# **B Data Appendix**

## **B.1 Computing Value Added Content**

As noted in the text, our measures of domestic content in foreign production and foreign content in domestic production can be motivated as an application of the ‘global value chain’ decomposition of final goods developed in Los, Timmer and de Vries (2015).<sup>60</sup> We briefly describe the computation here.

As in the main text, let _i, j ∈{_ 1 _,_ 2 _, . . . , C}_ denote countries and _s ∈{_ 1 _,_ 2 _, . . . , S}_ denote industries. The World Input-Output Database includes an input shipments matrix, _IIt_ , with ( _S × S_ ) dimensional block elements _IIijt_ ( _s, s_<sup>_′_</sup> ) that record input shipments from sector _s_ in country _i_ to sector _s_<sup>_′_</sup> in country _j_ . These matrices can easily be re-written in share form. Let _Aijt_ be a ( _S × S_ ) dimensional matrix with elements _Aijt_ ( _s, s_<sup>_′_</sup> ) = _IIijt_ ( _s, s_<sup>_′_</sup> ) _/Yj_ ( _s_<sup>_′_</sup> ), which record the share of inputs from sector _s_ in country _i_ used by sector _s_<sup>_′_</sup> in country _j_ as a share of gross output in sector _s_<sup>_′_</sup> in country _j_ . Then assemble blocks _Aijt_ into the global input-output matrix _At_ . The Leontief inverse of the global input-output matrix, [ _I − At_ ]<sup>_−_1</sup> , times any ( _SC ×_ 1) vector of final goods output equals yields the ( _SC ×_ 1) vector of gross output (from all countries and industries) required to produce those final goods.

Let _fit_ be the ( _S ×_ 1) vector of final goods produced in country _i_ , which are directly reported in the World Input-Output Database. Stack these into a ( _SC ×_ 1) vector _ft_ , and compute _Yt ≡_ [ _I − At_ ]<sup>_−_1</sup> _diag_ ( _ft_ ). Breaking this down, _Yt_ contains block elements _Yijt_ which are _S × S_ matrices describing output from country _i_ used (directly or indirectly) to produce final goods in country _j_ . Each sub-component _Yijt_ ( _s, s_<sup>_′_</sup> ) is the amount of output from industry _s_ in country _i_ used in producing final output in industry _s_<sup>_′_</sup> in country _j_ .

These output requirements can be translated into value-added content requirements if we know the value added to output ratios in each sector _s_ and source country _i_ : _Rit_ ( _s_ ). The total amount of value added from country _i_ embodied in country _j_ ’s production in a particular industry _x ∈S_ is: _V A_<sup>_j_</sup> _xit_<sup>_≡_�</sup> _s_<sup>_Rit_(</sup><sup>_s_)</sup><sup>_Yijt_(</sup><sup>_s, x_).We use these value added elements</sup> to construct proxies for country _i_ ’s domestic value added embodied in foreign production of each sector _s ∈S_ in trading partner _j_ = _i ∈C_ ( _DV A_<sup>_j_</sup> _sit_<sup>)andforeignvalueadded</sup> embodied in country _i_ ’s domestic production of _s_ ( _FV A_<sup>_i_</sup> _st_<sup>).Specifically,foragivengood</sup><sup>_x_,</sup> _DV A_<sup>_j_</sup> _xit_<sup>_≡V Aj_</sup> _xit_<sup>and</sup><sup>_FV Ai_</sup> _xt_<sup>_≡_�</sup> _c_ = _i∈C_<sup>_V A_</sup> _xct_<sup>_i_.</sup> We compute value added content using the disaggregated 40 country version of the WIOD data set. We then aggregate value-added content across EU countries to form the EU composite, because EU countries have common external tariffs and trade policy.

> 60The global value chain traces backward through the production chain from final goods to identify the sources of value added in those goods. This is different than the value-added export decomposition developed by Johnson and Noguera (2012), which traces value added forward through the production chain to determine where value added from each country is ultimately consumed. It is also different than the decomposition of gross exports advanced by Koopman, Wang and Wei (2014).

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