57. FPFO
FPFN r ω w
Figure 5.6: Factor price determination when
each technology only uses one kind of labor

58. In that configuration:
An increase in K increases both wages
An increase in H reduces both wages

59. More generally:

60. 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

61. Computing the neutral path

62. More generally

63. 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?

64. H raises the skill premium and K reduces it iff
That is equivalent to

65. Technological assumption #3
The new technology is more capital-efficient:

66. 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

67. 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

68. 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

69. Individuals Productivity li = raw labor endowment
Years of education ei
Human capital hi = liei

70. 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

72. Testing the 2-technology hypothesis

73. Testing H-L substitutability A2

74. Testing capital efficiency A3

75. 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)

76. Observation #1
The returns to skills have gone up in the US but not in Germany
Ln z
Ln z e e
Germany
United States

77. Observation #2
K/L and H/L have grown more in line with each other in Germany than in the US
Germany
United States
Neutral path

78. 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