STEVEN PENNINGS 4 The findings in this paper are also related to GI2011, who provide a range of evidence on the extent of real rigidities in pricing. One of their findings is a large response of import prices to the TWI (orthogonal to the bilateral RER), and another is sizable pass-through of import competitors’ prices, both of which are consistent with evidence presented here. This paper provides a more systematic analysis by deriving a measure of competitors’ RERs from theory, comparing magnitudes in theory vs data, considering implications for bilateral pass-through, examining pass-through to US producer prices (as predicted by theory) and testing the mechanism which works through foreign competitors’ prices (rather than all competitors’ prices).<sup>6</sup>

# 2. Simple Model

As a guide to the empirical work, I begin with a simple reduced-form model based on Burstein and Gopinath (2014) and GI2011 where the firm’s markup depends on a sectoral/aggregate price, and then extended it to a three-country setting. The model produces four key qualitative predictions which are outlined in Testable Predictions 1-4, for which I find supporting evidence in BLS microdata in Section 3 (results summarized in Box 1). In Section 4, I show how a similar specification comes from a multi-country version of AB, which I use to produce quantitative estimates from regressions run on simulated data.

2.1. **Model set-up.** There are three countries: the US, country i and some other third country c (this could be the “competitor” country). Let pijk be the log of the price of an imported good k produced in country i, in sector j, at the docks in the US (I suppress the firm/good index k and the sector j), relative to some numeraire. Then:

# pi = μi + mci

where μi ≈ μ ̄i − Γ [pi − p] is the log markup, which I assume is related to the relative price pi − p, with reduced form elasticity Γ ≥ 0 (which might depend on country-, sector- or firm-specific characteristics). That is, the higher is the price of good k from country i relative to the sectoral/aggregate price index p, the lower the desired markup. In the AB model (in Section 4), higher prices relative to the sectoral/aggregate price reduce market shares which reduce desired markups, though the microfoundation varies across models (I ̄ assume the firm’s direct contribution to p here is small). Let the log marginal cost be mci = mci +(1 − φus − φc)(wi − ai) + φusvus + φcvc which depends on unit labor costs (wi − ai) in the country of production with weight 1 − φus − φc and the price of imported intermediate inputs from the US (vus) or the third country (vc). For simplicity, assume intermediate inputs produced in c or the US and sold in i are produced by competitive firms using only labor with constant returns to scale such that vc = wc − ac and vus = wus − aus. Substituting and suppressing constants, the expression becomes: Adding Γpi to both sides, rearranging, and subtracting log US unit labor costs (ULC, wus − aus) from both sides yields the pricing Equation 2.

Where reri = wi − ai − [wus − aus] is the log real bilateral ULC-based real exchange rate, and pRi, pR and vRc are respectively the log real import price of the firm, the sectoral/aggregate price and imported intermediate price (from c), relative to US ULC. Define rerc = wc − ac − [wus − aus] as the log bilateral real exchange rate of the US with the other third country (the competitors’ RER). The two real exchange rate movements reri, rerc are the only shocks in the model.<sup>7</sup>

> 6See Section 3.6 for a comparison with GI2011 and the online appendix for a discussion of how well the TWI proxies for competitors’ RERs (they have a correlation of around 0.8). Using a model with a translog demand function, Bergin and Feenstra (2009) show that a change in the USD-Mexican peso exchange rate can affect the price of Chinese goods imported to the US, but they only discuss this result in passing.

> 7Relative to Burstein and Gopinath (2014) I assume marginal costs do not depend on output, and I only consider variations in the real exchange rate. Intermediate inputs from the US drop out of Equation 2 because they move one-for-one with US ULC. An increase the RER represents an appreciation of country i or c’s exchange rate relative to the US.