STEVEN PENNINGS 12 the US. The other terms on the right hand side are the “competitors’ exchange rates” which appear very naturally in the model. In Equation 14 (producer prices) there is no bilateral exchange rate, so all of the exchange rates are those of foreign competitors.<sup>16</sup> With many countries, the specification in Equations 13 and 14 will have a large number of estimated coefficients — and so each coefficient is likely to be estimated imprecisely. Instead, I use a summary measure to capture the effects of competitors’ RERs. Let β<sup> ̃</sup> C =<sup>�</sup> i<sup>′</sup> =US,i<sup>βi′jk(equivalentlyβ ̃</sup> C<sup>P P I</sup> =<sup>�</sup> i=US<sup>β</sup> ijk<sup>P P I</sup> for producer prices). It turns out that the relative size each competitors’ structural β -coefficient is almost identical to the country’s sectoral import share, i.e βi<sup>P P I′</sup> jk<sup>/ �</sup> i=US<sup>β</sup> ijk<sup>P P I</sup> ≈ Si<sup>C,P P I′</sup> j . In the three-country model for PPI for example, βi<sup>P P I′</sup> jk<sup>/ �</sup> i=US<sup>β</sup> ijk<sup>P P I</sup> and Si<sup>C,P P I′</sup> j line up almost exactly along the 45-degree line with a correlation of over 98% (the analogous figure for import prices is similar). As such, I can replace βi′jkwith β<sup> ̃</sup> C Si<sup>C′</sup> j<sup>andβ</sup> i<sup>P P I′</sup> jk<sup>withβ ̃</sup> C<sup>P P I</sup> Si<sup>C,P P I′</sup> j which yields Equations 15 and 16, which can be taken to the data. The final term in each of these equations is the import-weight exchange rate for the sector, which excludes the bilateral RER for the import price Equation 15 (with weights rescaled so they add to one). This is a measure that I construct in each sector in the model and in every 6 digit NAICS manufacturing sector in the data (see Appendix B).

To generate estimates of pass-through of competitors’ exchange rates in the model (to compare to the data) I first solve the full model in steady state and calculate the set of structural β coefficients. Then I draw a sample of exchange rates, use Equation 13 and 14 to generate a vector of firm-level prices, and then estimate variants of Equations 15 and 16 on the simulated data (sampling in proportion to size) — see the online appendix for further details.<sup>17</sup> 4.1. **Calibration.** The calibration of the model is challenging due to the absence of microdata on quantities (and hence sector shares) in the BLS data on the demand side, as well as the lack of firm-specific information in the many producing countries on the supply side (for example the share of intermediates in costs, and their source). Moreover, there is also the challenge of defining a “sector” — which will determine the number of firms as well as elasticities of demand — both of which are important determinants of the firms’ pricing behavior. In all reasonable calibrations the model has difficulty matching the extreme degree of incomplete pass-through estimated in the data. However, these are common problems in the literature and my parameters are reasonably standard, though these challenges should be noted as a caveat.

There are two calibrations of the model used in the paper (parameters are listed in Table 2). The first is the baseline asymmetric calibration with 11 countries (US+10), which is the closest to the estimated data. In each sector, I keep the number of US firms the same as AB (KUS = 20), but set K = 3 firms per foreign

> 16One can also derive a related structural pass-through equation with firm market shares on the LHS. I don’t have data on firm-level market shares to test this relationship, but it is an interesting area for future research. A previous draft of this paper also investigated the relation between changes in country shares and exchange rates, with mixed results. As mentioned in the introduction, this model belongs to a class of model that has difficulty in matching both short-run and long-run responses of quantities to exchange rates.

> 17Amiti et al (2016) argue that OLS estimation of the response to competitors’ prices in structural equations like Equations 2 or 12 will be biased due to the correlation between unobserved idiosyncratic demand shocks (in the error term) and competitors’ prices via the price setting game. They provide several instruments for competitors’ prices, one of which is foreign exchange rates, which they argue will be uncorrelated with local demand shocks. This suggests that estimated pass-through of competitors’ exchange rates in Equations 15 and 16 will also be unbiased, because exchange rates are plausibly exogenous to firm/sector level demand shocks. While estimates of pass-through competitors’ prices such as those in Equation 8 might be biased in theory, the IV and OLS estimates of the coefficient on ∆p−it in Amiti et al (2016) are fairly close, which suggests that in practice the size of the bias is reasonably small.