Skill-Biased Structural Change∗
Francisco J. Buera

Joseph P. Kaboski

Washington University in St. Louis

University of Notre Dame

Richard Rogerson

Princeton University

Juan I. Vizcaino
Washington University in St. Louis
October 5, 2018

Abstract
We document for a broad panel of advanced economies that increases in
GDP per capita are associated with a systematic shift in the composition ofvalue added to sectors that are intensive in high-skill labor, a process we label
as skill biased structural change. It follows that further development in these
economies leads to an increase in the relative demand for skilled labor. We
develop a two-sector model of this process and use it to assess the contributionof this process of skill-biased structural change to the rise of the skill premium inboth the US, and a broad panel of advanced economies, over the period 1977 to
2005. We find that these compositional changes in demand account for between
20 and 27% of the overall increase of the skill premium due to technical change.

∗

We thank Daron Acemoglu, David Dorn, Chad Jones, Pete Klenow as well as seminar participants at the 2015 AEA Meetings, the Canon Institute for Global Studies, Chicago Fed, Paris
School of Economics, Pittsburgh, Stanford, University of Houston, USC, the World Bank and Yonsei
University for useful comments.

1

1

Introduction

The dramatic increase in the wages of high skilled workers relative to low skilledworkers is one of the most prominent secular trends in the US and other advanced
economies in recent decades. Isolating the underlying causes of this trend is importantfor projecting future trends and evaluating the extent to which policies might beeffective or advisable. The literature has consistently concluded that skill-biased
technological change (SBTC) is a quantitatively important driver of the increasein the relative demand for high skilled workers.1 In this paper we argue that a
distinct process – which we label skill-biased structural change – has also played
a quantitatively important role. We use the term skill-biased structural change todescribe the systematic reallocation of sectoral value-added shares toward high-skill
intensive industries that accompanies the process of continued development among
advanced economies.
The economic intuition behind our finding is simple. If (as we show is indeed thecase in the next section) the process of development is systematically associated witha shift in the composition of value added toward sectors that are intensive in highskill workers, then the demand for high-skilled workers will increase, independently ofwhether development is driven by skill-neutral or skill-biased technical change. This
channel is absent in analyses that adopt an aggregate production function, since inthat case development that comes from skill-neutral technical change has no effect on
the relative demand for high-skilled workers.
To assess the quantitative significance of this channel, we develop a simple generalequilibrium model of structural transformation that incorporates an important rolefor skill and use it to study the evolution of the US economy between 1977 and 2005.
In order to best highlight the shift in value added to high skill-intensive sectors, westudy a two-sector model in which the two sectors are distinguished by their intensity of high-skill workers in production. We allow for sector-specific technologicalchange, which is a (sector-specific) combination of skill-neutral and skill-biased technical change. We show how the model can be used to infer preference parameters and1

Important early contributions to the literature on the skill premium that stress skill biased
technical change include ?, ?, ?, ? and ?. This is not to say that SBTC is the only factor atwork, as the literature has also highlighted the effect of other factors on overall wage inequality.
For example, ? argue that labor market institutions such as minimum wages and unionization haveplayed an important role in shaping wage inequality overall, ? emphasize the role of offshoring, and? emphasize the role of trade.

2the process for technical change using data on the change in the composition of employment by skill, the change in aggregate output, changes in sectoral factor shares,
the skill premium, relative sectoral prices and the distribution of sectoral value added.
In the data, our measure of the skill premium increases from 1.41 to 1.90 between 1977 and 2005, an increase of 49 percentage points.2 Our calibrated model
perfectly matches this increase. We then use the model to decompose this increase
into three different components: one due to the changes in the relative supply ofhigh-skill workers, one part that is due to skill-biased technical change, and a thirdpart due to other technological changes. If there had been no change in technology,
our model predicts that the increase in the relative supply of high-skill workers would
have lowered the skill premium to 0.88, a drop of 53 percentage points. It follows that
overall changes in technology created an increase in the skill premium of 102 percentage points. In our benchmark specification, between one quarter and one third of thisincrease comes from changes in technology other than skill-biased technical change,
operating through their effect on the composition of value added. We conclude thatsystematic changes in the composition of value added associated with the process ofdevelopment are an important factor in accounting for the rise in the skill premium.
In fact, if skill-biased technical change had been the sole source of technical changeover this period, our model predicts that the skill premium would have increased byonly 22 percentage points instead of by 49.
Having established the importance of this effect for the US, we repeat the analysis for a set of nine other OECD countries. While there is some variation in thecontribution of compositional changes in value added to changes in the skill premium
across countries, ranging from around 15 percent to slightly less than 50 percent, theaverage for this sample is 25 percent, very much in line with our estimates for theUS.
Our paper is related to many others in two large and distinct literatures, one on
SBTC and the skill premium and the other on structural transformation. Importantearly contributions to the literature on the skill premium include ?, ?, ?, ? and?. Given that the increase in the skill premium occurred in the face of a large
increase in the supply of high skill workers, all of these papers sought to identify
2

Our measure of the skill premium compares those with at least college degrees to those withhigh school degrees or less, and is based on total compensation and not just wages and salaries,
which explains why this increase is larger than what the literature typically reports.

3

factors that would increase the relative demand for high-skilled workers. In addition
to skill-biased technological change, each of them noted compositional changes indemand as a potentially important element of the increased relative demand for skill.
Relative to them, our contribution is fourfold. First, we document the importance ofcompositional effects that are systematically related to the process of development.
Second, we show how to uncover the different dimensions of technological change in a
multi-sector framework. Third, we present a general equilibrium model in which one
can assess the driving forces behind compositional changes. Fourth, and perhaps mostimportantly, our structural approach finds a much larger role for structural change.
An early contribution in the second literature is ?, with more recent contributions
by ? and ?. (See ? for a recent overview.) Relative to this literature our main
contribution is to introduce heterogeneity in worker skill levels into the analysis andto organize industries by skill intensity rather than broad sectors.
The paper that we are most closely related to is ?. Like us, they study the interaction between development and the demand for skill, though their primary contribution
is conceptual, building a somewhat abstract model to illustrate the mechanism. Relative to them our main contribution is to build a simple model that can easily beconnected to the data and to use the model to quantitatively assess the mechanism. ?
considers a similar mechanism to us, but focuses on how demand varies by education
attainment as opposed to income more broadly, and finds relatively small demand
effects.3 An important antecedent of our work is the paper by ?. Like us, they study
the relationship between development and structural change in a model that features
heterogeneity in factor intensities across sectors. But differently than us, they focus on differential intensities for physical capital and the role of the relative price ofphysical capital rather than human capital. Their work is also primarily theoretical.
An outline of the paper follows. Section 2 presents aggregate evidence on the relation between development and the value added share for high skill intensive services
in a panel of advanced economies, in addition to some other important empiricalpatterns. Section 3 presents our general equilibrium model and characterizes theequilibrium. Section 4 shows how the model can be used to account for the evolutionof the US economy over the period 1977 to 2005, and in particular how the data can3? use a similar framework to show that compositional changes in value added associated with
development can explain part of the decrease in the gender wage gap that has occured in the US
over time.

4

be used to infer preference parameters and the process of technical change. Section
5 presents our main results about the contribution of various factors to the evolutionof the skill premium. Section 6 assesses the contribution of skill-biased structuralchange for relative prices, and in Section 7 we extend our analysis to a set of nineother countries. Section 8 concludes.

2

Empirical Motivation

This section documents the prominence of what we refer to as skill-biased structuralchange, as well as some of its salient features. In particular, using data for a broad
panel of advanced economies, we document two key facts. First, there is a strong
positive correlation between the level of development in an economy, as measured by
GDP per capita, and the share of value added that is attributed to high skill services.
Second, there is also a strong positive correlation between the level of development
and the price of high skill services relative to other goods and services. Interestingly,
these relationships are very stable across countries, and in particular, the experienceof the US is very similar to the average pattern found in the data.
We supplement the above aggregate time series evidence for a panel of countries
with some evidence about cross-sectional expenditure shares in the US economy. In
particular, we show that the expenditure of higher income households contains ahigher share of high skill intensive value-added. This fact will serve two purposes.
First, it is suggestive evidence for a non-homotheticity in the demand for high skill
services, which is a feature we will include in our model. Second, this cross-sectional
moment provides important information about preference parameters that is not readily available from aggregate time series data.

2.1

Aggregate Panel Evidence

The starting point for our analysis is the earlier work of ?. They divide industries
in the service sector into two mutually exclusive groups: a high skill-intensive group
and a low skill-intensive group, and show that whereas the value-added share of thehigh skill-intensive group rose substantially between 1950 and 2000, the value added
share of the low skill intensive group actually fell over the same time period. Thisfinding suggests that the traditional breakdown of economic activity in the structural

5

transformation literature, into agriculture, manufacturing and services, is perhaps
not well suited to studying the reallocation of economic activity in today’s advanced
economies. Here we pursue this line of work further, modifying their aggregation
procedure to include goods-producing industries, and extending their analysis to abroad panel of advanced economies.
The analysis uses data on value-added and labor compensation. The value-added
data come from the EUKLEMS Database (“Basic Table”).4 These data exist in comparable form for a panel of countries over the years 1970-2005. Our focus is on
advanced economies’ growth experience in the services sector, so following ?, we focus on the 15 countries with income per capita of at least 9200 Gheary-Khamis 1990
international dollars at the beginning of the panel in 1970.5 The sectoral value-added
data are available at roughly the 1 to 2-digit industry level. We focus on a two-way
split of industries into high skill intensive and low skill intensive based on the shareof labor income paid to high-skill workers.6 While one could consider more detailed
splits, including more than two skill categories and perhaps interacting skill intensitywith goods vs. services, this two-way split both facilitates exposition and allows us
to focus on a robust pattern in the cross-country data.
Labor compensation data come from the EUKLEMS Labour Input Data. We
define high skill-intensive service sectors as: “Education”, “Health and Social Work”,“Renting of Machinery and Equipment and Other Business Activities”, and “Financial
Intermediation”. In 1970, the economy-wide average share of labor compensation paid
to high-skill workers in the U.S. was 20 percent; the corresponding shares for thesehigh skill-intensive industries were 76, 32, 72, and 28 percent, respectively. These
industries remain well above average throughout the time period.7
Finally, we demean both the value-added share data and the (log) GDP per capita
data by taking out country fixed effects.
Figure 1 shows the relationship between development, as proxied by real GDP
4

See ?.
These countries are Australia, Austria, Belgium, Canada, Denmark, France, Germany, Ireland,
Italy, Japan, the Netherlands, Spain, Sweden, the United Kingdom, and the United States. We
exclude Luxembourg given its small size. The U.S. data for value-added go back to only 1977, while
the Japan data go back to only 1973.
6
High-skill is defined as a college graduate and above.
7
The next highest industries are a mix of goods and service producing industries: “Chemicals
and Chemical Products” (27 percent), “Public Admininistration and Defense ” (23 percent) “RealEstate ” (23 percent), “Coke, Refined Petroleum, and Nuclear Fuel” (21 percent), and “Electricaland Optical Equipment” (20 percent).
5

6

.9

Low-Skill Sectors.7.7

Share of Total Value Added.8

Low-Skill Sectors.8

Share of Total Labor Compensation.9

1

Value Added

1

Labor Compensation.5.6

y = -0.146 ln(x) + 2.264
R2=0.852

.4

.4

.5

.6

y = -0.211 ln(x) + 2.884
R2=0.867.3

y = 0.146 ln(x) -1.263
R2=0.852

.2

.2

.3

y = 0.211 ln(x) -1.884
R2=0.86700.1High-Skill Sectors.1

High-Skill Sectors

9.5

10

10.5

Real GDP per-capita(log scale)

11

9.5

10

10.5

Real GDP per-capita(log scale)

11

Figure 1: Structural Change by Skill-intensity and Economic Development.
per capita and the rise of the high skill service sector. Real (chain-weighted) GDP
per capita data is from the Penn World Tables 7.1. We use two different measures
for the size of the high skill service sector: the share of total labor compensationaccounted for by this sector, and the share of total value added accounted for by this
sector. Labor compensation is more relevant from the perspective of labor demand,but value added is the more typical metric for theories of structural change. The
left panel of Figure 1 shows the relationship using labor compensation, while theright panel shows the relationship using value added. The small squares show the
relationship for countries other than the US, and the larger circles represent data for
the US.
Both panels lead to the same conclusion: the relative size of the high skill service
sector increases with log GDP/capita, with highly significant (at a 0.1 percent levels)
semi-elasticities of 0.22 and 0.15 respectively. The regression line implies an increaseof roughly 30 percentage points of labor compensation and 21 percentage pointsof value added, as we move from a GDP per capita of 10, 000 to 40, 000 (in 2005
PPP terms). Per capita income alone explains 87 percent of the variation in thelabor compensation share data, and 81 percent of the value added share variation.
Moreover, we see that the relationship found in the US data is quite similar to theoverall relationship. Indeed, the tight relationship suggests that from the perspective
7

of time series changes, cross-country differences in the details for funding of educationor health, for example, are second order relative to the income per capita relationshipin terms of their effects. (Recall that we have removed country fixed effects in Figure1.) In sum, the tendency for economic activity to move toward high skill-intensive
services as an economy develops is a robust pattern in the cross-country data.
One of the common explanations for structural change is changes in relative prices.
(See, for example, ? and ?.) Using value-added price indices from the same EUKLEMS Database, we can examine the correlation between changes in the relative
price of the high-skill service sector and the changes in its value added share that accompanies the process of development.8 Figure 2 is analogous to Figure 1, but plots
the value added price index of the high skill service sector relative to the low-skill
intensive sector. We have again taken out country fixed effects, and normalized therelative price indices to 100 in 1995. As before, the larger circles represent the U.S.
data.

y = 47.50 ln(x) -390.73
R2=0.735

60

80

100

120

P HS Sectors/P LS Sectors(1995 = 100)140

High-Skill Intensive Sector Relative Price

9.5

10

10.5

Real GDP per-capita(log scale)

11

Figure 2: Relative Price of Skill-intensive Sector and Economic Development.
Figure 2 reveals a strong positive relationship between the relative price of highskill services and development. The linear regression is highly significant, explains 74
8

We construct sector-level aggregate indices as chain-weighted Fisher price indices of the priceindices for individual industries. Calculation details are available in the online data appendix,
http://www3.nd.edu/~jkaboski/SBSC_DataAppendix.zip.

8percent of the variation in the demeaned data, and is quantitatively important: therelative price of the high skill service sector almost doubles over the range of the data.
In this case the relationship in the US data is a bit stronger than in the overall dataset, but the strong relationship exists even abstracting from the US. We conclude thatchanges in relative prices are another robust feature of the structural transformation
process involving the movement of activity toward the high-skill intensive sector.

2.2

Income Effects: Cross-Sectional Household Evidence

A second common explanation for structural change is income effects associated with
non-homothetic preferences. (See, for example, ?.) With this in mind it is of interest
to ask whether high-skill intensive services are a luxury good, i.e., have an income
elasticity that exceeds one. To pursue this we examine the relationship between theskill intensity of value-added consumption and income in the Consumer Expenditure
Survey (CEX), a cross-section data set of household expenditure. To the extent
that all households face the same prices at a given point in time and have common
preferences (or at least preferences that are not directly correlated with income), thecross-sectional expenditure patterns within a country abstract from the relative pricerelationship in Figure 2 and allow us to focus on the effect of income holding prices
constant.
One complication with pursuing this approach is that it involves mapping household expenditure data through the input-output system in order to determine theconsumption shares of value added. We briefly sketch the steps of this procedure
here, and provide more details in the online appendix. We start with the household
level CEX data for the United States from 2012. We adapt a Bureau of Labor Statistics mapping from disaggregated CEX categories to 76 NIPA Personal Consumption
Expenditure (PCE) categories and then utilize a Bureau of Economic Analysis (BEA)
mapping of these 76 PCE categories to 69 input-output industries that properly attributes the components going to distribution margins (disaggregated transportation,
retail, and wholesale categories). Using the 2012 BEA input-output matrices, we canthen infer the quantity of value added of each industry embodied in the CEX expenditures. We classify the 69 industries as high skill intensive or low skill intensive using
the EUKLEMS data as previously noted.99The classification of real estate has a substantial impact on these results. We classify it as
low skill intensive, while the related industries of finance and insurance are high skill intensive. In

9This procedure generates household-level data for the share of total expenditurethat represents valued added by high skill intensive sectors and low skill intensive
sectors, which we can regress on household observables, most importantly income or
education, and potentially a host of other household level controls. In our empirical
work we restrict ourselves to the primary interview sample, and each observation isa household-quarter observation.
Table 1 presents results for regressions of the total share of expenditures that ishigh skill intensive. The first column presents results from an OLS regression onlog after tax income and a set of demographic controls, including age, age squared,
dummies for sex, race, state, urban, and month, and values capturing householdcomposition (number of boys aged 2-16, number of girls aged 2-16, number of men
over 16, number of women over 16 years, and number of children less than 2 years).
The coefficient on log income in the first column indicates that the semi-elasticityof the share of value-added embodied in expenditures is 0.010. The second column
replaces log income with the log of total expenditures, and finds a larger semi-elasticity
of 0.030.10
Table 1: Household High-Skill Intensive Expenditure Share vs. Income or
Total Expenditures
OLS
OLS
IV
IV
OLS
Ln Income
0.010***.
0.029***
.
.
SE
0.000
.
0.001
.
.
Ln Expenditures.
0.030***.
0.045***
.
SE
.
0.001
.
0.002
.
High Skill Head.
.
.
.
0.023***
SE
.
.
.
.
0.002
R2
0.11
.
0.05
.
0.12
Observations
24,21327,31824,21327,3188,883*** indicate significance at the 1 percent level.
Controls include: age; age squared; dummies for sex, race, state, urban, and month; numberof boys (2-16 year); number of girls (2-16 years); number of men (over 16 years); number ofwomen (over 16 years);and number of infants (less than 2 years). High skilled is defined as
16 years of schooling attained, while low skilled is defined as 12 years attained.
general, real estate has very little labor compensation in its value-added, so this categorization not
only fits our criterion but is also conservative because the income effects are much weaker using thisclassification.
10
The larger coefficient for expenditures may be driven by certain lumpy expenditures like higher
educational expenses and car purchases driving both up in particular months. We nonetheless reportthese coefficients for the sake of completeness.

10Both income and expenditure are certainly mis-measured in the micro data, andeven if properly measured, income would only proxy for permanent income, leading
to a likely attenuation bias. The third and fourth columns attempt to alleviate thismeasurement error by instrumenting for log income or log expenditures, respectively,
using the years of schooling attained by the head of household. Instrumenting forincome in this fashion increases the coefficient roughly three-fold to 0.029. Likewise,
instrumenting for log total expenditures increases the coefficient by about 50 percent
to 0.045.
The last column uses education as a direct regressor, replacing log income or log
expenditures with a dummy for whether the head of household is high skilled or not.
Here high skill is defined as having exactly 16 years of education, while low skill isdefined as having exactly 12 years. (The rest of the households are dropped, leading
to the smaller sample size.) The coefficient indicates that the share of value-added
embodied in expenditures is 2.3 percentage points higher in households with a highskilled head.
We have examined the robustness of the results in Table 1 along various dimensions. Table 1 uses “quarterly” expenditures of the household across the three months
they are surveyed, but if we use the monthly data directly, we find nearly identicalresults. By defining high skill as those with at least 16 years of education, and low
skill as those with less than 16 years of education, we expand the sample somewhat,
but the raw estimates are similar (0.032 rather than 0.023). Dropping demographic
controls increases the sample by about 15 percent and lowers the coefficients on income by roughly 25 percent and the coefficient on expenditures by roughly one-third,
but the coefficients remain highly significant. Dropping the controls has essentially no
impact on the high-skilled head of household coefficient. The main effect of dropping
the controls is substantially lower R2 values.
Quantitatively, even the larger, instrumented, expenditure coefficient of 0.045 is
substantially smaller than the aggregate time series value of 0.17 for value-addedin Figure 1, but not negligible in comparison. We therefore take this as suggestive
evidence that, in addition to relative prices, non-homotheticities may also play a rolein accounting for the observed pattern of skill-biased structural change.
Lastly, we note an important limitation in directly applying the micro elasticity
as an income effect. Because the CEX captures only out-of-pocket expenditures, it
underestimates the true consumption of certain goods like insurance premiums (a11substantial share of which is paid by employers) and higher education (a substantial
share of which is paid by government).11

2.3

Summary

In summary, we have documented a robust relationship in the time series data foradvanced economies regarding the movement of activity into high-skill services andthe process of development. We refer to this process as skill-biased structural change,
so as to emphasize both its connection to the traditional characterization of structuralchange and the special role of skill intensity. This relationship is remarkably stable
across advanced economies, thus suggesting that it is explained by some economic
forces that are robustly associated with development, with country specific tax andfinancing systems not playing a central role in explaining the time series changes.
In documenting this relationship we have used a two-way split into high and low
skill intensive sectors. This masks important within sector heterogeneity. Indeed,within the low skill intensive sector, a pattern emerges that the relatively more skill
intensive sectors within this category, e.g., manufacturing industries like electricalequipment and chemicals, expand relative to the less skill intensive sectors like agriculture or textiles.12 In principle, our simple dichotomy may understate the true
extent of skill-biased structural change.13 However, the relative price patterns, use
patterns (consumption and investment), and trade patterns make the analysis at amore disaggregated level more difficult to interpret and much less directly tied to
traditional structural change forces.
The traditional structural transformation literature emphasizes the role of both
non-homotheticities and relative price changes as drivers of structural change, and wehave also presented evidence that both of these effects seem relevant in the context ofskill-biased structural change as well. Specifically, we documented a strong positive11

The estimated income semi-elasticity of the share of out-of-pocket insurance is actually significantly negative in the CEX data although overall insurance consumption is certainly positive.
Similarly, although the expenditure share-income semi-elasticity of higher education is positive, it islikely understated. Finally, the lack of primary and tertiary expenditures may actually be overstatedin the CEX data because it neglects public expenditures, but we conjecture that this relationship issmall relative to the higher education relationship.
12? give a detailed analysis across 150 2-digit industry-occupation cells for the period, 1963-1987.
? present a recent account focusing on detailed occupation categories.
13
Our own empirical analysis summarized in Section 5.4 did not find that aggregation was quantitatively important, however.

12

correlation between the relative price of high skill services and GDP per capita in across-country panel as well as a positive correlation between household value added
expenditure shares on high skill services and income in the US cross-section. These relationships are not only highly statistically significant, but they are also economicallysignificant in a quantitative sense.

3

Model and Equilibrium

Our analysis emphasizes how intratemporal equilibrium allocations are affected bychanges in the economic environment that operate through changes in income andrelative prices. To capture these interactions in the simplest possible setting, we
adopt a static closed economy model with labor as the only factor of production.
Our model is essentially a two-sector version of a standard structural transformation
model extended to allow for two labor inputs that are distinguished by skill. In thissection, we describe the economy and its equilibrium at a point in time; later we
describe the features that we will allow to change over time to generate skill-biased
structural change as described in the previous section.

3.1

Model

There is a unit measure of households. A fraction fL are low-skill, and a fraction
fH are high skill, where fL + fH = 1. All households have identical preferences
defined over two commodities. In our empirical analysis these two commodities will
be connected to the low and high skill intensive aggregates studied in the previous
section. As a practical matter, all of our high skill intensive sectors are services andall goods sectors are in the low skill intensive sector. It is notationally convenient tolabel the two commodities as goods and services even though what we label as goods
includes low-skill services.
We assume preferences take the form:
ε−1

ε−1

Ui = aG cGiε + (1 − aG ) (cSi + c̄S ) εwhere cGi and cSi are consumption of goods and services by an individual of skill leveli, 0 < aG < 1, c̄S ≥ 0 and ε > 0. Note that if c̄S > 0, preferences are non-homothetic
and, holding prices constant, the expenditure share on services will be increasing in13

income.14 This non-homotheticity is motivated by the cross-sectional analysis in theprevious section. Note that households are assumed to not value leisure, since our
focus will be on the relative prices of labor given observed supplies.
Each of the two production sectors has a constant returns to scale production
function that uses low- and high-skilled labor as inputs. We assume that each ofthese production functions is CES:
ρ

 ρ−1
ρ−1
ρ−1
ρ
ρ
j = G, S
Yj = Aj αj Hj + (1 − αj ) Lj

where Lj and Hj are inputs of low- and high-skilled labor in sector j, respectively.
The parameter αj will dictate the importance of low- versus high-skilled labor in eachsector. While one could imagine that the elasticity of substitution between these two
factors also differs across sectors, our benchmark specification will assume that thisvalue is the same for both sectors. We consider the effects of cross-sectional variationin this parameter in our sensitivity analysis.
Before proceeding to analyze the equilibrium for our model we want to commenton the significance of abstracting from capital and trade. By excluding capital we
implicitly adopt a somewhat reduced form view of skill-biased technological change.
For example, changes in relative demand for skilled labor due to capital-skill complementarity and changes in the price of equipment (as in (?), for example), will show
up in our model as skill-biased technological change. While it is obviously of interest
to understand the underlying mechanics of skill-biased technological change, for our
purposes we believe our results are strengthened by adopting a more expansive notionof skill-biased technological change rather than focusing on a specific mechanism.
Although we abstract from trade, we view our analysis as complementary to
those that emphasize the potential role of trade in shaping the evolution of the skill
premium. In particular, our analysis focuses on the extent to which compositionalchanges between goods and high-skill services diminish the role of skill-biased tech14
This is a simple and common way to create differential income effects across the two consumption categories. One can also generate non-homothetic demands in other ways. For example, ?
generate an income elasticity for medical spending that exceeds unity through the implied demand
for longevity. ?, ? and ? all consider more general preferences with the common feature being that
income effects associated with non-homotheticities do not vanish asymptotically. This property islikely to be relevant when considering a sample with countries at very different stages of development. Because we focus on a sample of predominantly rich countries, we have chosen to work withthe simpler preference structure in order to facilitate transparency of the economic forces at work.

14

nological change in accounting for changes in the skill premium. To the extent that
trade is dominated by trade in goods, it could diminish the role of skill-biased technical change by potentially affecting compositions within the goods sector. For example,
if the US increasingly exported high skill-intensive manufactured goods and imported
low skill-intensive manufactured goods, this would shift the composition of production within the goods sector, and in our analysis will be interpreted as skill-biased
technological change within the goods sector. Put somewhat differently, we believethat trade may serve to generate a process of skill biased structural change within
the goods sector, and in this sense represents an additional channel to the one that
we focus on. Having said this, we will carry out a simple exercise later on to assess
the potential role of trade in affecting the size of the high skill services sector.

3.2

Equilibrium

We focus on a competitive equilibrium for the above economy. The competitive
equilibrium will feature four markets: two factor markets (low- and high-skilled labor)
and two output markets (goods and services), with prices denoted as wL , wH , pG and
pS . We will later normalize the price of low-skilled labor to unity so that the priceof high-skilled labor will also represent the skill premium, though in what follows
immediately it is notationally convenient to not apply this normalization.
The definition of competitive equilibrium for this model is completely standard
and straightforward, so here we focus on characterizing the equilibrium. Individualsof skill i = L, H solve
ε−1

ε−1

max aG cGiε + (1 − aG ) (cSi + c̄S ) ε

cGi ,cSi

subject topG cGi + pS cSi = wi .

(1)

Using the first order conditions of this problem and normalizing wL to unity, the15

aggregate expenditure share for services is:1
pS [(1 − fH )cSL + fH cSH ]=ε  1−
1 − fH + fH w H
1−aG+ ppGSaG 1− ε
pS c̄S ppGS
 1 − aG−
aG
1 − fH + fH wH(2)

This expression serves to illustrate the two forces driving structural change in themodel: relative prices and income effects. Provided that  < 1, as pG /pS declines,
the expenditure share of services increases. And, provided that c̄S > 0, an increase
in income measured in units of services, (i.e., (1 − fH + fH wH )/pS ) also leads to anincrease in the expenditure share of services.
The problem of the firm in sector j = G, S is
ρ

 ρ−1
ρ−1
ρ−1
ρ
ρ
max pj Aj αj Hj + (1 − αj ) Lj
− wH Hj − Lj

Hj ,Lj

The first order conditions of the firm’s problem imply an equation for the price ofsector j output in terms of the skill premium wH :
1
 ρ
 1−ρ
αj
1
ρ
.
p̂j (wH ) =ρ−1 + (1 − αj )
Aj wH

(3)

The above expression implies that the search for equilibrium prices can be reduced toa single dimension: if we know the equilibrium wage rate for high-skilled labor thenall of the remaining prices can be determined.
Finally, we derive an expression for the market-clearing
 conditionρ for high-skilled
αj1labor that contains the single price wH . Using Hj /Lj = 1−αj wH , the production
function of sector j, and (3), we obtain a sector-specific demand function for highskilled labor:ραj p̂j (wH )Aj Yj
Hj =
(4)
wH
Aj ,
which, together with equilibrium in the goods market, yields the market-clearing

16

condition for high-skilled labor solely as a function of wH :ρ P
αS p̂S (wH )AS
i=L,H fi ĉSi (wH )
wH
AS
ρ P

αG p̂G (wH )AG
i=L,H fi ĉGi (wH )= fH .
+
wH
AG


(5)

Here we have used ĉji (wH ) to denote the demand for output of sector j by a householdof skill level i when the high-skilled wage is wH and prices are given by the functionsp̂i (wH ) defined in (3).

4

Accounting for Growth and Structural Transformation

In this section we calibrate the model of the previous section so as to be consistent
with observations on structural transformation, growth, and the skill premium under
the assumption that the driving forces are changes in technology (both skill-biased
and skill-neutral) and changes in the relative supply of skill. In particular, we will
use the above model to account for observed outcomes at two different points in time,that we denote as 0 and T for the initial and terminal periods respectively. Consistent
with the existing literature on technological change and the skill premium, we do notallow the parameter ρ to change over time. We also assume that preferences areconstant over time.

4.1

Targets for Calibration

Calibrating the model in the initial and terminal period requires assigning values for
14 parameters. Nine of these are technology parameters: 4 values of the αj (two ineach period), 4 values of the Aj (two in each period), and ρ. Three are preference
parameters: ε, aG and c̄S . Lastly we have the value of fH at the initial and terminal
dates. The two initial values of the Aj represent a choice of units, reducing the overall
number of parameters to be set to twelve. In our benchmark specification we will set
the two elasticity parameters ρ and ε based on existing estimates, further reducing
this number to ten.
As described below, we will directly measure the initial and final values of fH from17

the data. To calibrate the remaining parameters we will target the following values
which reflect the salient features of growth, structural transformation and demand forskill: the initial and final values for factor shares in both sectors, the initial and final
value added shares for the two sectors, the initial and final value of the skill premium,the change in the relative price of the two sectors, and the overall growth rate of theeconomy.
In choosing values for these targets we rely on the EUKLEMS data from Section
2. For the U.S., complete data are available for the years 1977 to 2005, so we choosethese two years as our initial and terminal year respectively.15 This period is ofinterest, since 1977 effectively marks a local minimum in the skill premium (see (?)
for earlier data), and it secularly increases after 1977.
Many of the values for targets have direct counterparts in the data and so require
no discussion, but the construction of targets for the labor variables does merit somediscussion. The data contain total compensation and total hours by industry, skill
level (“low”, “medium”, and “high”, which are effectively, less than secondary completion, secondary completion but less than tertiary completion, and four year college
degree or more), gender, and age groupings (15-29, 30-49, and 50 and over). Consistent with our calculations in Section 2, we combine the compensation of EUKLEMS
categories of “low” and “medium” educated workers of all genders and ages into ourclassification of low-skilled, and “high” educated workers into our classification ofhigh-skilled, in order to calculate labor income shares by skill at both the aggregate
and sectoral level. We use the same sectoral classification as in Section 2.
Setting targets for the skill premium and the relative supply of skilled workers
requires that we decompose factor payments into price and quantity components.
If all workers within each skill type were identical then we could simply use total
hours as our measure of quantity, but given the large differences in hourly wage rates
among subgroups in each skill type this seems ill-advised. Instead, we assume thateach subgroup within a skill type offers a different amount of efficiency units perhour of work. We normalize efficiency units within each skill type by assuming one
hour supplied by a high school-educated (“medium”) prime-aged (i.e., aged 30-49)
male is equal to one efficiency unit of low skill labor and that one hour supplied by a15

BEA data on value added and prices are also available for the period 1977-2007 and line up
quite closely with the KLEMS data. The BEA data does not allow consistent aggregation prior
to 1977. Data on labor compensation and hours are only available through 2005, which is why wechoose 2005 as our terminal date.

18

college-educated (“high”) prime-aged (i.e., aged 30-49) male is equal to one efficiency
unit of high skill labor.16 With this choice of units, the skill premium is defined as
the ratio of college-educated (“high”) to high school-educated (“medium”) prime-aged(i.e., aged 30-49) male wages. This premium rises from 1.41 in 1977 to 1.90 in 2005.17
Finally, we infer fH using the identity that the ratio of labor compensation equals
the product of the skill premium and the relative quantity of high- to low-skilled labor(fH and fL = 1 − fH , respectively). Equivalently, one could compute efficiency unitsof each skill type by using relative wages within each skill group to infer efficiency
units and directly aggregating efficiency units. Note that our implicit assumption
is that differences in wages between different low-skilled (high-skilled) demographic
groups reflect differences in efficiency units of low-skilled (high-skilled) labor. This
procedure implies that high skill labor was 19% of total labor supply in 1977 and rose
to 31% in 2005.
Table 2 summarizes the values used for the targets listed above.
Table 2
Values Used to Calibrate Technology Parameters

4.2

fH0

fHT

wH0

wHT

%∆ ppGS

%∆Y

θG0

θGT

θS0

θST

CS0
Y0

CST
YT

0.19

0.31

1.41

1.90

58.9

80.8

0.18

0.35

0.54

0.66

0.19

0.32

The Calibration Procedure

Having described the targets to be used in the calibration and the data used todetermine the values of these targets, we now describe the details of the mappingfrom targets to parameters. We proceed in two steps. The first step shows how the16

While one could obviously normalize units by choosing other reference groups, this group seems
most natural since its uniformly high rate of participation over time minimizes issues associated withselection.
17
Comparing earnings of full time workers using CPS data, Figure 1 in ? indicates values of
1.39 and 1.64 for 1977 and 2005 respectively. Our measure indicates a roughly 24 percentage point
greater increase. This difference reflects two factors. First, although our lower skill group includes
those with some college education, our high skill group includes those with post-graduate education,
for whom wage growth has been dramatic. ? find 31 percentage point log wage growth for thosewith 18+ years of education between 1979 and 2005 relative to 18.5 for those with 16 or 17 years.
Second, our measure is based on total compensation and not just on labor earnings. ? documentsthat the change in the 90-10 ratio over this time period is more than twenty log points higher whenusing total compensation than when using CPS wages. His analysis is based on firm level data andso does not allow a breakdown by educational attainment.

19technology parameters are inferred. In the second step, we describe how to infer
values for the preference parameters.
We begin with the determination of technological change. First, we show thatgiven a value for ρ, the four values of the αjt are pinned down by sectoral factor
income shares and the skill premium, wHt . To see this, from equations (3) and (4)
w Hjt
, is
note that the share of sector j income going to high skill labor, θHjt = p̂j (wHtHt )Yjt
θHjt =

ρ
αjt
ρ
ρ−1
αjt
+ (1 − αjt )ρ wHt

Therefore, given ρ, the skill premium wHt , and data for θHjt , the value of the αjt are
given by:
1
αjt =

1 .
1−θHjt ρ
1
1 + (ρ−1)/ρ θHjt
wHt

Next we turn to determining the values of the Ajt ’s. As noted previously, the twovalues in period 0 basically reflect a choice of units and so can be normalized. We
will normalize AS0 to equal one, and given the calibrated values for the αj0 and thevalue of wH0 , we choose AG0 so as to imply pG0 /pS0 = 1. In this case pGT /pST canbe easily identified with the change in the relative sectoral prices. As is well known
in the literature, with identical Cobb-Douglas sectoral technologies, relative sectoral
prices are simply the inverse of relative sectoral TFPs, so the change in relative prices
would therefore determine the values of the two AjT ’s up to a scale factor.18 This
precise result does not apply to our setting because of sectoral heterogeneity in the
αjt ’s. (The skill premium also plays a role in determining relative prices, which we
examine in Section 6.) Nonetheless, there is still a close connection between relative
sectoral prices and relative sectoral TFPs (i.e., the Ajt ). In particular, using equation(3) for the two sectors we have:
 αρ
pSt 
AGt
=
ASt
pGt

Gt
ρ−1
wHt
αρSt
ρ−1
wHt

+ (1 − αGt )ρ
ρ

+ (1 − αSt )1/(1−ρ).

(6)The scale factor will of course influence the overall growth rate of the economy
18

This same relation holds more generally, and in particular would also apply if the sectoral
production functions are CES with identical parameters.

20

between periods 0 and T , so we choose this scale factor to target the aggregate growthrate of output per worker.19
To this point, given a value for ρ, we have identified all of the technology parameters. For our benchmark analysis we set ρ = 1.41, which corresponds to the value usedin ?, and which is commonly used in the literature. Though this is a commonly usedvalue in the literature, it is worth noting that previous estimates using an aggregate
production function do not necessarily apply in our setting. For this reason we will
also do sensitivity analysis with regard to ρ over a fairly wide interval, ranging from0.77 to 2.50. Table 3 below shows the implied values for the technology parameters.
Table 3
Calibrated Technology Parameters (ρ = 1.42)
αG0

αS0

αGT

αST

AST /AS0

AGT /AG0

0.28

0.55

0.44

0.67

1.30

2.33

A few remarks are in order. Not surprising given the way in which we groupedindustries into the two sectors, the weight on low-skilled labor is greater in the goods
sector than in the service sector at both dates. More interesting is that in both sectors
technological change has an important component that is skill biased. While the level
rise in α is greater for the goods sector than the service sector, the changes are ofsimilar magnitude (16pp and 12pp).
However, overall technological progress is much greater in the goods sector thanin the service sector. The TFP term in the goods sector more than doubles between
1977 and 2005, corresponding to an average annual growth rate of 2.97%. In contrast,
the growth of the TFP term in the service sector averages only 0.80% per year.
We now turn to the issue of determining the values for the three preference parameters: aG , c̄S and ε. While technological change can be inferred without specifying
any of the preference parameters, we cannot evaluate some of the counterfactual exercises of interest without knowing how relative demands for the sectoral outputs are
19

Note that to compute aggregate output at a point in time (and thus also the growth rate inaggregate output) it is necessary to know the sectoral distribution of output. The relations imposedthus far guarantee that maximum profits will be zero in each sector but do not determine the scaleof operation. Intuitively, the split of activity across sectors at given prices will be determined by
the relative demands of households for the two outputs. Below we will describe how preference
parameters can be chosen to match the sectoral distribution of value added at both the initial andfinal date. At this stage we simply assume this split is the same as in the data.

21

affected by changes in prices. As noted above, the calibration of technology parameters used information about sectoral expenditure shares without guaranteeing thatobserved expenditure shares were consistent with household demands given all of theprices. Requiring that the aggregate expenditure share for goods (or services) is consistent with the observed values in the data for the initial and terminal date would
provide two restrictions on the three preference parameters. It follows that we would
either need to introduce an additional moment from the data, or perhaps use information from some outside study to determine one of the three preference parameters.
As noted earlier, for our benchmark results we will follow the second approach andfix the value of ε, and then use data on aggregate expenditure shares to pin down
the values for aG and c̄S . Our main finding is relatively robust to variation over alarge range of values of ε, thereby lessening the need to tightly determine its value.
Nonetheless, in Section 5 we will describe how cross-sectional data on expenditure
shares could be used as an additional moment and allow us to determine all threepreference parameters.
The empirical literature provides estimates of ε that correspond to the categories
of “true” goods and “true” services, but not for our definitions of the two sectorsthat are based purely on skill intensity. The key distinction is that we have grouped
low-skill services with goods. However, given that our goods sectors does contain allof the industries that produce goods, while our service sector does consist entirelyof service sector industries, it seems reasonable that information about the elasticity
of substitution between the true goods and services sectors should be informative
about the empirically plausible range of values for ε in our model. Recalling that theobjects in our utility function reflect the value-added components of sectoral output,
the relevant estimates in the literature would include ?, ?, and ?. All of these studies
suggest very low degrees of substitutability between true goods and true services. For
this reason we consider values for ε in the set {0.125, 0.20, 0.50}, with ε = 0.20 chosen
as our benchmark.20
Given a value for ε, equation (2) can be used to determine values for aG and c̄S if
we require that the model match the initial and final sectoral value added shares.
Table 4 shows the values for the preference parameters in the different scenarios.
20? redo the exercise in ? for a more general class of preferences and find an elasticity of
substitution that is somewhat higher, though around 0.50, which is our upper range.

22

Table 4
Calibrated Preference Parameters
ε

aG

c̄S

Benchmark

0.20

0.97

0.09

High ε

0.50

0.61

0.20

Low ε

0.125

0.99

0.08

The qualitative patterns in this table are intuitive. Note that in each case thechanges in income, relative prices and the aggregate expenditure shares are the same.
As we move from ε = 0.20 to ε = 0.125 we decrease the elasticity of substitution
between the two goods, implying a smaller response in relative quantities but a larger
response in relative expenditure shares. In order to compensate for this larger effect,
we need to decrease the impact of income changes on relative expenditure shares,
implying a lower value for c̄S . The lower value for c̄S will in turn lead to a higher
expenditure share on services in the initial period, since the non-homotheticity is now
less important. Hence, in order to match the expenditure shares for the initial period
we need to attach a lower weight, aG , to consumption of goods. As we move fromε = 0.20 to ε = 0.50 we see the reverse pattern.

5

Decomposing Changes in the Skill Premium

Our model is calibrated so as to account for the observed change in the skill premium between 1977 and 2005. In this section we use the calibrated model to perform
counterfactuals that allow us to attribute changes in the skill premium to the various
exogenous driving forces in the model. Our primary objective is to decompose theeffect of changes in technology on the skill premium into a piece due to skill biased
technological change and a residual piece that is due to other forms of technological change. The residual piece affects the relative demand for skilled individuals
indirectly, through its impact on the relative consumption of services.
Table 5 reports the results of our counterfactual exercises for each of the three
specifications that differ with respect to the value of ε. As we will see, the key results
are very similar across the three specifications, so to better focus our discussion wewill concentrate on the ε=.20 case and later summarize the other cases.

23

Table 5
Decomposing Changes in the Skill Premium
US, 1977-2005
ε = 0.50

ε = 0.20

ε = 0.125

wH0

1.41

1.41

1.41

wHT

1.90

1.90

1.90

wHT –changes in fi only

0.91

0.88

0.88

wHT –changes in fi and Aj only

1.10

1.09

1.09

wHT changes in fi and αj only

1.64

1.63

1.63

The first two rows of the table report the starting and ending values for the skill
premium, which are the same in our model as they are in the data. The rest of thetable decomposes this change into several pieces by considering several counterfactual
exercises in our model. The first counterfactual assesses the role of “supply” versus“demand” factors. Specifically, the share of labor supply coming from high-skilledworkers increases between 1977 and 2005, and in the absence of any other changes
exerts downward pressure on the skill premium. As noted above, focusing on the
ε = .20 case for now, the third row of Table 5 shows that if the change in relative
supply of skill (i.e., the fi ’s) had been the only change between 1977 and 2005 the skill
premium would have decreased from 1.41 to 0.88, a 53 percentage point fall. Given
that we in fact observe an increase in the skill premium of 49 percentage points, itfollows that the overall effect of technological change is to increase the skill premiumby 102 percentage points.
Our next goal is to decompose the 102 percentage point increase in the skill
premium due to the overall effect of technological change into one part that is due toskill biased technological change (i.e., changes in the αjt ’s) and a second part due toother dimensions of technical change (i.e., changes in the Ajt ’s).
There are two natural calculations that one could perform to assess the contribution of changes in the Ajt ’s to changes in the skill premium. In both calculations westart from the previous counterfactual in which we change only the supply of skill.
In the first calculation we add in the change in the Ajt ’s and compute the fractionof the overall 102 percentage point increase that they account for. In the second
calculation we instead add in the changes in the αjt ’s and compute the fraction of
the 102 percentage point increase that is not accounted for. In a linear model thesetwo calculations would give the same answer, but to the extent that nonlinearities
24

are present they may differ. It will turn out that the answers do differ, but only to a
relatively minor extent.
The final two rows in Table 5 present the results of these two calculations. Specifically, moving from the third row to the fourth row we see that the change in the Ajt ’s
increases the skill premium from 0.88 to 1.09, an increase of 21 percentage points.
This represents roughly 20 percent of the overall 102 percentage point increase accounted for all technical change. Moving from the third row to the fifth row, we seethat the changes in the αjt ’s cause the skill premium to increase from 0.88 to 1.63.
The residual is 27 percentage points, which represents approximately 27% of the 102
percentage point increase due to all changes in technology. Based on this we conclude
that non-skill biased technical change accounts for between 20 and 27 percent of theoverall change in the skill premium due to technical change. Put somewhat differently, according to our calibrated model, if skill biased technical change had been the
only force affecting the relative demand for skill then the skill premium would haveincreased by only 22 percentage points instead over the period 1977 to 2005 insteadof increasing by 49 percentage points.
If we redo these calculations for the other two values of ε the answers are similar.
For ε = 0.50 the two methods imply that changes in the Ajt ’s account for 19% and
26% of the overall change in the skill premium due to technical change, whereas for
ε = 0.125 the two values are effectively identical to those for the ε = 0.20 case,being equal to 20% and 27%. From this we conclude that our finding of a significant
contribution of changes in the Ajt ’s is robust to a large variation in the value of ε.

5.1

Sources of Structural Change

In the introduction we stressed the fact that aggregate production function analyses
abstract from compositional changes, and that our main objective was to assess thequantitative importance of the compositional changes that are associated with theprocess of structural transformation during development. The previous calculations
decomposed the overall changes in the skill premium into parts due to skill-biased
technological change and skill-neutral technological change. In order to make theconnection between this decomposition and compositional changes it is of interest to
examine the connection between technological change and changes in sectoral value
added shares. Table 6 reports the results for each of the three values of ε.

25

Table 6
Technical Change and Value Added Share of Skill-Intensive Services
US, 1977-2005
ε = 0.50

ε = 0.20

ε = 0.125

Model 1977

0.19

0.19

0.19

Model 2005

0.32

0.32

0.32

Model 2005 with fixed Aj

0.17

0.16

0.16

Model 2005 with fixed αj

0.35

0.34

0.34

The first two rows of the table remind us that the (skill-intensive) service sector
grew significantly between 1977 and 2005, increasing its share of value added from
19 percent to 32 percent. Recall that our calibrated model perfectly replicates thechange in the data. The last two rows provide two different ways of assessing the roleof changes in the Aj ’s and the αj ’s in accounting for this compositional change. The
third row reports the service sector value added share that would have resulted if thechanges in the change in the αjt ’s had been the only source of technological change,
whereas the fourth row reports the service sector value added share that would haveresulted if the change in the Ajt ’s had been the only source of technological change.
Both calculations lead to the same conclusion: effectively all of the compositionalchange is accounted for by changes in the sectoral TFPs. It follows that our previous
decomposition of changes in the skill premium due to the two different sources oftechnical change can effectively be interpreted as statements about the importance ofstructural change.
Non-skill biased technological change in our model still has two distinct dimensions: one which increases the overall level of TFP in the economy and the otherof which increases relative TFP in the goods sector. As we noted above, both ofthese changes tend to reallocate activity from the goods sector to the service sector, thereby indirectly increasing the relative demand for skill. Next we examine therelative magnitude of these two effects.
Note that for given changes in the Ajt ’s the relative magnitude of these two effects
is dictated by the preference parameters ε and c̄s : as ε becomes smaller, relative TFPchanges have larger effects, and as c̄S becomes larger then sector neutral changes
in the Ajt ’s have larger effects. Because our calibration procedure implies that asε becomes smaller the value of c̄S decreases, we expect to find that sector neutral26

change plays a larger role for smaller values of ε.21
To evaluate this we consider the counterfactual in which we hold all parameters
fixed from the original calibration, allow the fit ’s and the αjt ’s to change as before,
but counterfactually force the Ajt ’s to grow at the same rate, with this rate chosen
so as to yield the same overall change in aggregate output as in the data. When wedo this, the implied values of the skill premium are 1.83, 1.72, and 1.69 for the casesof ε = 0.50, 0.20, and 0.125 respectively. It follows that when ε = 0.50 it is income
effects that dominate the overall impact of the Ajt ’s on the skill premium, whereas
for the smaller values of ε the sector biased nature of TFP growth is somewhat more
important than the income effect. So while the three different specifications offer very
similar decompositions regarding the overall effect of changes in the Ajt ’s on the skill
premium, they have distinct implications for the mechanics through which changes
in the Ajt lead to changes in the skill premium.
The preceding discussion has focused on the role of technological change in bringing about changes in the composition of final demand. But one may also ask to what
extent increases in the supply of skill can act as a driving force behind structuralchange? To assess our model’s predictions for this we compute the change in the
expenditure share for services that would result if the change in the relative supplyof skill had been the only driving force. The result is that instead of increasing from
.29 to .44, the expenditure share for services actually decreases modestly to .27. Intuitively, there are two effects at work. First, the increase in the relative supply of skill
serves to decrease the skill premium and hence the relative price of services. Withε < 1 this leads to a decrease in the services expenditure share. Second, the changes
in the skill premium and the price of services lead to a change in income measured
in units of services. In our calibrated economy this change in income is positive (i.e.,the decrease in the price of services dominates the effect of a decrease in the skill
premium), leading to an increase in the services expenditure share. As noted above,
the net quantitative effect is a modest decrease. The main message is that increases
in the supply of skill do not serve to expand the size of the high skill service sector.
21

Although the exact values of c̄S and ε are not important to our overall results, one might betempted to use the measured cross-sectional relationship estimated in Table 1 to identify them.
Recall, however, that we argued that this relationship is likely to have underestimated the true
importance of income effects in the time series. Indeed, the contributions of relative prices arelimited by the Leontieff case of ε = 0. Even in this case, matching the structural change facts
requires too strong of an income effect, i.e., too large of a c̄S , to simultaneously match the measured
cross-sectional relationship.

27

5.2

Sensitivity Exercises

For the results in the previous section we assumed that ρ = 1.42, which we noted wasa standard value in the literature, and the value implied by the analysis in ?. However,
we also noted that the aggregate analyses that have supported this estimate are notnecessarily appropriate in our multi-sector economy. For this reason we also consider
a wider range of values for ρ to assess the extent to which the above conclusions arerobust to variation in this parameter.
We consider two alternative values of ρ, corresponding to higher and lower elasticities of substitution. Specifically, we consider ρ = 0.77 and ρ = 2.5. In each case
we redo the calibration procedure as before. While the value of ρ does affect thequantitative findings, it leaves our main message largely unchanged. For example,
focusing on the case of ε = 0.20 we find that when ρ = 0.77, the share of changes inthe skill premium due to technical change that are accounted for by changes in the
Ajt is 23% and 38% from the two methods. When ρ = 2.50 the corresponding values
are 15% and 18%. We conclude that our main finding of a significant role for changes
in demand composition induced by technical change in accounting for changes in theskill premium is robust to considering a wide range of values for ρ, though higher
values of this elasticity parameter do lead to modest declines in the estimated role
played by demand composition.
Our analysis has assumed that the value of ρ is the same in both sectors. Absent
any empirical evidence on the extent of heterogeneity in ρ across sectors, this seemeda natural benchmark. However, ? suggests that the elasticity of substitution between
high and low-skilled workers may be lower in services. It is therefore important toassess whether our results are sensitive to the assumption of ρ being constant acrosssectors. To do this we redo our exercise for several specifications in which we allow
the two values of ρ to vary across sectors, allowing for the ratio ρG /ρS to be bothlarger and smaller than one. In all cases we assume that the weighted average ofthe two elasticities–(HG /H)ρG + (HS /H)ρS –is equal to 1.42 when evaluated at theinitial factor shares, so that our analysis can be interpreted as assessing the effect ofheterogeneity holding the aggregate elasticity of substitution constant. We consider
values for ρS of 0.77, 0.91, 1.11, and 2.00, which lead to implied values for ρG of 2.23,
2.06, 1.82, and 0.73. Table 7 reports the same statistics as in Table 5, focusing on
the case of ε = 0.20.

28

Table 6
The Effect of Sectoral Variation in ρ
US, 1977-2005
ρS
ρG = 0.35

ρSρG = 0.44

ρSρG = 0.61

ρSρG = 1.00

ρSρG = 2.73

wH0

1.41

1.41

1.41

1.41

1.41

wHT

1.90

1.90

1.90

1.90

1.90

Counterfactual wHTchanges in: fi only

0.99

0.97

0.94

0.88

0.74

fi and Aj only

1.11

1.11

1.10

1.09

1.08

fi and αj only

1.71

1.70

1.68

1.63

1.48

For ease of comparison, the fourth column repeats the results from our benchmark
specification. For values of ρS /ρG < 1 the implications are affected very little, andto the extent that a very large value of ρS /ρG influences the quantitative results, ityields a larger role for the demand effects that we focus on (between 29% and 36%).
Noting that we are considering a very wide range of variation in the relative valuesof ρ, we conclude that our results are quite robust to variation in ρ across sectors.
Lastly, we consider the extent to which mis-measurement of relative prices might
influence our results. Our quantitative analysis utilized information about changes
in the relative price of the high skill intensive sector. Between 1977 and 2005 thisrelative price increased by more than sixty percent. One possible concern is thatprice inflation in the high skill intensive sector might be upward biased because of
the failure to properly account for quality improvements.
Here we report the results of a simple exercise to assess the extent to which ourconclusions are affected by this possibility. In particular, consider the case in which
the true increase in the relative price of the high skill intensive sector was only half as
much as indicated by the official data. This means that real value added in this sector
increased by roughly 30% more than indicated by the official data, and aggregate GDP
grew by roughly 15 additional percentage points. We set ρ = 1.42 and ε = 0.20 andcarry out the same calibration procedure as previously. Not surprisingly, given that
we are holding ε fixed and decreasing the role of relative price changes, the calibration
procedure yields a larger value for c̄S , indicating a larger role for nonhomotheticities.
However, we find that the contribution of demand factors is virtually identical towhat we found in our benchmark calculation. So while mismeasurement of relative
price changes has implications for relative magnitudes of preference parameters, it29has virtually no effect on our assessment of the role of demand factors.

5.3

Comparison with Earlier Literature

The increase in the relative demand for high-skilled labor that we attribute to structural change is substantially higher than the overall effects of relative demand shifts
found in the earlier literature on the topic. For example, in the overlapping yearsof our samples, 1979-1987, using a shift-share analysis, Katz and Murphy (1992),
KM hereafter attributed 4.6 percentage points of increase in relative demand forhigh-skilled labor to changes in industrial composition (i.e., their “between industry”
analysis, see Table VIII). Given their estimated elasticity of substitution, this accounts for only 11 percent of the increase in the skill premium over their period ofstudy. Bound and Johnson (1992) estimate a small but slightly negative contributionof industrial composition. In contrast, when we restrict attention to the overlapping
years 1979-1987, our simulations attribute between 25 and 28 percent of the increasein the skill premium to the increase in the relative demand of high-skilled labor associated with skill-biased structural change. Why do we find an effects that are between
two and three times larger than KM? This is the question that we take up in thissubsection.
One obvious difference between the analysis in KM an ours is that they use shift
share analysis and we carry out explicit model based counterfactuals. As we show
below, this is a quantitatively significant. But there are also many other differences,including different data sources (CPS versus EU KLEMS), different measures of payments to workers (wages versus compensation), different sample periods (1963-1987
versus 1977-2005), different measures of skill intensity (relative employment versus
relative compensation), different measures of industry size (compensation versus value
added), and different degrees of disaggregation (50 sectors versus 2 sectors).22 Eachof these could be important and our goal here is to assess which factor or factors arebehind the very different conclusions.
To explore this we have carried out a sequence of exercises that change one element
at a time and which cumulatively will take us from the KM shift share analysis to ourmodel based counterfactuals. The sequence of results is presented in Table 7, with
22

In addition, Katz and Murphy use experience, while we use age, and our demographic cells areslightly different as well. These difference are negligible, however, but their minimal impact is shownin the online appendix.

30

each row corresponding to one additional departure as we move from the KM results toour results. In each case the focus of our attention is on the implied percentage of theoverall demand for skilled labor that is accounted for by changes in the compositionof demand across sectors.
Table 2: Table 7
Row

Data
Source

1
2
3
4
5
6
7
8
9

CPS
IPUMS
World KLEMSWorld KLEMSWorld KLEMSWorld KLEMSWorld KLEMSWorld KLEMSEU KLEMS

Years

Industry
Aggregation

1979-1987
1979-1989
1980-1990
1980-1990
1980-1990
1977-2005
1977-2005
1977-2006
1977-2005

50**
31
31
31
2
2
2
3
2

Skill
Intensity

Analytical
Methods

Relative Quantities
Shift-Share
Relative Quantities
Shift-Share
Relative Quantities
Shift-ShareFactor Shares
Shift-ShareFactor Shares
Shift-ShareFactor Shares
Shift-ShareFactor Shares
Model Counterfactual
Factor Shares
Model Counterfactual
Factor Shares
Model CounterfactualIndustry
Size Measures
Labor Compensation
Labor Compensation
Labor Compensation
Labor Compensation
Labor Compensation
Labor Compensation
Labor Compensation
Value Added
Value Added

Contribution
to
Skill Premium*
11%
10%
10%
19%
23%
19%
24%
33%
18%
25%
20%
27%

The first row of Table 7 starts with a benchmark calculation that implements themethod of KM for the period 1979-1987 using the CPS data and disaggregating thedata into 50 different industries. This departs slightly from the specification in KM(1992) in that they also allowed for 3 occupation categories, leading to 150 distinct
categories. As the first row shows, abstracting from the occupational disaggregation
has no impact on the implied result, as we obtain the same 11% share as reported in
KM.
A key feature of the analysis in KM is that it is based on an analysis of micro
data. In contrast, the EU KLEMS data that we use only reports statistics at various
levels of aggregation. The underlying micro data that serves as the source for thevarious aggregates reported in the EU KLEMS is IPUMS. The first departure that we
consider from the KM benchmark is to redo the analysis using the IPUMS micro datarather than the CPS. Data availability forces us to also consider the period 1979-1989
instead of 1979-1987.23 24 Also, the industrial classification in IPUMS only allows us
to allow for 31 industries rather than 50. Row 2 shows that the effect of using IPUMS
rather than the CPS is effectively negligible.
As we move from Row 2 to Row 3 we now switch from using a micro data set to adata set that only reports outcomes at various levels of aggregation. However, instead
23

The Census decenial data that is available for the years 1980 and 1990 reports data on questions
asked for the years 1979 and 1989.
24
IPUMS data that map closely into the micro data that KM utilize and also act as a bridgeto the KLEMS data we utilize. Using KM’s methods on the period 1979-1989, which covered by
the IPUMS decadal Census data but is quite close to the 1979-1987 period that KM study, we findnearly identical results.

31

of moving directly to the EU KLEMS data set, in this step we move to the WorldKLEMS data set. IPUMS is also the underlying micro data used to construct the aggregates in World KLEMS. The reason that we move first to the World KLEMS data
set rather than EU KLEMS is that the concordance between industry categories in
IPUMS and World KLEMS is much stronger than between IPUMS and EU KLEMS
and we do not want to introduce an additional variation at this step. But anotherchange that occurs at this step is that we move from wage based measures to compensation based measures. Importantly, using the aggregated data in World KLEMS
and compensation based measures yields the same result as using the micro data in
IPUMS.
To this point, the key message is that we are effectively reproducing the resultsfrom KM. Moving to Row 4, however, leads to roughly a doubling of the role forchanges in the composition of demand. The key change here is the method used tomeasure differences in skill intensity across sectors. In our analysis, we use relativecompensation paid to skill types as a measure of skill intensity. Assuming a given wage
per efficiency unit of labor of each skill type, our measure of relative skill intensity
across sectors is equivalent to the relative ratio of quantities of efficiency units of thetwo skill types across sectors. Importantly, we allow for efficiency units to vary acrossworkers within a given education/age/gender cell, since this is how we account forwage differences within a given cell. In contrast, KM assume that all workers within agiven cell supply the same number of efficiency units and measure relative quantities
of skilled and less skilled labor without using data on compensation. This turns out tohave very significant implications. For example, when we later condense the analysis
to consider only two sectors, our method implies a skill difference between the two
sectors of 28 percent whereas KM’s method implies a skill difference of only 4 percent.
Intuitively, demand shifts will have much smaller effects if the differences in skill
intensity across sectors are smaller, and Row 4 reflects the quantitative significanceof this, as the contribution of demand shifts increases from 10 percent to 19 percent.
Row 5 decreases the level of disaggregation. Consistent with our analysis, we now
carry out the shift share analysis based on a two sector decomposition. This results
in a modest increase for the role of demand shifts. Implicitly there are demand shifts
within our two sector aggregates that serve to offset these changes. As we move toRow 6 we now change the sample period to correspond to the sample that we use
in our analysis: 1977-2005. The effect of this is to shift the contribution of demand32

shifts back to 19%. Note, of course, that as we change the sample period we arechanging both the numerator and denominator that goes into this calculation, sinceboth demand shifts are different and the overall change in the demand for skill haschanged. Notably, the combined effect of Rows 5 and 6 is to bring us back to thesame value as shown in Row 4.
Row 7 introduces the second important difference in our results: moving from
KM’s local approximation of endogenous movement in industry to our fully solved
general equilibrium evaluation of exogenous shifts in technology parameters. As KM
acknowledge, their linear approximation underestimates the true contribution of demand shifts because the skill premium rose during the period of analysis. A risingskill premium disproportionately increases the price of the skill-intensive output (seeour equation (8)), reducing the movement of resources into that sector relative towhat would be observed with perfectly elastic labor supply (i.e., the full shift in demand).25 Whereas they are able to analytically sign the bias, the added structure of
our model enables us to actually quantify this bias. In addition, our analysis uses a
global solution of the model, instead of a local approximation. Moreover, since we
map industrial shifts into exogenous technology parameters, the interpretation of oureffects are slightly different as well, and they depend on the exact counterfactual.
We measure the impact of sectoral productivity changes as demand shifters. The
impact of these changes depends on whether they happen alongside our skill-biased
technical change or on their own. Moving from the local approximation to our global
method attributes an increase to 24 percent to our SBSC parameters in a counterfactual world with the initial values for the skill-bias parameters αj (which corresponds
to the change moving from row 3 to row 4 in Table 5) and 33 percent in a world withthe final values of αj (which correspond to the difference between row 2 and row 5 ofTable 5). The fact that the latter are higher indicate that SBSC and SBTC reinforce
one another.
To this point, the analysis in Table 7 has used labor compensation shares tomeasure the sizes of the sectors, as this is what KM did. However, our results werebased on a calibration exercise in which we targeted the value added shares of thetwo sectors. Recall that we only have sector-specific relative price movements for
25

Bound and Johnson adjust for the increase in relative supply of high-skilled labor without
accounting for the fact that the relative wage nevertheless rose. This appears to account for theirmuch lower estimate than KM.

33

value-added, so this model has a clearer mapping to the data. Row 8 shows thatthe contribution of SBSC is somewhat smaller when we use value added instead ofcompensation to measure the change in relative sector sizes. When using value-added,
the contributions for the two counterfactuals fall from 24 and 33 percent to 18 and25 percent, respectively.
The final step in our analysis is to move from World KLEMS to EU KLEMS.
The reason that EU KLEMS is of interest is that it allows for greater comparability
in terms of cross-country analysis. Row 9 shows that using the more internationallycomparable EU KLEMS data increases these contributions slightly to 20 and 27
percent.
In summary, while there are many small variations, there are two important factors that explain why we find a substantially larger role for skill-biased structuralchange in accounting for increases in the skill premium relative to what the earlier
literature attributed to industrial composition. The first is that we use wage data tocontrol for unobservable differences among workers within a cell. This implies larger
differences in skill intensity across sectors, thereby increasing the potential impact ofcompositional changes on the relative demand for skill. The second is that our structural approach allows us to precisely disentangle the role of different driving forcesby solving an explicit model-based, globally-solved counterfactual from exogenous
technology parameters.

6

Decomposing Changes in Relative Prices

While our main focus has been to understand the relative importance of different
factors in generating the observed changes in the skill premium, our model also allows
us to assess the importance of different factors in generating the change in the relative
price of skill intensive services over time. In particular, our model suggests two distinct
channels at work. As is standard in the literature on structural change with uneventechnological progress across sectors, differential growth in sectoral TFP will lead tochanges in relative sectoral prices. But our model also features an additional channel:
because the sectors have different factor shares, changes in the relative price of factors
will also lead to changes in relative sectoral prices. In particular, since the high-skill
intensive sector uses skilled labor more intensively, any increase in the relative priceof skilled labor will lead to a higher relative price for this sector. This effect was34

previously documented in equation (3).26
Here we perform some counterfactuals in our benchmark specification (i.e., ρ =1.42 and ε = 0.20) to assess the relative importance of these two forces. In thedata, the relative price of high-skill intensive services increases by 62 percentage
points between 1977 and 2005, and by virtue of our calibration procedure, our model
perfectly accounts for this increase. To assess the pure role played by the increase in
the skill premium, we compute the implied relative price from equation (3) assumingthat all technology parameters remain fixed at their 1977 values, but letting the skill
premium increase from 1.41 to 1.90, as in the data. The result is an increase in therelative price of skill intensive services of 11 percentage points, or roughly 18% of theoverall increase. In interpreting this magnitude it is important to recall our earlier
discussion of the possibility that estimates of the change in relative prices are biased
upward due to a failure to properly control for quality increases in the service sector.
If the true change in relative prices was indeed only half as large as in the data, thenthe change in the skill premium would account for 36% of the overall change. Whilestill not the dominant factor, this suggests that changes in the skill premium maywell be a significant factor behind changes in relative prices.
The issue of price mismeasurement notwithstanding, the direct effects of technological change are the dominant force behind the increase in the relative price of skill
intensive services in our benchmark calibrated model. Moreover, it is the difference
in sectoral TFP growth rates that drives this direct effect. To see this, take equation(3), hold the skill premium and sectoral TFPs constant and consider the pure effect ofskill biased technological change. The result is that the relative price of skill intensive
services would have decreased by 19 percentage points.
This last calculation examined the direct effect of changes in skill-biased technological change, but without incorporating the general equilibrium effect on wages.
Our previous counterfactuals (see row 5 in Table 5) argued that if we eliminatedchanges in sectoral TFP, so that skill-biased technical change was the only source oftechnological change, the skill premium would have increased from 1.41 to 1.59. If we
include this effect in combination with the direct effect of skill biased technologicalchange, the result is that the relative price of skill intensive services decreases by 15
percentage points. We conclude that skill-biased technological change is not a source
26? highlight this effect in a theoretical model in which the difference in skill-intensity across the
goods and service sectors arises endogenously.

35

of increases in the relative price of services.
In summary, we conclude that although increases in the skill premium may directly
account for a non-trivial share of the increase in the relative price of high-skill intensive
services, the dominant factor behind this increase is the relatively slow sectoral TFP
growth in this sector.

7

Cross Country Analysis

In this section we extend our analysis to nine other OECD countries for which theavailable data exists and thereby address two distinct issues. The first issue concerns
model validation, and the second issue is to assess the importance of skill-biased
structural change for a larger set of countries.

7.1

Model Validation Using Cross-Country Data

Our calibration procedure assigned parameter values by targeting the same numberof moments as there were parameters. While both the production structure and our
method for inferring technological change are very standard, we inferred values forutility function parameters by requiring that the model match the beginning andfinal values for sectoral valued added shares. If our utility function were mis-specified
in an important way, this procedure would still allow us to fit the initial and final
sectoral value added shares, but in this case we might be wary of using our calibrated
specification for the counterfactual exercises.
One simple test of the specification is to consider its ability to fit not only the two
endpoints of our sample, but also the entire time series. Unfortunately this is not avery stringent test for the period we are studying, since the key series in our analysis
are fairly linear, and the model is able to match them fairly well.
As a somewhat more stringent test, we turn to cross country data. For thisexercise we use data from the following nine countries: Australia, Austria, Belgium,
Denmark, Germany, Italy, Japan, the Netherlands, Spain and the United Kingdom.
We assume that the utility function for each country is the same as the one impliedby our benchmark calibration with ρ = 1.42 and ε = 0.20, i.e., we impose the impliedvalues for aG and c̄S . Additionally, we assume that ρ is the same for all countries.
However, using the same procedures as earlier, for each country we measure the

36

2.25
Predicted Skill Premium

Predicted Skill-Intensive
Service Share

0.50
0.45
0.40
0.35
0.30
0.25
0.20
0.15
0.10
0.1

0.3

Actual Skill-Intensive Service Share

2
1.75
1.5
1.25
1
0.75
0.75

0.5

1

1.25 1.5 1.75

2

2.25

Actual Skill Premium

Figure 3: Model Fit in a Panel of Countries: Structural Change (left panel) and the
Skill Premium (right panel).

0.3
0.1
-0.1
-0.3
-0.5
-0.7
-0.9
-1.1
-1.3
-1.5
$10,000

Skill-Biased Technology Parameter

Log Productivity Level

relative supply of skilled labor from the data and we use our model to infer the timeseries for technological change. Because preference parameters are imported fromthe calibration using US data, we have not imposed that the model will fit the timeseries of interest for each country. Nonetheless, Figure 3 shows that this specification
provides a reasonably good fit to the actual data for this set of countries. Because thebehavior of the skilled labor share and the skill premium do differ across countries,
we believe that this finding is supportive of our parsimonious structure.

ASAG$50,000
Real GDP per Capita (Log Scale)

0.6
0.5

aS

0.4
0.3
0.2

aG

0.1
0
$10,000$50,000
Real GDP per Capita (Log Scale)Figure 4: Calibrated Technological Processes: Sector-Biased (left panel) and SkillBiased (right panel) Technologies. The diamonds (squares) correspond to the high(low) -skill intensive sector.
37

It is of interest to note that the above procedure implies processes for technologicalchange that are broadly similar across countries, as shown in Figure 4.27 To the extent
that we believe the process of technology adoption and diffusion are at least generally
similar across rich countries, we would view it is as somewhat problematic if ourprocedure indicated dramatically different processes across these countries.

7.2

Skill-Biased Structural Change and the Skill Premium in
Cross Country Data

In this subsection we assess the extent to which skill biased structural change has influenced the skill premium in each of the countries studied in the previous subsection.
We could carry out this calculation for the specifications in the last subsection, i.e.,
assuming the same preference parameters for these countries as in the US. A potential disadvantage of this method is that although the model with common preference
parameters across countries offers a good fit to the cross country time series data, it
does not necessarily account for all of the changes in the skill premium for each of
the countries. Alternatively, we could assume country specific values for aG and c̄S
and simply repeat the analysis that we have carried out for the US for each of theadditional economies. These two methods provide fairly similar answers, and in theinterest of space we only report the results of the second exercise, which are shownin Table 8.
To compute the values in Table 8 we first calculate the contribution of all formsof technological change by computing the difference between the actual skill premiumin 2005 versus the skill premium that would have existed in 2005 if there had beenno technological change relative to 1977 but allowing for the observed change in the
supply of skill. We then isolate the fraction of this overall contribution of technologicalchange that is due to skill biased structural change by computing the fraction of thischange that is accounted for by changes in the Aj ’s. We do this in two ways. The
second column gives the impact at the initial level of αj (which corresponds to thechange moving from row 3 to row 4 in Table 5). The third column is the impact at
the final level of αj (which correspond to the difference between row 2 and row 5 ofTable 5).
27

The plots in Figure 4 have removed country fixed effects in order to focus on the changes intechnology over time rather than the cross-sectional differences.

38

Table 8
Contribution of SBSC Across Countries
Initial αjFinal αjAustralia

4%15%Austria

21%

28%

Belgium

14%

16%

Denmark

9%

14%

Spain

20%

25%

Germany

23%

24%

Italy

20%

47%

Japan

11%

17%

Netherlands

18%

21%

UK

5%

32%

US

20%

27%

Median18%

24%

Again, we see that the magnitudes are larger given the final values of αj ,which
again indicates that SBTC and SBSC reinforce each other. The magnitude of thecontribution of SBSC varies significantly, from a low of 4% in Australia (14% in
Denmark) to a high of 23% in Germany (47% in Italy). Nevertheless, the medianvalues of 18% and 24% are very much in line with our estimates from the US. We
conclude that the demand side forces associated with skill biased structural change
seem to be quantitatively significant in a broad group of advanced economies.

8

Conclusion

Using a broad panel of advanced economies, we have documented a systematic tendency for development to be associated with a shift in value added to high-skill intensive sectors. It follows that development is associated with an increase in the relative
demand for high skill workers. We coined the term skill-biased structural change todescribe this process. We have built a simple two-sector model of structural transformation and calibrated it to US data over the period 1977 to 2005 in order to assess
the quantitative importance of this mechanism for understanding the large increasein the skill premium during this period. We find that technological change overall
increased the skill premium by roughly 100 percentage points, and that between 20
39and 27 percent of this change is due to technological change which operated throughcompositional changes.
Our findings have important implications for predicting the future evolution of theskill premium, since the continued growth of the value added share of the high-skill
intensive sector will exert upward pressure on this premium even in the absence ofskill-biased technological change.
In order to best articulate the mechanism of skill-biased structural change we have
purposefully focused on a simple two-sector model. As we noted in Section 2, there isgood reason to think that the mechanism we have highlighted is also at work at a moredisaggregated level, so it is of interest to explore this mechanism in a richer model.
The early literature has also emphasized the possibility that increases in trade mightlead to changes in the composition of valued added across sectors. ? specifically
noted this possibility, and more recent analyses include ? and ?. We think it isimportant to note that the compositional effects we have focused on are not likely tobe reflecting changes due to trade. The reason for this is that our high-skill intensive
sector is composed entirely of industries from the service sector. It is plausible thatpart of what we identified as within sector skill biased technical change may at leastin part reflect compositional effects due to trade, to the extent that trade had caused
manufacturing activity in the US to shift to more skill intensive industries.

40