Figure 6. Relative Growth: Markets and Products <!-- Start of picture text --> 260111 260111<br>100590 100590<br>710813 710813<br>270900 260112 270900 260112<br>20721 720712 17011190111 120100 20721 720712 17011190111 120100<br>230400 230400<br>20741 20741<br>281820 281820<br>470329 470329<br>240120 240120<br>170199 170199<br>88024020230 88024020230<br>870323 271000 870323 271000<br>-10 0 10 20 30 -10 0 10 20 30<br>World: Export Growth, 2006-2011(%) World: Export Growth, 2006-2011(%)<br>40 40<br>30 30<br>20 20<br>10 10<br>0 0<br>-10 -10<br><!-- End of picture text --> _Source:_ World Integrated Trade Solution; authors’ calculation.

A cross-country gravity model can be used to evaluate Brazil’s pairwise export relationships with its trading partners. The model uses bilateral export values between 2005 and 2010.<sup>4</sup> Based on a theorygrounded model, this exercise allows us to compare pairwise observed export relationships with the predicted value from the gravity equation. Figure 7 shows all bilateral trade relationships in the dataset of 181 countries (light grey dots). Brazil’s bilateral exports are colored in blue, and key trading partners are labeled according to their 3-digit ISO (International Organization for Standardization) code in red.

If an observation is above (below) the 45-degree line, the observed export relationship in the period is more (less) than what the gravity model predicts and the exporter is said to be overtrading (undertrading) with its trading partner. Controlling for size of trading partners, trade frictions, sample selection and firm heterogeneity, this analysis suggests that the country is trading above the predicted level with China and Russia. Interestingly, although the gap between actual and predicted exports with Russia is shrinking over time, the gap with China seems to have increased lately (table 3). On the other hand, Brazil trades less than what the model predicts with the United States, with actual exports lagging predicted exports by about 5 percent over most of this period.

> 4 Specifically, the model used bilateral exports for 181 countries for each year between 2005 and 2010. The gravity equation regresses observed bilateral exports against the following bilateral characteristics: distance, contiguity, common language, colony, common colonial power, as well as country of origin and country of destination fixed effects. This model also incorporates three innovations to the standard model. _First_ , a measure of remoteness is computed by summing distances weighted by the share of GDP of the destination in world GDP. This is to take note of the fact that relative distances matter greatly, alongside absolute distances. _Second_ , the model controls for zero trade flows with the use of the Heckman sample selection correction method. When observations with nonexistent bilateral trade are dropped, as ordinary least squares (OLS) does, the dependent variable is not really measuring bilateral trade, but one _contingent_ on an existing relationship. An important variable left out of the model therefore is the probability of being included in the sample, that is, having a nonzero trade flow. To the extent that the probability of selection is correlated with GDP or distance, this has the potential to bias OLS estimates. _Third_ , following Helpman, Melitz and Rubinstein (2008), the model controls for firm heterogeneity without using firm-level data, utilizing the fact that the features of marginal exporters can be inferred from the export destinations reached. With these steps, the gravity results are better grounded on modern trade theory.

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