since their inclusion does not add any explanatory power to the model (see, for example, section 2.2 of Baltagi, 2001). More precisely, in a model with country fixed effects, a landlocked dummy is simply an average of the fixed effects coefficients of landlocked countries. The problem is similar to a violation of the full rank assumption—if, controlling for all other factors, country _i_ trades less with its partners, is it because it is landlocked or due to other unobserved country characteristics (country fixed effect)? In this case, dropping the landlocked dummy will simply scale the country fixed effect coefficient without reducing the explanatory power of the model. Therefore, excluding the island and landlocked dummies allows their effects to be absorbed by the importer and exporter fixed effects without any loss of model predictive power, while including them reduces efficiency and could lead to multicollinearity problems.

Our dataset is an unbalanced panel of 13,317 observations for 55 importers and 169 exporters for the years 2000 through 2002. All values are expressed in current US dollars. The GDP and real exchange rate series were collected from the World Development Indicators (WDI) data provided by the World Bank, distance and control dummies from Centre d’Etudes Prospectives et d’Informations Internationales (CEPII), and the PTA variable was obtained from the PTA database developed in section 3.1. The dependent variables—log of total bilateral imports and log of preferential bilateral imports—were calculated from the dataset discussed in section 3.2 by summing trade flows by country of origin and destination across all tariff lines for the former and across tariff lines with the MFN duty above 3 percent for the latter. Following earlier discussion, the model was estimated using importer and exporter fixed effects—a specification supported both by theoretical considerations and empirical tests.<sup>31</sup> Since our specification adds a (short) time-series dimension to the theoretical gravity equation, we also include year fixed effects in the model. The estimation

> 31Random effects are a common alternative to estimating panel data using fixed effects. In general, fixed effects are more appropriate when differences between panels can be best characterized by parametric shifts in the functional relationship. The underlying restriction is that the unobserved characteristics must remain the same within the panels, but may vary across panels. On the other hand, random effects allow the unobserved characteristics to vary both within and across panels by assuming that the dataset is a random sample drawn from a larger population. Therefore, the fixed effects estimator is always consistent but may be inefficient, while the random effects approach may be more efficient but does not guarantee consistency. A common method to decide between the two approaches is a Hausman test, which takes advantage of the above properties of the estimators. Specifically, the Hausman test checks a more efficient specification against a less efficient but consistent model to make sure that the more efficient model also gives consistent results. The null hypothesis is that the random effects estimates are the same as the fixed effects estimates, and the test statistic is distributed as a _χ_<sup>2</sup> with the degrees of freedom equal to the number of panels. In our model, the _χ_<sup>2</sup> is 681.70 and significant at the 1 percent level, which confirms that estimating the model with random would be inconsistent

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