the year 2012, which is available from the BEA. From the latter we impute a _K × K_ matrix by using product-sector concordance tables from UNCTAD. The obtained matrix will serve to compute input-output-repercussion indirect effects of trade policies on sensitive products.

# **3 Effects of pandemic-related trade policy measures on trade costs and imports**

We are interested in distinguishing between direct and indirect effects (i.e. through imported inputs) of the trade policy measures of interest during the time period January 2018-December 2021. For this, let us use _gjk,t_ to denote the import-value equivalent for importing country _j_ , product _k_ , and month _t_ . We will establish later how to estimate it. We postulate that _gjk,t_ is linearly composed of the direct effects associated with the four import- and (partner-)export-related policy measures which are collected in ∆ _jk,t_ , and with as many corresponding indirect effects.

Suppose a _JK × JK_ input-output matrix _H_ exists. This matrix is obtained from _H_ = _O_<sup>_⋆_</sup> _◦ M_<sup>_⋆_</sup> , where _M_<sup>_⋆_</sup> is a _JK × JK_ (block-diagonal) expenditure-shares matrix consisting of _J × J_ blocks of expenditure shares for each product _k_ (Eaton and Kortum, 2002; Caliendo and Parro, 2014). For this, start with _M_ , a _JK × J_ imports matrix. The diagonal elements (expenditure on domestic produce) can be predicted from exporter and importer fixed effects in a gravity equation per product, assuming domestic sales frictions are zero. The matrix _M_ is then row-normalized (dividing by aggregate expenditure by product) to obtain _M_<sup>_⋆_</sup> . _O_<sup>_⋆_</sup> , a _JK × JK_ input-output matrix is obtained after row-normalizing _O_<sup>ˆ</sup> = _COC_<sup>_′_</sup> , where _O_ in our case is the _S × S_ input-output matrix of the United States with sector number _S < K_ , and _C_ is a _K × S_ conversion matrix which associates products with sectors.<sup>2</sup> Assuming that an estimate of the (global country-product-pair) Leontieftype (at least pseudo-)inverse ( _IJK − H_ )<sup>_−_1</sup> exists, where _IJK_ is a ( _JK × JK_ ) identity matrix, we can define The latter is nothing else than ∆ _t_ + (<sup>�</sup><sup>_∞_</sup> _q_ =1<sup>_Hq_)∆</sup><sup>_t_,wherethefirsttermcapturestheindirect</sup> relevance of the application of policy measures in ∆ _t_ for each importer _j_ and product _k_ from other units (the same or other importers and the same or other products) in month _t_ . As ∆ _t_ is _JK ×_ 4, so is Λ _t_ , and the latter has typical row Λ _jk,t_ .

Using _ηk_ and _ξk_ for the 4 _×_ 1 parameter vectors on the columns of ∆ _jk,t_ and Λ _jk,t_ , respectively, we can define Conditional on the direct effects ∆ _jk,tηk_ , Λ _jk,tξk_ measures the indirect effects of the policy measures in ∆ _jk,tηk_ on _gjk,t_ .

We can estimate _gjk,t_ from bilateral product-level data on exports or imports _xijk,t_ , assuming a customary level-multiplicative or log-additive gravity model of product-level sales of country _i_ to _j_ in month _t_ :

> 2Conversion tables for traded products and various sector classifications are available from the United Nations Conference on Trade and Development.

3