PASS-THROUGH OF COMPETITORS’ EXCHANGE RATES 21 unfortunately data on sector shares for US manufacturing are unavailable below the 6 digit level, and the number of prices in each industry is small (important for calculating competitors’ prices).

The competitors’ RER variable has a correlation with the Federal Reserve’s Broad Trade Weighted Index of about 0.8 (calculated over the life of the good for either import or producer price samples), which might be considered an alternative measure of competitors’ RER (and was used in GI2011). See the online appendix for a discussion.

B.4. **Construction of competitors’ prices.** In the main specification, I construct an index of foreign competitors’ prices using import price microdata from the same NAICS 6 sector. For regressions where the dependent variable is an import price, the set of foreign competitors will change depending on the country producing the good, resulting in a different price index for each country × sector. That is, the foreign competitors’ price index for a German firm includes the prices of imports from all other countries selling in the US in the same sector (excluding all other German firms). For regressions where the dependent variable is a US producer price, the foreign price index includes the prices of all foreign producers in the same sector.

The index is constructed using a similar method as that in GI2011: I take the average growth rate of competitors’ prices in the same sector in the month, and cumulate growth rates to get an index. As the BLS samples according to size, no weighting adjustment is needed. Alternative methods produce similar results.<sup>29</sup> As an extension in Section 6, I consider pass-through of the prices of two other types of competitors in the same NAICS 6d sector: (i) other firms from the same country (compatriots), and (ii) US firms. Other compatriots’ prices are constructed from BLS microdata in a similar manner to foreign competitors’ prices and aggregate US producer price indices by NAICS 6d sector are taken from the BLS website.

# Appendix C. Intermediate inputs in the quantitative model.

In a model with imported intermediate inputs, Equation 11 is replaced by Equation 17, where Vc is the price of imported intermediates from country c, and φi,c is the input weight in the production function of inputs from country c used in production in country i and φi,i = 1 −<sup>�</sup> c=i<sup>φi,cistheweightondomestic</sup> costs. In the model in the main text φi,c = 0 ∀i=c.

I assume that imported intermediates are produced in competitive markets only with labor, such that Vc = Wc/Ac (κ is a normalizing constant). Log-linearizing and rearranging, with aijk = ΓAB(sijk)[ρ − 1]/ [1 + ΓAB(sijk)[1 − sijk][ρ − 1]] and bijk = [1 + ΓAB(sijk)[1 − sijk][ρ − 1]]<sup>−1</sup> as in the main text: One can then solve of the system of prices as in the model without imported intermediates (in the main text and online appendix), where now the “structural β-coefficients” will be a combination of effects through competitors’ prices, and effects through imported intermediates.

C.1. **Calibration.** Across major US trade partners, OECD data suggests the average imported intermediate share is 0.32 for manufacturing exports (Figure 4), though there is substantial variation across countries. In general, larger or more closed countries/regions have a lower intermediate share, with the US, EU, Brazil and Japan all having manufacturing intermediate shares around half the cross-country average. Table 5

> 29As a robustness test, I also constructed an index which uses the average of index values for each good Ij,c,tsector = ��c<sup>′</sup> =c<sup>I</sup> i,j,c<sup>good′</sup> ,t<sup>/ �</sup> c<sup>′</sup> =c<sup>I</sup> i,j,c<sup>good′</sup> ,t−1� Ij,c,t<sup>sector</sup> −1<sup>whichisclosertotheBLS’spre-1997methodologyandproducesalmostidentical</sup> results. Another issue is that around 40% of product-month prices are missing in the import price program (Nakamura and Steinsson 2012). I follow the BLS methodology (and that of Nakamura and Steinsson 2012) by pulling forward missing prices (replacing missing price pi,t with pi,t−1 for each good i). Nakamura and Steinsson (2012) argue that neither pulling prices, nor reweighing indices (as the BLS has done since 1997), substantially affects long-run pass-through.