any short-run variation in trade shares across sectors, and reduce the impact of zero observations. Having estimated equation (25) for each industry, we then obtain the predicted logarithm of industry _i_ exports to GDP from country _c_ to each of its trading partners indexed by _d_ , _LogX_<sup>�</sup> _icd_ . In order to construct the predicted overall industry _i_ exports as a share of GDP from country _c_ , we then take the exponential of the predicted bilateral log of trade, and sum over the trading partner countries _d_ = 1 _, ..., C_ , exactly as in Frankel and Romer (1999): That is, predicted total trade as a share of GDP for each industry and country is the sum of the predicted bilateral trade to GDP over all trading partners. This exercise extends and modifies the Frankel and Romer (1999) methodology in two respects. First, and most importantly, it constructs the Frankel and Romer (1999) predicted trade measures by industry. And second, rather than looking at total trade, it looks solely at exports.

Do and Levchenko (2007) discuss and justify this strategy at length. As mentioned above, the objective is to predict trade patterns, not trade volumes. How can this procedure yield different predictions for _X_<sup>ˆ</sup> _ic_ across sectors if all of the geographical characteristics on the right-hand side of equation (25) do not vary by sector? Note that the procedure estimates an individual gravity equation for each sector. Thus, crucially for this strategy, if the vector of estimated gravity coefficients h _i_ differs across sectors, so will the predicted total exports _X_<sup>ˆ</sup> _ic_ across sectors _i_ within the same country. Indeed, Do and Levchenko (2007) show that the variation in these coefficients across sectors is substantial, generating variation in predicted trade patterns across countries.

There is another potentially important issue, namely the zero trade observations. In our gravity sample, only about two-thirds of the possible exporter-importer pairs record positive exports, in any sector. At the level of individual industry, on average only a third of possible country-pairs have strictly positive exports, in spite of the coarse level of aggregation.<sup>10</sup> We follow the Do and Levchenko (2007) procedure, and deal with zero observations in two ways. First, following the large majority of gravity studies, we take logs of trade values, and thus their baseline gravity estimation procedure ignores zeros. However, instead of predicting in-sample, we use the estimated gravity model to predict out-of-sample. Thus, for those observations that are zero or missing and are not used in the actual estimation, we still predict trade.<sup>11</sup> In the second approach, we instead estimate the gravity regression in levels using the Poisson pseudo-maximum likelihood estimator suggested by (Santos Silva and Tenreyro, 2006). The advantage of this procedure is that it actually includes zero observations in the estimation, and can predict both zero and non- zero trade values in-sample

> 10These two calculations make the common assumption that missing trade observations represent zeros (see Helpman et al., 2008).

> 11More precisely, for a given exporter-importer pair, we predict bilateral exports out-of-sample for all 61 sectors as long as there is any bilateral exports for that country pair in at least one of the 61 sectors.

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