2.3 Firm-Level Analysis
2.3.4 Firm-Level Impacts of Changes in Skill Premia and Barriers to
and, in the case of an endogenous choice of the optimal level of technology in production, εK¯N =κ. This implies that relative high- to low-skilled production labor demands
H L = 1
¯ w
εK¯N
ln ¯w−εK¯N
. (2.13)
depend on the level of technology in the case of high-productivity firms since Nh = T. In contrast, low-productivity firms’ relative high- to low-skilled production labor demands are independent of their level of technology Nl. However, low-productivity firms’ production techniques and relative high- to low-skilled production labor demands are given by their common determinants κl and the skill premium.
2.3.4 Firm-Level Impacts of Changes in Skill Premia and
the skill premium, increases. As a result, l-firms’ productivity is dampened. Since a greater scope for technology in production implies a more productive use of technology, an increase in κ leads to a choice of more sophisticated production techniques and a higher productivity. Consequently, a graduate increase in barriers to technology adoption will restrict higher κ (high-productivity) firms first. Moreover, given that neither type is constrained, h-firms have to downgrade their production techniques by more than l-firms when the skill premium increases since the latter has a stronger impact on more technology intensive production processes13.
In contrast to the above analysis, assume that a high-productivity firm’s choice is re-stricted by the barrier. Then, the adoption of higher technology levels when the wage gap shrinks is not feasible. Remark that I abstract in the following from very sharp skill premium increases which may induce high-productivity firms to choose optimal technol-ogy levels below the barrier, i.e. N∗ < T. Whether N∗ > T decreases to N∗∗RT, where N∗ > N∗∗, is in fact determined by firm-level parameters κ and σ in combination with the extend of the skill premium rise and the level of the barrier. For example, if high-productivity firms are endowed with a relatively small scope for technology in production, their choice of technology would be more prone to a decrease as a result of a sharp rise in the wage gap. However, considering cases where N∗ > T is dampened to N∗∗ < T would not add insights to the present analysis.
Proposition 2.2 Given wages, a firm’s choice of technology is constrained if and only if T < ln ( ¯w)(1−κσ)2κµ . Moreover, high-productivity firms are constrained while low-productivity firms are not if and only if κl < 2µ1
ln ( ¯w)T+σ < κh.
The proof is given in Appendix 2.7.4. Lower skill premia involve lower adoption costs and increase a firm’s optimal technology level which is then obviously more likely to be constrained. Furthermore, firms that are endowed with a greater κusually choose higher levels of technology in production, and are consequently more prone to become constrained by the barrier. The more restrictive the latter is (i.e., the smaller T) the more likely it constrains firms’ production techniques. Since the skill premium represents the implicit costs of technology in production, a lower wage gap decreases technology adoption costs
13See the first chapter for proofs as well as an detailed discussion of the unconstrained cases.
and makes firms more prone to become technologically constrained. To sum up, a relative restrictive barrier constrains a firm’s choice if it has a great scope for technology and faces a rather low skill premium.
In essence, the difference in their respective scopes for technology in production implies whether high-productivity firms are restricted in their endogenous choice of technology while low-productivity firms are not. Remark that κh > κl is not sufficient but that h-firms’ technology type has to be greater than a threshold whilel-firms’ scope for technology has to be smaller. Moreover, this requires rather medium levels of the skill premium and the barrier to technology adoption. Note that in comparison to the case where both are unrestricted the technology gap is smaller if barriers constrain high-productivity but not low-productivity firms’ choices.
Proposition 2.3 If a firm’s choice of technology in production is constrained by the bar-rier, productivity increases when the barrier is lowered (i.e. T increases), ∂T∂φ =φκ−εTKT¯ >
0, and decreases when the skill premium rises, ∂∂φw¯ = −εw¯KT¯ln ¯wφ < 0. Furthermore, relative production labor demands increase if the barrier is reduced.
Assume that high-productivity firms’ technology choices are restricted while low-productivity firms’ are not. Then, φ∆ increases when the barrier is lowered,
∂φ∆
∂T =φ∆κh−εTKT¯ >0, and decreases for higher skill premia, ∂φ∂w¯∆ =−φ∆εKTw¯¯ln ¯−κwl <0. The proof is given in Appendix 2.7.4. Given that barriers to technology adoption indeed restrict a firm’s choice the latter is confined to produce with less sophisticated technologies.
Since higher levels of technology augment production a firm’s productivity is necessarily dampened. A reform in policies and institutions that involves lower barriers implies the adoption of more productive technologies. Note that the increase in productivity is proportional to the difference κ−εK¯T. The closerT is to N∗ the smaller is the marginal gain from a rise in T since the cost elasticity of technology adoption (εK¯N) increases in the level of technology and dampens the positive effect of technology on productivity. If κ=εK¯T barriers do not impede an optimal choice of technology and the marginal gain of lower barriers vanishes.
Similar to the case of unrestricted choices a higher wag gap rises the cost of technology and implies lower levels of technology in production and, consequently, a lower productivity.
However, the downgrade is somewhat dampened by the factor εK¯T < κ as the lower technology level in the constrained case requires relatively less high-skilled labor. In a similar vein, lower barriers imply more sophisticated production techniques that require relatively more high-skilled workers.
In the case of heterogeneous firms, high-productivity firms’ use of technology in production is more efficient than low-productivity firms’ whereas the former’s optimal technology choice is constrained in contrast to the latter’s. In particular, this case emerges when low-productivity firms manage to influence politics to protect their vested interests. Resulting e.g. from a reform in regulations, lower barriers to technology adoption enableh-firms to use more sophisticated production techniques and increase their productivity while having no impact onl-firms when wages are exogenous. As an immediate result, the productivity gap rises proportionally to κh −εK¯T. That is, akin to ∂T∂φ, increases in the productivity gap abate if T approaches high-productivity firms’ optimal technology level.
On the other hand, h-firms have to employ relatively more high-skilled labor due to the complementarity of technology and skills. They will suffer more in terms of productivity from a skill premium increase. The relative loss is again proportional to εK¯T −κl and, thus, smaller than in the unconstrained case as restricted h-firms employ relatively less high-skilled labor than they would in optimum.