Is Technological Change Biased?
An Analysis based on
Global Production Functions
Marcel Timmer
Groningen Growth and Development Centre,
University of Groningen, The Netherlands
Tor Vergata, Rome, November 6, 2015.
The World input-output database (WIOD) project was funded by the European
Commission, Research Directorate General as part of the 7th Framework Programme,
Theme 8: Socio-Economic Sciences and Humanities. Grant Agreement no: 225 281
Two stylised macro-economic facts on factor incomes:
Increasing income share for capital.
Hollowing out of the middle of the labour income distribution
Relative wages cannot explain these, so consensus view that
“technical change is biased” (skill-, capital-, routine-bias……)
All studies based on cross-country/industry regressions of domestic
cost shares (Hijzen et al. EJ, 2005; Autor et al. REStat 2008; Michaels et
al REStat 2014; Goos et al AER 2014):
Motivation
However, there is internationally fragmentation of production processes:
offshoring
Problem: Bias in technical change might be observational equivalent to
offshoring as long as you only consider domestic factors of production (cf.
Feenstra and Hanson, Handbook of International Economics 2003).
The observed changes in factor income shares will be (partly) due to
offshoring driven by international factor price differences.
Motivation
Observational equivalence of
“biased technical change” and “offshoring”
Production (say car) requires three tasks to be fulfilled:
two low-skilled tasks (LS) and
one high-skilled (HS)
Each task requires one unit of labour. Wage HS is double the wage of LS (=1).
Initially all tasks are carried out domestically.
Cost shares in domestic production
Costs
Cost
shares Costs
Cost
shares Costs
Cost
shares
High-skilled 2 0.5 2 0.67 2 0.67
Low-skilled 2 0.5 1 0.33 1 0.33
Total 4 1.0 3 1.00 3 1.00
Initial
situation
After
offshoring After BTC
Observational equivalence of
“biased technical change” and “offshoring”
Production (say car) requires three tasks to be fulfilled:
two low-skilled tasks (LS) and
one high-skilled (HS)
Each task requires one unit of labour. Wage HS is double the wage of LS (=1).
Initially all tasks are carried out domestically. Two scenarios (wages remain):
1. offshore one LS task or
2. biased technical change (say labour requirement in the LS tasks halves)
Cost shares in domestic production
Costs
Cost
shares Costs
Cost
shares Costs
Cost
shares
High-skilled 2 0.5 2 0.67 2 0.67
Low-skilled 2 0.5 1 0.33 1 0.33
Total 4 1.0 3 1.00 3 1.00
Initial
situation
After
offshoring After BTC
With international fragmentation we need to adapt the standard
conceptualization of a production function:
FROM One-stage domestic production function:
Value added = F [K(dom), L(dom)], or
Gross output = G [K(dom), L(dom), Intermediate inputs]
TO Multi-stage global production function, which nets out intermediate inputs:
Final output = H [K(dom), K(foreign), L(dom), L(foreign)]
Current empirical studies rely on domestic production function and will not
provide accurate estimates of the factor bias in technological change
The need for global production functions
This paper
Approach
Derive factor cost shares in a global production function using the
global value chain approach (Timmer et al. JEP, 2014).
Model global factor prices
Econometrically estimate biases in technical change within
system of factor cost share equations
Findings:
Strong bias in TC against low-skilled labor and in favour of high-
skilled labour and capital.
Which is robust to alternative models and across different data
samples
But smaller than when measured with domestic data only
Production is based on combination of both domestic and foreign factors:
Final output = H [K(dom), K(for), L(dom), L(for)]
Global Value Chain (GVC) approach: trace all activities that are needed in
the production process, using a global Leontief input-output model
Starting point: a final product identified by “country-industry of
completion”. This is the country-industry where the last stage of production
takes place (before being sold to final user), e.g. GVC of cars from Germany.
Factor content of GVC determined by:
last stage: based on domestic industry-statistics of factor use
previous stages: proxied by tracing backward linkages using Leontief’s
trick in a global input-output model
The Global Value Chain approach to
production (Timmer et al. JEP, 2014)
The Global Value Chain approach to production
(Timmer et al. JEP, 2014)
Country 1Capital and
labour
Intermediate
goods
Domestic
intermediate
goods
Country 2Capital and
labour
Intermediate
goods
Domestic
intermediate
goods
Country 3Capital and
labour
Final goods
for domestic
and foreign
demand
VA by
L1
VA by
K1
VA by
L2
VA by
K2
VA by
L3
VA by
K3
Final output = H [K(dom), K(for), L(dom), L(for)]
The GVC accounting framework
G = v(I-A)-1F
Leontief’s trick:
compute value added
in all industries
associated to final
demand for a specific
product …
Industry
1 …
Industry
N …
Industry
1 …
Industry
N
Industry 1
…
Industry N
… …
Industry 1
…
Industry N
World
GDPTotal final output value
Final products of a global value chain,
Value
added
identified by country-industry of completion
Country 1 Country M
Value added from
country-industries
participating in
global value chains
Country 1
Country M
…
Country
1 …
Country
M
Industry
1 …
Industry
N …
Industry
1 …
Industry
N
Industry 1
…
Industry N
… …
Industry 1
…
Industry N
Use by country-industries Final use by countries
Total
use
Gross output
Country 1
Country
M
Supply from
country-
industries
Country 1 Country M
Value added by labour and capital
Input cost shares
of industries (A)
Factor cost shares of
final products (G)
v
F
FROM: World input-output table
TO: GVC cost-share table
Related recent literature in international trade using
the Input-Output methodology
Vertical specialisation in trade: Johnson and Noguera (2012, JIE) who
extended Hummels, Ishii and Yi (2001, JIE) into multi-regional setting.
Value added content of exports: Koopman, Wei and Zhang (2014, AER; Los,
Timmer and De Vries AER forthcoming) and Bems, Johnson and Yi (2011, AER)
Factor content of trade: Reimer (2006, JIE) and Trefler and Zhu (2010, JIE)
Length of production chains: Dietzenbacher and Romero (2007, IRSR) and
Antràs et al. (2012, AER)
G = v(I-A)-1F (after Leontief, 1936; text book see Miller and Blair, 2009)
The World Input-Output Database (www.wiod.org):
• Annual tables 1995-2011 including values of all flows of products across
industries and countries (A).
• Based on benchmark national supply- and use-tables combined with time-
series on output, value added and final demand (F) from National accounts,
and bilateral trade data from official statistical sources (by use category).
• 40 countries (EU27 + 13 major economies) + Rest of the world region;
35 industries; at basic prices, exchange rate converted into US$
• Time-series on factor inputs for each industry-country (v):
• hours worked and wages by three skill types (educational attainment levels)
• capital (tangible capital stocks as quantities and compensation as gross
value added minus labour income).
World Input-Output Database (WIOD)
DATA: World Input-Output Tables
World Input-Output Table (WIOT) represents flows of goods and
services across industries and countries (40 countries and rest-of-the -
world region), 1995-2008. Two data challenges in construction:
1. Times-series of input-output tables.
Based on harmonised official benchmark national supply and use
tables (34 industries and 59 product groups)
Adjusted to, and interpolated with, industry output and main final
demand time series from the National Accounts (RAS-like method)
2. Allocation of imports to three use categories
using improved BEC-classification (based on COMTRADE HS 6-
digit level) rather than standard proportionality assumption (Feenstra
and Jensen, 2012)
Breakdown of imports by country of origin, using bilateral trade
statistics on goods and services (export shares by mirroring imports)
GVCs in this study
588 GVCs (=21 x 28) ending in
21 advanced countries: 15 EU (Austria, Belgium, Denmark, Finland, France,
Germany, Greece, Ireland, Italy, Luxembourg, Netherlands,
Portugal, Spain, Sweden and United Kingdom)
6 non-EU (Australia, Canada, Japan, South Korea, Taiwan
and the United States).
and 28 sectors (ISIC rev 3, 2-digit
industries) include products from 14 manufacturing industries
and 14 services sectors
In base line model we look at 3 factors of
production: capital, high-skilled labour (college
and above) and low-skilled (other labour).
ISIC
rev.3
code
Industry name
15t16 Food, Beverages and Tobacco
17t18 Textiles and Textile Products
19 Leather, Leather Products and Footwear
20 Wood and Products of Wood and Cork
21t22 Pulp, Paper, Printing and Publishing
23 Coke, Refined Petroleum and Nuclear Fuel
24 Chemicals and Chemical Products
25 Rubber and Plastics
26 Other Non-Metallic Mineral
27t28 Basic Metals and Fabricated Metal
29 Machinery, Not elsewhere classified
30t33 Electrical and Optical Equipment
34t35 Transport Equipment
36t37 Manufacturing, Not elsewhere classified; Recycling
E Electricity, Gas and Water Supply
F Construction
50 Sale and Repair of Motor Vehicles and Motorcycles; Retail Sale of Fuel
51 Wholesale Trade, Except of Motor Vehicles and Motorcycles
52 Retail Trade and Repair, Except of Motor Vehicles and Motorcycles;
H Hotels and Restaurants
60 Inland Transport
61 Water Transport
62 Air Transport
63 Other Supporting Transport Activities
64 Post and Telecommunications
J Financial Intermediation
71t74 Renting of Machinery & Equipment and Other Business Activities
O Other Community, Social and Personal Services
Not included
AtB Agriculture, Hunting, Forestry and Fishing
C Mining and Quarrying
70 Real Estate Activities
L Public Administration and Defence; Compulsory Social Security
M Education
N Health and Social Work
P Private Households with Employed Persons
Kernel distributions
of changes in factor income
shares (between 1995-2007)
in 588 GVCs
-0.35 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.150
1
2
3
4
5
6
7
8
9
Changes in Non-College Labour Share (% points)
All Value Chains
-0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.250
5
10
15
Changes in High-skilled Labour Share (% points)
All Value Chains
-0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.40
1
2
3
4
5
6
7
Changes in Capital Share (% points)
All Value Chains
Capital High Skill
Low Skill
1995: 49% change -8%
1995: 37% change +3% 1995: 14% change +5%
Data
Annual changes in factor incomes and prices for sets of Global Value Chains.
The GVCs are identified by industry-country of last stage of production, that
is, ending in each of 28 sectors in each of 21 advanced nations.
The 28 sectors include 14 manufacturing industries and 14 services sectors
(ISIV rev 3, 2-digit industries)
For each GVC
Factor prices are weighted averages across countries-industries
participating in the GVC (and hence weights are different for each GVC)
Factor cost shares derived through GVC accounting for each GVC (with
Leontief transformation as outlined above )
In base line model we will look at 3 factors of production: capital, high-skilled
labour (college and above) and low-skilled (other labour).
All data from the World Input-Output Database (www.wiod.org)
Modelling of global factor prices
Modelling of offshoring along the lines of the model by Grossman and Rossi-
Hansberg (2008, AER)
Production of final good process is modelled a series of tasks to be carried out.
There are two types of tasks: low- (LS) and high-skilled (HS) tasks.
Tasks require the same factor input irrespective of location.
A firm can substitute between LS and HS tasks. But not among LS or HS tasks
(Leontief, such that we can sum hours worked of each type).
Modelling of global factor prices
Production of final good process is modelled a series of tasks to be carried out.
There are two types of tasks: low- (LS) and high-skilled (HS) tasks.
Tasks require the same factor input irrespective of location.
A firm can substitute between LS and HS tasks. But not among LS or HS tasks
(Leontief, such that we can sum hours worked of each type).
The firm can also offshore part of the LS tasks (costless). As LS wage is lower
abroad, a firm will always offshore up to the maximum possibility. This maximum
is determined exogenously by global coordination technologies (CT).
The factor prices facing the firm will be an average of domestic and foreign prices,
the weights depending on the amount of offshoring (which is exogenously given,
see above). As CT improves, global prices of LS will decline.
Factor-specific technical change symmetrically affects all workers of the same
type irrespective of their location. Hence it has no impact on global factor prices.
0
.05
.1.1
5.2
.25
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9Annual Changes in Factor Price (%)
Non-College High-Skilled
Capital
All Value Chains
Mean change:
LS: 2.3%
HS: 3.0%
K: 1.7%
Kernel distributions of changes in global factor prices
(annual average, 1995-2007)
Econometric methodology
Consider a cost-minimizing firm facing exogenous global factor prices. Under
these conditions, we can use a standard translog cost framework (following
Baltagi and Rich, JOE, 2005 and Hijzen et al. EJ, 2005), but now for a global
production function with factors 𝑖 ∈ 𝐹 .
For each GVC :
Bias in technical change is captured by 𝛾𝑖𝑇’s
ln𝐶 𝒑𝑡, 𝑦𝑡, 𝑡 = 𝛼 + 𝛽𝑖 ln𝑝𝑖𝑡𝑖∈𝐹
+1
2 𝛾𝑖𝑗 ln𝑝𝑖𝑡 ln𝑝𝑗𝑡𝑖∈𝐹𝑗∈𝐹
+𝛽𝑌 ln 𝑦𝑡 +1
2 𝛾𝑖𝑌 ln𝑝𝑖𝑡𝑖∈𝐹
ln𝑦𝑡 +1
2𝛾𝑌𝑌 ln 𝑦𝑡
2
+𝛽𝑇𝑡 +1
2 𝜸𝒊𝑻𝑡 ln𝑝𝑖𝑡𝑖∈𝐹
+1
2𝛾𝑇𝑇𝑡
2
Econometrics (continued)
Under standard assumptions cost share equations can be derived. In
baseline we have three factors and drop the equation for capital.
Constant returns to scale implies 𝛽𝑖𝑖∈𝐹 = 1, and 𝛾𝑖𝑗 = 0𝑗∈𝐹 for any
i. Without loss of generality we also impose symmetry such that
𝛾𝑖𝑗 = 𝛾𝑗𝑖. Finally, by definition: 𝛾𝑖𝑌𝑖∈𝐹 = 𝛾𝑖𝑇𝑖∈𝐹 = 0.
FBTC is modelled as linear trend. Alternative used is a set of time-
dummies (Baltagi and Griffin JPE 1988).
Fixed effects ISUR (incl. country and industry dummies).
𝑆𝐿𝑡 = 𝛽𝐿 + 𝛾𝐿𝐿 ln 𝑝𝐿𝑡 𝑝𝐾𝑡 +𝛾𝐿𝐻 ln(𝑝𝐻𝑡/𝑝𝐾𝑡) + 𝛾𝐿𝑌ln𝑦𝑡 + 𝛾𝐿𝑡 t 𝑆𝐻𝑡 = 𝛽𝐻 + 𝛾𝐻𝐿 ln(𝑝𝐿𝑡/𝑝𝐾𝑡) + 𝛾𝐻𝐻 ln(𝑝𝐻𝑡/𝑝𝐾𝑡) + 𝛾𝐻𝑌ln𝑦𝑡 + 𝛾𝐻𝑡 t
Are observations consistent with cost minimization behaviour?
Test whether H-diag(s)+ss’ is negative semi-definite, where H
refers to the symmetric matrix containing all 𝜎𝑖𝑗 of factors, and s is
a column vector of cost shares of each factor (Diewert and Wales,
1987).
In base line regression we found for less than 6% of the
observations positive eigenvalues.
Simpler test: evaluate only at average of cost shares. This is
satisfied in all regressions of the study.
Check on assumptions
underlying econometric model
Results: base line Benchmark Specification Year Dummies
Variables M S All M All
γLL 0.0838 0.1105 0.0918 0.0836 0.0912
0.0029*** 0.0039*** 0.0025*** 0.0029*** 0.0025***
γLH 0.0166 -0.0229 0.0001 0.0173 0.001
0.0025*** 0.0036*** 0.0023 0.0025*** 0.0023
γHH 0.0247 0.0477 0.0285 0.0241 0.0276
0.0029*** 0.0038*** 0.0023*** 0.0025*** 0.0025***
γLY -0.0049 -0.0053 -0.0058 -0.0052 -0.0062
0.0008*** 0.0015*** 0.0008*** 0.0008*** 0.0008***
γHY -0.0005 -0.0042 -0.0014 -0.0003 -0.001
0.0005 0.0009*** 0.0005** 0.0005 0.0005*
γLT -0.0072 -0.0064 -0.0067
0.0001*** 0.0002*** 0.0001***
γHT 0.0036 0.0037 0.0036
0.0001*** 0.0001*** 0.0001***
Obs. 3496 3503 6999 3496 6999
R2-LS 0.8546 0.8169 0.8208 0.8555 0.8213
R2-HS 0.8497 0.8484 0.8255 0.8511 0.8262
Implied BTC over 95-07, (% points)
L -8.64 -7.66 -8.10
H 4.35 4.39 4.35
K 4.29 3.27 3.75
Significance level: *: 0.1, **: 0.01, ***:0.001. All specifications exclude 2003.
All specifications use iterated seemingly unrelated regression (iSUR).
M: manufacturing value chains, S: service value chains, ALL=M+S.
Price and (Allen-Uzawa) substitution
elasticities in benchmark model
Price elasticities of demand of factor i w.r.t. price of j is given by
𝜀𝑖𝑗 = (𝛾𝑖𝑗𝑆𝑖𝑆𝑗+ 1)𝑆𝑗 (for 𝑖 ≠ 𝑗)
𝜀𝑖𝑖 =𝛾𝑖𝑖𝑠𝑖+ 𝑠𝑖 − 1
Implied Price Elasticity Elasticity of Substitution
(Allen Uzawa)
L H K L H K
Ben
ch
m
ark
- A
ll
L -0.345 0.169 0.177 - 1.002 0.464
H 0.453 -0.662 0.210 1.002 - 0.552
K 0.210 0.093 -0.303 0.464 0.552 -
Year-dummy model: cumulative factor bias in technological change
Factor-biased technical change,
all 24 sectors
-10
-8
-6
-4
-2
0
2
4
6
1995 1997 1999 2001 2003 2005 2007γLT
γHT
γKT
Capital 3.8%
High Skill 4.4%
Low Skill -8.1%
Benchmark Specification Last Stage Production
Variables M S All M S A
γLL 0.0838 0.1105 0.0918 0.0953 0.1163 0.0954
0.0029*** 0.0039*** 0.0025*** 0.0063*** 0.0060*** 0.0043***
γLH 0.0166 -0.0229 0.0001 -0.0144 -0.0370 -0.0149
0.0025*** 0.0036*** 0.0023 0.0060* 0.0058*** 0.0042***
γHH 0.0247 0.0477 0.0285 0.0459 0.0617 0.0423
0.0029*** 0.0038*** 0.0023*** 0.0060*** 0.0059*** 0.0041***
γLY -0.0049 -0.0053 -0.0058 -0.0133 -0.0180 -0.0148
0.0008*** 0.0015*** 0.0008*** 0.0017*** 0.0025*** 0.0015***
γHY -0.0005 -0.0042 -0.0014 -0.0056 -0.0056 -0.0052
0.0005 0.0009*** 0.0005** 0.0009*** 0.0014*** 0.0008***
γLT -0.0072 -0.0064 -0.0067 -0.0085 -0.0062 -0.0074
0.0001*** 0.0002*** 0.0001*** 0.0003*** 00004*** 0.0003***
γHT 0.0036 0.0037 0.0036 0.0044 0.0035 0.0039
0.0001*** 0.0001*** 0.0001*** 0.0002*** 0.0002*** 0.0001***
Obs. 3496 3503 6999 3452 3411 6863
R2-LS 0.8546 0.8169 0.8208 0.7447 0.7952 0.7648
R2-HS 0.8497 0.8484 0.8255 0.7881 0.8216 0.775
Implied BTC over 95-07, (% points)
L -8.64 -7.66 -8.10 -10.19 -7.39 -8.87
H 4.35 4.39 4.35 5.24 4.16 4.66
K 4.29 3.27 3.75 4.95 3.23 4.21
Last stage production Mimicking traditional estimation approach using only domestic
production data (last stage of GVC).
The difference with the benchmark indicates biases in traditional studies.
To identify factor bias in technical change one needs to model
production as Global value chains (GVCs) that have domestic and
foreign factor inputs.
Factor income shares and prices can be measured using the WIOD and
Leontief’s method.
We find in 588 GVCs of advanced countries for 1995-2007, on average:
Increase in income shares of high-skilled labour and capital, relative to
other labour.
Increase in “global” price of high-skilled labour relative to other labour,
and relative decline in price of capital.
Using cost-minimization framework, we find econometrically that there is
a bias in technical change in favour of high-skilled labour and capital.
This bias is smaller than when estimated on basis of domestic factor
inputs only (as done so far).
Concluding remarks
Timmer, Marcel P., Bart Los, Robert Stehrer and Gaaitzen J. de Vries (2013).
“Fragmentation, Incomes and Jobs. An Analysis of European
Competitiveness.” Economic Policy.
Los, B., M.P. Timmer and G.J. de Vries (2015), “How global are Global Value
Chains? A New Approach to Measure International Fragmentation”, Journal
of Regional Science.
Timmer, M.P., A.A. Erumban, B. Los, R. Stehrer and G.J. de Vries
(2014),"Slicing Up Global Value Chains", Journal of Economic
Perspectives.
Timmer, Marcel P., Erik Dietzenbacher, Bart Los, Robert Stehrer and
Gaaitzen J. de Vries (2015),“An Illustrated User Guide to the World Input-
Output Database: the Case of Global Automotive Production”. Review of
International Economics
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