extract SITC categories corresponding to final goods using the BEC classification, and then concord SITC categories to our WIOD industries via ISIC industries.<sup>74</sup>

**Estimation and Results** Using these instruments, we re-estimate the linear specifications in Table 5 and present the results in Table C3, along with the baseline OLS estimates from Table 5 for reference. In Columns (1) and (3), we instrument for the three ratios on the right hand side of Equation 19 by constructing the ratio of the instruments for the numerator in each ratio to the instrument for final goods imports.<sup>75</sup> In columns (2) and (4), we do the same for DVA and instrument for final goods imports to identify _γ_<sup>_IP_</sup> + _γ_<sup>_FV A_</sup> .

In Panel A, IV estimates are negative for domestic value added, negative for foreign value added, and positive for final goods production. These are consistent with the OLS sign estimates. In terms of magnitudes, the IV point estimates tend to move away from zero relative to OLS. That said, the 2SLS point estimates are substantially less precise than OLS. Nonetheless, one can reject the null that the import penetration and FVA ratios are exogenous in a Durbin-Wu-Hausman endogeneity test.<sup>76</sup> In Panel B, we replicate the IV estimates for the sample excluding RTAs. The IV estimates here also broadly confirm the OLS estimates, though the details are more nuanced. The point estimate on DVA doesn’t move between the OLS and IV estimates, but becomes insignificantly different than zero in the IV estimation due to the loss of precision. We cannot reject that DVA is exogenous in a Durbin-Wu-Hausman endogeneity test. Given our prior results concerning the role of DVA – both in Panel A and in previous IV-specifications, we see no reason to change our views on the sign of the DVA effect based on these results. Turning to FVA, the coefficient on FVA becomes negative and significant when we instrument here. This brings the FVA results in this sub-sample more in line with the full sample, including RTAs. Further, we can easily reject exogeneity of the FVA-Ratio here.

Together with our previous IV results, these results corroborate our interpretation of the OLS estimates as indicative of causal relationships. In particular, the new concern in this specification concerns the role of FVA. Recalling that the principal endogeneity concern is that tariffs raise FVA and thus bias the the FVA coefficient upward (toward zero/positive values), we argued in the text that our OLS estimates likely understate FVA effects. The IV results are broadly consistent with this interpretation. That said, we are reluctant to take the magnitude of the FVA estimate too seriously here due to the wide confidence interval.

One final point to note is that we report two-stage least squares standard errors (clustered by importer-exporter pair) in the table. The appropriateness 2SLS standard errors is not obvious: the high correlations among endogenous variables and therefore the instruments we use for them could give rise to weak instrument problems. Therefore, in the table, we report various weak-IV statistics to gauge the reasonableness of the 2SLS standard errors.

> 74Because country definitions have changed over time, we concord historical countries to modern entities as best we can. For example, Germany today corresponds most closely to the former Federal Republic of Germany. Russia today corresponds to the former USSR. And so on. Further, more trade flows in the NBER-UN data are zero in 1970 than are zero today, likely due both to true changes from zeros to positive values over time and differences in reporting thresholds and/or missing data in the two data sources. In order to use the whole sample, we replace zeros in 1970 with the smallest values observed in the data.

> 75Including the instruments separately, without imposing this ratio restriction, yields similar results.

> 76Testing the exogeneity of the DVA-Ratio alone, one cannot reject exogeneity.

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