Identifying Skill-Biased Technological Change

In this subsection I define the concept of SBTC. This concept is defined in terms of its effects as follows: in the context of an aggregate production function with constant elasticity of substitution, technological change is skill-biased if the marginal effect of an increase in technology on the relative marginal product of skilled to unskilled workers is nonnegative. More formally, following Acemoglu [2009], for a production functionY =F(H, L, A), technological change is skill-biased if

∂ ∂F(H,L,A)/∂H ∂F(H,L,A)/∂L ∂(A) ≥0

with A denoting technology, Y output, H skilled and L unskilled labour. The definition of skill is open to interpretation and varies in the literature, but most

commonly the distinction between skilled and unskilled workers is drawn by college attendance, whereby a worker qualifies as skilled if she has at least some college education or higher degrees, and as unskilled otherwise.13 _{Importantly, skills can} refer to either observable or unobservable characteristics. However, while there is substantial unexplained variation within observable groups, I follow the bulk of the literature and address observed differences in educational attainment only.

Technology is commonly defined as knowledge, i.e. the knowledge of how to combine and organize inputs to produce something desirable, and so is generally not observed directly.14 As result, the literature attempts to identify SBTC in terms of its effects. Any empirical investigation therefore faces the problem of relating observed changes in the relative marginal product of skilled and unskilled workers to unobserved changes in technology.

Several strategies have been suggested. In the literature on aggregate out- comes, three different approaches can be distinguished. All of them start from a simple demand and supply framework with workers of different skill groups being imperfect substitutes. Consequentially, changes in relative labour market outcomes, such as relative wages or employment or the skill premium, can be thought of as the result of changes in supply or demand curves for different worker groups. SBTC affects relative labour market outcomes via relative skill demand. I discuss the three approaches in turn.

Katz and Murphy Approach

The most widely used approach identifies SBTC with residual changes in relative labour market outcomes after controlling for relative skill supply.15 More formally, assume the aggregate production function takes the following form:

Y = h α(AHH) σ−1 σ _{+ (1}−_{α) (ALL)} σ−1 σ i σ σ−1

where Y is aggregate output, H and L are skilled and unskilled workers, and AH and AL denote technologies complementing skilled or unskilled workers

respectively, with elasticity of substitution between skilled and unskilled labour being σ > 1. Assuming a perfectly competitive labour market we can define the skill premiumω as the ratio of marginal products of skilled to unskilled workers as

13

Alternative measures often used are based on distinguishing non-production versus production workers, whereby the former refer to skilled and the latter to unskilled workers, or by distinguishing workers by occupation based on their hypothesized skill requirements.

14

See Mokyr [1990].

ω= 1−α α H L −_σ1 AH AL σ−_σ1

Ifσ >1, that is if skilled and unskilled workers are imperfect substitutes, an increase in technology, as defined by an increase inAH/AL, raises the skill premium

and is therefore said to be skill biased. In logs, the expression becomes

logω= log 1−α α − 1 σlog H L +(σ−1) σ log AH AL (4.1)

Based on equation 4.1 one can identify the skill-bias in two ways. First, solv- ing this expression for log(AH/AL) and using data on the skill premium, relative skill

supply, and the structural parameters of the production function, one can calculate the skill bias of technology. To get SBTC, one can simply compute the above ex- pression in first differences. Second, as done in the original paper, assuming smooth SBTC, one can regress the skill premium on a constant, relative skill supply, and a time trend, retrieving the average skill bias over the period from the estimated time trend coefficient. The regression equation corresponding to the above expression is:

logωt=β0+γt+β2log H L t +εt (4.2)

As this approach does not control for other inputs, demand shifts identified by the residual reflect changes in prices and supplies of any inputs not explicitly accounted for in the above production function. Either approach can be said to identify SBTC in residual terms, as inference about SBTC is based on interpreting the discrepancy of observed changes in relative skill supply in accounting for observed changes in skill premia as indicating SBTC.

The validity of this approach is based on several assumptions. The confidence with which one can identify relative demand shifts with SBTC rests on controlling for all confounding variables. Several explanations are possible for the observed changes in relative wages in a simple demand and supply framework: changes in relative skill supply, changes in relative demand, and, by extension, institutional changes directly affecting factor prices. Demand changes in turn can be due to several factors, the most important mentioned in the literature being trade and SBTC. Note that although the combined evidence suggests that trade only plays a minor role, most studies also cite institutions as important alternative explanations, and several studies examining the role of institutional change on wage inequality, even for the US alone, have found these to be important.16 This suggests that studies

examining SBTC based on such a supply and demand framework should control for relative skill supply, trade intensification, and institutions. If any of these variables are omitted, identifying SBTC via unexplained changes in the dependent variable does not actually identify SBTC, but some combination of SBTC and the omitted variable.

Shift-Share Analysis

Alternatively, one can use a shift-share analysis to examine the sources for changes in relative skill demand. Specifically, using industry-level data, one can decompose aggregate changes in relative labour market outcomes, such as employment or wage bill shares, into changes within and between industries. It is then hypothesized that changes in favour of more skilled workers reflect demand shifts due to SBTC if they take place within industries, whereas such changes reflect demand shifts due to, say, trade intensification, if they take place between industries.17

Note that shift-share analyses relate within-industry shifts to SBTC without controlling for changes in relative skill supply. It is, of course, assumed that relative skill supply is increasing at the same time. The reasoning is that if the aggregate wage bill share for high skilled workers increases because all industries use relatively more skilled labour, despite increasing relative skill supply, one may conclude that factors raising relative demand for skilled labour are sufficiently general to apply to all industries. Technology, in contrast to trade, is thought to exhibit such a general effect across industries. Changes reflecting between-industry shifts are assigned to competing explanations. A shift towards industries using relative more high skilled labour, for instance, is presumably driven by trade. While such decompositions are suggestive about driving factors, their inability to control explicitly for relative skill supply conceptually limits their ability to assess and compare the magnitude of SBTC across countries. Also, not all competing explanations can be assigned to between-industry shifts. For instance, if institutional change affects workers with high and low wages differently, e.g. via deunionization, within-industry shifts may partly reflect institutional change.

Technology Proxies

Finally, one can use proxies for technology, e.g. the fraction of workers using com- puters, research and development (R&D) expenditures, or ICT capital intensity, to examine demand shifts more directly. Three approaches have been used in the

[1996]; Card and DiNardo [2002].

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literature. First, one can use augmented wage equations to assess the impact of ICT usage at the micro-level. Second, starting from cost functions, one can derive expressions relating labour market outcomes to observable inputs and unobserved labour demand, and based on the hypothesis that unobserved demand changes are driven by technological change, use proxies for technological change to control for these unobserved demand changes. Third, one can test whether these proxies take up substantial parts of the variation in changes in relative labour market outcomes.18 The use of such proxies for technology differences across countries is limited, however, if proxies and particular technologies are not directly linked. Recall that technology is defined as knowledge. Technology can therefore be associated with, but not reduced to, ICT capital goods. For instance, the technology embodied in ICT capital refers to the knowledge how to produce and to employ this type of capital in the wider production process. Using the same ICT capital goods differently amounts to using a different technology. The link between measures for ICT capital and technology may therefore differ across countries and change over time as ICT capital goods are used in different ways.19 In this context, measures for ICT capital are not equivalent to SBTC measures across countries because the use of ICT capital by skilled and unskilled workers can differ across countries.20