PASS-THROUGH OF COMPETITORS’ EXCHANGE RATES 3 size, geographic proximity and industrial composition, and so might differ across Belgium, the US or other countries and is difficult to calibrate with available data. Nonetheless, indicative simulations suggest that the variable markup mechanism is still needed to explain estimates in the data.

**Bias in bilateral pass-through** One contribution of this paper is to show that simple measures of bilateral pass-through — defined in Section 2 as the response of import prices to producers’ relative costs, other things constant — are generally upward biased in a multi-country world. For the US this exacerbates the puzzle of low pass-through documented in the literature (see Burstein and Gopinath 2014 for a survey of recent literature).<sup>3</sup> That is, standard bilateral pass-through regressions suffer from omitted variable bias because competitors’ exchange rates also affect import prices and competitors’ exchange rates and bilateral exchange rates are generally positively correlated. In the example above, if the yen, the euro and Canadian dollar all appreciate at the same time against the USD in real terms and the Japanese car manufacturer raises prices in the US, it might appear that the Japanese producer is responding strongly to the yen appreciation, when in fact it is responding partially to the yen appreciation and partially to the appreciation of its competitors’ currencies. A corollary is that in order to better measure the direct effect of foreign producers’ costs on import prices, researchers can include competitors’ exchange rates (or a simpler proxy like the TWI excluding the bilateral rate) as an additional control.<sup>4</sup> Quantitatively, the bias in bilateral pass-through (PT) is about 7ppts, or around a third of bilateral PT in my sample of US import prices. However, its size depends on the estimate of pass-through of competitors’ RERs, the correlation of RERs and also their variances which means the size of the bias will likely vary across samples and countries.

**Competitors’ Prices** The main mechanism in the model works through changes in foreign competitors’ prices — I show that pass-through of foreign competitors’ prices is around 0.6 to import prices, and 0.16 to US producer prices. Quantitatively, the model is able to explain about a third of this for import prices and two-thirds for producer prices. As an extension in Section 6, I also show that importing firms respond particularly strongly to the prices of US firms in the same sector and, to a lesser extent, other compatriot firms’ prices. This is consistent with a general model of variable markups discussed in Section 2.

1.1. **Related Literature.** My empirical evidence and multi-country model are related to a broad class of models of incomplete pass-through surveyed in Burstein and Gopinath (2014), where a firm’s markup is falling in its price relative to some aggregate/sectoral price (described in Section 2).<sup>5</sup> An empirical role for competitors’ RERs is consistent with this broad class of models, so long as the aggregate/sectoral price is correlated with competitors’ exchange rates.

The results presented here are complementary to contemporaneous work by Auer and Schoenle (2016) and Amiti et al (2016). Using novel market share data, Auer and Schoenle (2016) show that in industry aggregation models and the BLS microdata, own cost pass-through is U-shaped in firm market shares, and competitors’ price pass-through is hump-shaped in firm market shares. Although Auer and Schoenle don’t discuss pass-through of competitors’ exchange rates — and I don’t discuss market shares — one might expect that many of the firms responding to competitors’ prices in Auer and Schoenle are the same firms responding to competitors’ RERs here.

Amiti et al (2016) use a new firm-level dataset matching Belgian domestic manufacturing prices, costs, imported intermediate input usage and competitors’ prices, which allows them to control for firm-level marginal costs, and instrument competitors’ prices (which they argue are endogenous due to the price-setting game). They find 2/3 cost pass-through and 1/3 competitors’ price pass-though into Belgian domestic manufacturing prices, with higher rates of competitors’ price pass-through in larger firms. They also find a 30% pass-through rate of the TWI into domestic prices, and use a calibrated model to argue that most of this is through the cost of intermediates. This is consistent with my finding of lower ER pass-through into the PPI after controlling for materials prices.

> 3Low bilateral pass-through is important because it underlies a disconnect between exchange rates and macroeconomic aggregates and, in many cases, a departure from the Law of One Price (Obstfeld and Rogoff 2000). Since Gopinath and Rigobon (2008) and Gopinath and Itskhoki (2010) found low pass-through conditional on a price change and over long horizons, research has focused on models including real rigidities.

> 4This finding is related, in an abstract sense, to Anderson and van Wincoop’s (2003) argument for the inclusion of “multilateral resistance” terms in gravity regressions to remove omitted variable bias due to aggregate price indices.

> 5Specific mechanisms include industry aggregation (AB), additive local distribution costs (Corsetti and Dedola 2005), nonCES demand (Melitz and Ottaviano 2008, Kimball 1995), consumer search (Alessandria 2009), and customers-as-capital (Drozd and Nosal 2012a). In the final two cases, the firm’s price can be written to reflect two forces: a marginal cost term and a second aggregate wage/price term.