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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