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

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

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

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

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

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

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

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)

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

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

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

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)

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

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.

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

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

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

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

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

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

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

FPFO FPFN r ω w 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 Ln z Ln z e e Germany United States

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

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