This paper analyzes whether technical change is skill-biased when accounting for international fragmentation of production. Using data from the World Input Output Database, the authors estimate factor cost shares across 280 manufacturing industries and 20 countries from 1995-2007. Their results from translog cost function regressions provide support for skill-biased technical change, with high-skilled labor and capital showing positive and significant coefficients, while low-skilled and medium-skilled labor show negative coefficients. The findings are robust across specifications and imply cumulative biases over the period in favor of high-skilled labor and capital, and against low-skilled labor. The discussant comments that this makes a significant contribution but raises questions around the use of a Leontief

1. Is Technical Change Factor Biased?
An analysis of Cost Shares in Vertically Integrated Production
Author: Marcel P. Timmer and Xianjia Ye
Discussant: D.S. Prasada Rao

2. The main objective of the paper is to test if technical change is
skill biased taking into account international fragmentation of
production.
Objectives

3.  There is a general consensus view that technical change is
biased in favour of skilled labour
 Most of the studies are based on cross-country regressions of
labour cost shares.
 In the presence of off-shoring of production tasks, there is an
identification problem: bias in technical change is
observationally equivalent to offshoring if only domestic
factors are considered.
 Given increased internationalization of production process, it
is important to test whether technical change is skill biased.
Background of the paper

4. Observational equivalence of offshoring and technical change
Offshoring Offshoring
Original
situation
Traditional
analysis This paper
HS Design
(35%)
HS Design
(50%)
HS Design
(35%)
LS Parts
(35%)
LS Parts
(50%)
LS Parts
(35%)
LS Assembly
(30%)
LS Assembly
(not observed)
LS Assembly
(30%)
Factor cost shares
Domestic HS 35% 50% 35%
Domestic LS 65% 50% 35%
Foreign LS 30%
biased tech ch no bias
Example of
activities in car
production
(cost shares)
BIASED
technical
change
NO BIAS

5. Econometric methodology
The paper makes use of a standard translog cost function framework using:
where yt is output and pi is the price of i-th input.
ln 𝐶 𝒑 𝑡, 𝑦 𝑡, 𝑡 = 𝛼 +
𝑖∈𝐹
𝛽𝑖 ln 𝑝𝑖𝑡 + 1
2 𝑗∈𝐹 𝑖∈𝐹
𝛾𝑖𝑗 ln 𝑝𝑖𝑡 ln 𝑝𝑗𝑡
+𝛽 𝑌 ln 𝑦 𝑡 + 1
2 𝑖∈𝐹
𝛾𝑖𝑌 ln 𝑝𝑖𝑡 ln 𝑦 𝑡
+𝛽 𝑇 𝑡 +
1
2 𝑖∈𝐹
𝛾𝑖𝑇 𝑡 ln 𝑝𝑖𝑡 +
1
2
𝛾 𝑇𝑇 𝑡2

6. Econometric methodology
 Under the standard assumptions, cost share equations can be derived. As
cost shares add up to 1, one of the factors can be dropped.
 In this paper four factors: capital; low-skill labour; medium-skill labour;
and high-skill labour are used.
 The factor share equations for the three labour inputs are:
 Here the factor biased technical change is modelled using linear trend
(last term in each of the equations)
 Alternatively, time dummy variables could be used in this model implying
the level of technical change varies across years.
𝑆 𝐿𝑡 = 𝛽𝐿 + 𝛾 𝐿𝐿 ln 𝑝 𝐿𝑡 𝑝 𝐾𝑡 + 𝛾 𝐿𝑀 ln(𝑝 𝑀𝑡/𝑝 𝐾𝑡) + 𝛾 𝐿𝐻 ln(𝑝 𝐻𝑡/𝑝 𝐾𝑡) + 𝛾 𝐿𝑌ln𝑦𝑡 + 𝛾 𝐿𝑡 t
𝑆 𝑀𝑡 = 𝛽 𝑀 + 𝛾 𝑀𝐿 ln 𝑝 𝐿𝑡 𝑝 𝐾𝑡 + 𝛾 𝑀𝑀 ln(𝑝 𝑀𝑡/𝑝 𝐾𝑡) + 𝛾 𝑀𝐻 ln(𝑝 𝐻𝑡/𝑝 𝐾𝑡) + 𝛾 𝑀𝑌ln𝑦𝑡 + 𝛾 𝑀𝑡 t
𝑆 𝐻𝑡 = 𝛽 𝐻 + 𝛾 𝐻𝐿 ln(𝑝 𝐿𝑡/𝑝 𝐾𝑡) + 𝛾 𝐻𝑀 ln(𝑝 𝑀𝑡/𝑝 𝐾𝑡) + 𝛾 𝐻𝐻 ln(𝑝 𝐻𝑡/𝑝 𝐾𝑡) + 𝛾 𝐻𝑌ln𝑦𝑡 + 𝛾 𝐻𝑡 t

7. Vertically integrated internationalized production system
Engine
countries-
industries
delivering
factor inputs

8. Factor shares in a Vertically integrated Production Function
(VIPF)
We start with a input-output coefficient matrix A – drawn from the World Input
Output Database (WIOD)
Factor costs w in VIPF can be derived as
w=v(I-A)-1f
where there are S sectors; N countries; number of factors = F;
(I-A)-1 = 1+A+A2+A3+…. ; A is of order SN x SN; v direct factor requirements and f
is final demand
Next step in the process is to compute cost shares for three labour inputs (low,
medium and high skill) and capital.

9. Computation of factor shares within a VIPF
 WIOD is the main source of data for the computations.
 Flows of goods and services across 34 industries and 41 countries
 Capital and labour quantities and prices by three types of labour
 This study focuses on:
 14 manufacturing product groups
 20 advanced countries where last stage of production took place
 Cost-shares are obtained for production in 280 product groups
 13 year period: 1995-2007
 Basic procedure:
 For any given factor used in a particular VIPF, factor use is
aggregated across all industries and countries
 Factor prices are derived implicitly as values divided by quantities –
they reflect global average factor price
 Cost-minimization – decision making by industry-country where last
stage of production takes place. Decision is about how much quantities
to use of each factor, given exogenous global prices

10. Factor shares in 280 products (global value chains)
0
10
20
30
40
50
60
70
80
0 10 20 30 40 50 60 70 80
0
10
20
30
40
50
60
0 10 20 30 40 50 60
Figure 1 Factor shares in 280 global value chains of manufactures.
(a) Shares of capital (b) Shares of high-skilled labour
(c) Shares of medium-skilled labour (d) Shares of low-skilled labour
0
10
20
30
40
0 10 20 30 40
0
10
20
30
40
50
60
0 10 20 30 40 50 60

11. Baseline results
Table 3 Regression results, 1995-2007.
Pooled ISUR Fixed Effect ISUR Fixed Effect with year dummies
Variable Coef std. E coef std. E coef std. E
βL 0.1972 0.0115 *** 0.1566 0.0103 *** 0.1602 0.0103 ***
βM -0.0006 0.0132 -0.0623 0.0121 *** -0.0765 0.0122 ***
βH 0.0036 0.0110 -0.2065 0.0099 *** -0.2049 0.0100 ***
γLL 0.1310 0.0033 *** 0.0316 0.0024 *** 0.0275 0.0024 ***
γLM -0.1125 0.0028 *** 0.0109 0.0024 *** 0.0116 0.0024 ***
γLH -0.0002 0.0022 -0.0047 0.0018 ** -0.0016 0.0019
γMM 0.2514 0.0053 *** 0.0743 0.0047 *** 0.0771 0.0049 ***
γMH -0.0693 0.0046 *** -0.0096 0.0038 ** -0.0121 0.0039 **
γHH 0.0809 0.0051 *** 0.0655 0.0038 *** 0.0650 0.0038 ***
γLY -0.0007 0.0007 -0.0005 0.0006 -0.0012 0.0005 *
γMY -0.0024 0.0006 *** -0.0022 0.0006 *** -0.0017 0.0006 **
γHY 0.0045 0.0004 *** 0.0020 0.0005 *** 0.0022 0.0005 ***
γLT -0.0026 0.0003 *** -0.0052 0.0001 *** -
γMT -0.0043 0.0003 *** -0.0016 0.0001 *** -
γHT 0.0037 0.0002 *** 0.0032 0.0001 *** -
Country Dummies NO YES YES
Product Dummies NO YES YES
Year Dummies NO NO YES
Number of observations 3258 3258 3258
R2
- LS 0.4237 0.9437 0.9467
R2
- MS 0.4320 0.9193 0.9215
R2
- HS 0.1650 0.8733 0.8748

12. Comments on the regression results
 Model is estimated using seemingly unrelated regression framework.
 Own and cross-price elasticities are all meaningful.
 Testing for the regularity conditions:
 Testing for the negative semi-definiteness of the Hessian matrix at the average cost
shares, the condition is satisfied in all regressions of the paper.
 Testing at specific observations, the condition is violated in 184 out of 3258 observations
in the sample.
 More importantly:
 Coefficient Ht is positive and significant.
 Coefficients for low and medium skill levels, the coefficients are negative and significant.
 This offers support for the proposition skill-biased technical change.
 Are these results robust to different specifications? The answer is, yes.

13. Cumulative factor bias in technical change, 1995-2007
Original model versus model with dummy variables

14. Results by product group
Table 5 Regression results for product groups, 1995-2007.
Light
manufacturing
Heavy
manufacturing
Machinery
and electronics
All
manufacturing
Variable
γLT -0.0056 -0.0047 -0.0054 -0.0052
0.0002***
0.0002***
0.0002***
0.0001***
γMT -0.0018 -0.0008 -0.0015 -0.0016
0.0002***
0.0002***
0.0002***
0.0001***
γHT 0.0038 0.0026 0.0031 0.0032
0.0002***
0.0001***
0.0001***
0.0001***
Obs. 1079 1090 1089 3258
R2
- LS 0.9495 0.9572 0.9472 0.9437
R2
- MS 0.9373 0.9216 0.9223 0.9193
R2
- HS 0.9006 0.8945 0.9004 0.8733
Implied FBTC over 12 years (% points)
L -6.73 -5.66 -6.43 -6.28
M -2.21 -0.98 -1.76 -1.89
H 4.54 3.08 3.69 3.87
K 4.39 3.56 4.50 4.29

15. Results for Model with quasi-fixed capital
Table 6 Alternative regression results with capital as quasi-fixed, 1995-2007.
Light
Manufacturing
Heavy
Manufacturing
Machinery
and Electronics
All
Manufacturing
Variable
γLT -0.0073 -0.0065 -0.0066 -0.0068
0.0003***
0.0002***
0.0003***
0.0001***
γMT 0.0000 0.0012 0.0003 0.0001
0.0002 0.0002***
0.0003 0.0001
Obs. 1079 1090 1089 3258
R2
- LS 0.9586 0.9699 0.9638 0.9603
R2
- MS 0.9645 0.9542 0.9422 0.9480
Implied FBTC over 12 years (% pts)
L -8.79 -7.82 -7.90 -8.21
M -0.04 1.45 0.31 0.11
H 8.83 6.38 7.60 8.11

16. Conclusions
 To identify factor bias in technical change, it is important to consider global value
chains and to model all inputs in production, domestic and foreign.
 The paper makes use of vertically integrated production functions that have factor
inputs across all countries
 Using WIOD data for 280 manufacturing goods, the paper finds definite bias in
technical change in favour of high-skilled labour and capital; and bias against low-
skilled capital.
 The findings are robust to alternative model specifications.

17. Discussion/comments
■ This makes a significant contribution to the debate surrounding the nature of bias in
technical change.
■ The paper also demonstrates how the newly available World Input Output Database
cane be used in modelling vertically integrated production systems that can
accommodate use of inputs across all countries.
■ I have no significant comments on this very well executed paper but will raise a couple
of analytical issues:
■ Use of a Leontief fixed coefficient input-output coefficient matrix A, which allows for no
substitution, to generate data that is then used in a estimating a translog cost function
and to provide estimates of elasticities of substitution.
■ Use of a single global factor price for three types of labour inputs.
■ The whole idea of offshoring is that low-skilled is cheaper in low-income countries
compared to that in high-income countries.
■ It is not generally possible to shift all low-skilled labour operations overseas. In that
case low-skilled labour may be used in different countries at different prices