There are a number of empirical approaches to controlling for MR in estimation. First, since MR terms are country-speci...c, they can be controlled for by including country ...xed e¤ects. This is not appropriate for our purposes as we want to identify the e¤ect of country-speci...c logistics quality. Second, some attempts have been made to control for MR by using price data to construct the appropriate price indices. Data limitations are among the problems with this method. As noted in Feenstra (2004), published price indices are typically stated relative to an arbitrary base period, making comparison of levels impossible. Furthermore, they tend to include too many non-tradeable goods and thus fail to capture the additional costs embedded in internationally traded goods (Anderson & van Wincoop, 2004). Third, Anderson & van Wincoop (2003) propose solving for a system of price indices together with the gravity equation, but this involves a potentially problematic customized non-linear program. The research community has shown that, while gravity models are popular in empirical trade, estimating the entire non-linear system is not.<sup>3</sup> Fourth, Baier & Bergstrand (2009) introduce a method by which the MR terms are approximated using a ...rst-order Taylor expansion, yielding a log-linear expression for MR which contains exogenous variables only. These approximated MR terms can then be included in a single linear equation. This approach has the advantage of yielding tractable comparative statics; in particular, the role of country size in determining the appropriate comparative static e¤ect is made explicit, while Baier & Bergstrand show that the approximation error associated with this method is small for the majority of country pairs.

# 2.1.2 Firm heterogeneity

Models of monopolistic competition with ...rms of heterogeneous productivity predict selection into export markets in the presence of ...xed costs of trade. The reason is that the least productive ...rms do not generate pro...ts su¢ cient to cover the ...xed costs incurred, preventing entry into overseas markets. As illustrated by HMR, this has at least two further implications. First, the impact of a change in a trade barrier a¤ects both the amount a given ...rm exports, the intensive margin, and the number of ...rms that export, the extensive margin. The latter is a ...rm selection e¤ect. ‘Traditional’gravity equations con‡ate these two e¤ects, whereas HMR’s method allows for their decomposition. Second, for ...xed costs su¢ ciently high, no ...rms in a given country may ...nd it pro...table to export to a particular destination. This is o¤ered as an explanation of the ‘zeros’observed in bilateral trade data: many country-pairs do not appear to trade at all. This is a country selection e¤ect, and it induces bias in traditional gravity estimates. HMR propose a two stage estimation procedure to construct controls for both of these e¤ects. In the procedure described below, we use the elements of their approach that allow us to control for the e¤ects of ...rm heterogeneity and simultaneously account for MR using the Baier & Bergstrand (2009,

> country than a large country” (p. 177).

> 3 Furthermore, this method is especially demanding when considering about 100 countries and allowing for asymmetries in trade frictions. Bergstrand, Egger & Larch (2007) have shown that the system solution can yield complex numbers.

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