Appendix 1: List of manufacturing industries contained in the WIOD
|
No.
|
NACE
|
Description
|
|---|
|
1
|
15–16
|
Food, beverages and tobacco
|
|
2
|
17–18
|
Textiles and textile products
|
|
19
|
Leather, leather and footwear
|
|
3
|
20
|
Wood and products of wood and cork
|
|
4
|
21–22
|
Pulp, paper, paper, printing and publishing
|
|
5
|
23
|
Coke, refined petroleum and nuclear fuel
|
|
6
|
24
|
Chemicals and chemical products
|
|
7
|
25
|
Rubber and plastics
|
|
8
|
26
|
Other non-metallic mineral
|
|
9
|
27–28
|
Basic metals and fabricated metal
|
|
10
|
29
|
Machinery, nec
|
|
11
|
30–33
|
Electrical and optical equipment
|
|
12
|
34–35
|
Transport equipment
|
|
13
|
36–37
|
Manufacturing, nec; recycling
|
- Textiles (17–18) and leather (19) had to be combined for calculation of imported value added
Appendix 2: Derivation of offshoring measure: share of imported value added
Our indicator for offshoring should describe the value of imported value added, i.e. value added purchased abroad, relative to the total value of industry’s production. The difference between one and the indicator’s value should thus be the share of value which is added domestically. The indicator should also account for the cases in which imported intermediate goods (e.g. German motor imports from the Czech Republic) contain parts which were previously produced domestically (e.g. the crankshaft produced in Germany). These parts should be classified as domestic and not as foreign value added.
The indicator is derived from the WIOD. The WIOD assumes that each industry (s, r = 1, …, S) in each country (i, j, k = 1, …, L) produces a single, homogenous good, which is different from the same industry’s goods produced in other countries. Hence, there are LS different goods produced in the world.
The input–output tables of the WIOD consist of four components. (i) The intermediate inputs matrix, W, of dimension (LS × LS), describes the values of bilateral trade in intermediate goods between all countries of the world. The element in row is and column jr describes the value of intermediate goods which industry r in country j purchases from industry s in country i. (ii) The final use matrix, C, of dimension (LS × L), describes the value of all LS goods sold to final users (private households, investors, the government, and changes in inventories) in all L countries. (iii) The vector y of dimension (1 × LS) describes the value added input of each industry, and (iv) the (1 × LS) vector of total production, p, describes the total output of each industry.
An industry’s total production (p) can be formally described as
$$ \mathop p\nolimits_{is} = \sum\limits_{j = 1}^{L} {\sum\limits_{r = 1}^{S} {\mathop w\nolimits_{is,jr} } } + \sum\limits_{j = 1}^{L} {\mathop c\nolimits_{is,j} } , $$
(3)
where p
is
is the sum of a product’s intermediate use and final use. Note that a matrix’ cell is denoted by a small letter here. Alternatively, total production can be written as
$$ \mathop p\nolimits_{is} = \sum\limits_{j = 1}^{L} {\sum\limits_{r = 1}^{S} {\mathop w\nolimits_{jr,is} } } + \mathop y\nolimits_{is} , $$
(4)
where p
is
is the sum of intermediate inputs and the industry’s value added.
Equations (3) and (4) can be combined using matrix notation:
$$ {\mathbf{p}} = {\mathbf{Ap}} + {\mathbf{CI}}_{{\mathbf{L}}} $$
(5)
$$ = {\mathbf{W}}^{{\mathbf{'}}} {\mathbf{I}}_{{{\mathbf{LS}}}} + {\mathbf{y}}. $$
(6)
where p = (p
11, …, p
1S
, p
21, …, p
2s
, …, p
L1, …, p
LS
) is the (LS × 1) vector of all production values and y = (y
11, …, y
1S
, y
21, …, y
2s
, …, y
L1, …, y
LS
) is the (LS × 1) vector of value added in all industries. In Eq. (5), matrix C is multiplied by the identity vector I
L
in order to aggregate across all countries that consume the respective good. The (LS × LS) matrix of input coefficients, A, is constructed by dividing each element of the W matrix along the vertical by the total output of that industry:
$$ {\mathbf{\rm A}} = {\mathbf{W}} \times {\text{diag}}{\mathbf{(p}}^{{ - {\mathbf{1}}}} {\mathbf{)}}, $$
(7)
Its elements a
is,jr
= w
is,jr
/p
jr
denote how many cents industry r in country j purchases from country i in order to produce one unit of output.
Matrix A contains input coefficients for a representative step in production. However, the production of many goods requires more than one production step, so that we have attribute the value added contributions of all intermediate inputs to their countries of origin as well. Ultimately, we would like to derive how many cents of value added each industry in each country contributes to one dollar of each final good. To that end, Eqs. (3) and (4) are rewritten so that the relationships between output and final use, and between output and value added can be used to derive a direct relationship between final use and value added:
$$ {\mathbf{p}} = {\mathbf{(I}}_{{{\mathbf{LS}}}} - {\mathbf{A)}}^{{ - {\mathbf{1}}}} \times {\mathbf{C}} \times {\mathbf{I}}_{{\mathbf{L}}} , $$
(8)
$$ {\mathbf{y}} = {\mathbf{[}}{\text{diag}}{\mathbf{(I}}_{{{\mathbf{LS}}}} - {\mathbf{A}}^{{\prime }} \times {\mathbf{I}}_{{\mathbf{L}}} {\mathbf{)]}} \times {\mathbf{p}}, $$
(9)
$$ {\mathbf{y}} = {\mathbf{V}} \times {\mathbf{p}}, $$
(10)
where V = diag(I
LS
− A′ × I
LS
).
Equation (8) describes the relationship between final use and output. Matrix B = (I
LS − A)−1 is the Leontief inverse; its elements b
is,jr
describe by how much of the output of industry s in country i contributes to each dollar of the final good of industry r from country j.
Equation (9), which is presented in a simplified way in Eq. (10), describes the relationship between value added and output. The diagonal elements of the (LS × LS) matrix V, v
ir
= y
ir
/p
ir
, denote the fraction of value added in total output of industry jr.Footnote 11 Substituting Eq. (8) into Eq. (10) results in:
$$ {\mathbf{y}} = {\mathbf{[V}} \times {\mathbf{(I}}_{{{\mathbf{LS}}}} {\mathbf{{-}A)}}^{{ - {\mathbf{1}}}} {\mathbf{]}} \times {\mathbf{C}} \times {\mathbf{I}}_{{\mathbf{L}}} , $$
(11)
$$ {\mathbf{y}} = {\mathbf{M}} \times {\mathbf{C}} \times {\mathbf{I}}_{{\mathbf{L}}} , $$
(12)
Matrix M = V × (I
LS − A)−1 contains all the information needed for the estimations. It describes the contribution of value added by all industries in all countries to one dollar of final good production. Its elements m
is,jr
denote how many cents industry is contributes to each dollar of the final good produced by industry jr.
For our estimations, we calculate a measure of narrow offshoring, OFF, for each German industry, i.e. the share of value added in industry production, which is imported from the same industry in all other countries. Specifically, we sum over the relevant elements of M:
$$ OFF = \sum\limits_{i \ne j} {m_{is,js} } , $$
where s is the respective industry, i is the country where the imported value added stems from, and j denotes Germany.
Appendix 3: Variable definitions and summary statistics
The econometric analysis is based on the German Socio-Economic Panel (SOEP), waves 1999–2007. We use all SOEP samples for the analysis. Yearly industry level information about trade and offshoring is merged with the SOEP on basis of industry classification provided in the SOEP (NACE 1.1). Variables are defined as follows (SOEP variable names are mentioned in parentheses).
See Tables 6 and 7.
Table 6 Variable definitions
Table 7 Summary statistics
Appendix 4: Results of the random effects probit models
See Tables 8 and 9.
Table 8 Random effects probit regression on dummy for unemployment in next period, 1999–2007, linear measure for employment duration
Table 9 Random effects probit regression on dummy for unemployment in next period, 1999–2007, dummies for groups of employment duration