from MFN tariffs, so that _t_<sup>_i,_</sup> _xjt_<sup>applied</sup> _− t_<sup>_i,MFN_</sup> _xt ≤_ 0 is the tariff preference granted by country _i_ to country _j_ in sector _x_ at date _t_ . Under this sign convention, more generous bilateral tariff preferences are more _negative_ and correspond equivalently to lower bilateral tariff levels.

# **2.2 Foreign Value Added in Domestic Production**

Thus far, we have focused on identifying the influence of domestic value-added in foreign production on tariffs, absorbing all variation in foreign value-added in domestic production via fixed effects. Now we turn to an alternative empirical specification to study these foreign value-added effects directly.

Returning to the non-reciprocal applied bilateral tariff in Equations (11) and (12), we can re-write the optimal bilateral tariff expression as: where _FG_<sup>_i_</sup> _xt_<sup>_≡pi_</sup> _xt_<sup>_q_</sup> _xt_<sup>_i_,</sup><sup>_γ_</sup> _xij_<sup>_IP≡_</sup> _ε_<sup>_i_</sup> _δx_<sup>_iγ_</sup> _xij_<sup>_FV A_</sup> _≡−_<sup><u>(1</u></sup> _ε_<sup>_−iδ_</sup> _<u>x</u>_<sup>_i_</sup> _<u>∗</u>_<sup><u>)</u></sup><sup>_εri_</sup> _<u>x∗</u>_<sup>,and</sup><sup>_γ_</sup> _xij_<sup>_DV A_</sup> _≡−_<sup><u>(1+</u></sup><sup>_δ_</sup> _ε_<sup>_i_</sup> _<u>xi</u>_<sup>_∗_</sup><sup><u>)</u></sup><sup>_εrj_</sup> _<u>xi</u>_ . _xj_<sup>_|λi_</sup> _xj_<sup>_|_,</sup> _xj_<sup>_|λi_</sup> _xj_<sup>_|_</sup> _xj_ Equation (18) breaks up the domestic political economy and foreign value added terms and collects imports with other observables to form three ratios. The first is the ratio of domestic final goods production ( _FG_ ) to bilateral imports, which we refer to as the inverse import penetration ratio (IP-Ratio for short). The second and third are the ratios of foreign value added and domestic value added to bilateral final goods imports, which we refer to as the FVA-Ratio and DVA-Ratio.<sup>31</sup> This ratio specification recognizes that the strength of domestic political economy and foreign value added forces varies bilaterally, due to variation in bilateral imports.

In taking Equation (18) to the data, we confront new econometric concerns. Each of the independent variables has imports in the denominator. Classical measurement error in imports then generates non-classical (multiplicative type) measurement error in the ratios. To deal with this problem, we replace the levels of each ratio with their logs.<sup>32</sup> Because an important component of the effect of FVA operates at the multilateral level, we also relax the set of fixed effects to use time-series variation, in addition to cross-sectional

> 31A subtle point is that import quantities are evaluated at exporter prices in the first two ratios and at importer prices in the third. We suppress this distinction in our empirical work, as we are not able to measure imports at different prices in the same data set that we use to construct the numerators.

> 32Intuitively, classical measurement error in imports is particularly influential over the value of the ratio when imports are small (equivalently, the ratio is large). Taking logs of the ratios down-weights variation among these large, poorly-measured observations.

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