ELEMENTOS DE LA EXPRESIÓN CORPORAL

Skill Premium and Technologies

Given that more and less productive firms enter the market and produce, the expected return of each investment strategy is zero and firms are consequently indifferent which strategy to choose.

Definition 2.2 Equilibrium with heterogeneous firms is given by a set of prices {ph, pl, wH, wL}, quantities {Yh, Yl, Hh, Hl, Lh, Ll}, and levels of technology{Nh, Nl} such

that with free entry of firms consumers choose consumption of each final good optimally, firms choose output, level of technology and labor inputs optimally, while labor and product markets clear.

While the above equilibrium definition is of a more general nature, I will restrict my analysis to the case where the technology choice ofh-firms is constrained by the barrierT. In the spirit of Parente and Prescott (2002), barriers to technology adoption are imposed by institutions such that technology choices of high-productivity firms are restricted. In this way, less productive firms avoid an increased competition15 _{and protect their vested} interests. As a consequence,h-firms’ first order condition of the optimal technology choice drops from the set of equilibrium equations and Nh is set toT.

Different to the homogeneous firms economy with free entry, the skill premium is not determined by relative total labor demands and supply. Rather, it is derived from the

15_{Note that in this class of CES-utility models competition occurs exclusively on labor markets, i.e.}

relation of free entry conditions phYh = w₁₋Lf_βh and plYl= w₁₋Lf_βl16: φ β 1−β ∆ = fh fl . (2.20)

While the above implicit skill premium equation holds irrespective whether the technology barrier binds or not, its explicit functional form differs.

Proposition 2.6 Assume that high-productivity firms are restricted in their technology

choice and that the technology barrier is lowered, i.e. T increases. Then, the skill premium

rises, dw¯ dT = ¯ wln ¯w T κh−ε_KT¯

ε_KT¯ −κl > 0, and the technology gap,

∂ T Nl ∂T = κh−κl Nl(ε_KT¯ −κl) > 0, widens.

However, relative productivities remain constant.

The proof is given in Appendix 2.7.6. Lower barriers to technology adoption enable high- productivity firms to approach or even attain their optimal levels of technology in produc- tion while having no direct effect onl-firms’ choices. However, higher technology levels of

h-firms imply a greater relative demand of high-skilled labor and drive up the skill pre- mium. As a consequence, l-firms face higher labor costs for maintaining their technology

level and are finally forced to downgrade their production techniques. This is illustrated by a simulation in Figure 2.117_{. N}∗

l depicts the optimal technology

choice of an l-firm for any wage gap while N_l∗∗ constitutes its optimal choice given a con- stant skill premium ¯w(T = 70). The increase in the technology gap Nh

N∗

l

is considerably sharper than that of Nh

N_l∗∗ since the latter does not include downgrades caused by widening

wage gaps. The difference in the two technology gaps increases for lower barriers and becomes agnostic to further reductions once high-productivity firms have reached their optimal level of technology. Although lower barriers to technology adoption lead to an increase in the technology gap, its positive impact on the productivity difference is exactly canceled by the simultaneous skill premium rise18_{. A higher level of technology in produc-} tion leads to a rise in high-productivity firms’ relative skill demand. This, in combination 16_{See the first chapter for an analysis of how that relates to the Rybczynski Theorem and how the}

technology choices of different firms are related through factor markets.

17_{Parameters are κh = 0.24, κl = 0.16, σ = 1/3, β = 0.75, fh/fl = 2.75, H}s _{= 15, L}s _{= 85, and} µ= 100. Remark that Acemoglu et al. (2007) compute implicit values ofκ= 0.135 and κ= 0.25 for the U.S..

Figure 2.1: Technology Gap and Skill Premia l h N N w w * l h N N * * l h N N * h N T h-firms are unconstrained

h-firms are constrained

The impact of lower barriers to technology adoption on the technology gap and the skill premium. To the left ofN_h∗,h-firms are constrained by the barrierT while to the right, they are not. The blue graph depicts the wage gap, the red Nh

N∗

l

, and the green Nh

N∗∗

l

.

with the skill premium increase, has a strong dampening effect on their productivity. On the other hand, low-productivity firms downgrade their level of technology and, conse- quently, their relative skill demand as a reaction to the widening wage gap. In this way, they alleviate the negative impact of the wage cost increase on their level of productivity. Note that the above result of a constant productivity gap differs from the firm-level equi- librium where firms consider wages as given and lower barriers imply growing differences in productivities. In essence, the existence of an equilibrium with positive numbers of both types of firms requires that the productivity gap is unaffected by altering the bar- rier. Otherwise, comparative static exercises for firm differences cannot be carried out as an increase in the barrier would imply an economy without low-productivity firms.