Baier and Bergstrand (2007. p. 78) also claimed that this unobserved heterogeneity could highly correlate with the decision of two countries to form an FTA and lead to the endogeneity bias we discussed in Section 3. In this sense, the aspects of time-varying heterogeneity across countries have to be taken into consideration in the estimation. In our fourth model, we simultaneously introduce country-and-time fixed effects (by generating a full set of exporter-and-time and importer-and-time dummy variables) and country-pair fixed effects to correct the bias induced by unobserved time-varying multilateral resistance terms. Doing so minimises omitted variable bias and "purifies" the actual impacts of the free trade agreement on bilateral trade flows. As countries with close political, cultural and historical relationships are likely to trade more with each other than normal and these country-pair factors may have a significant impact on the level of bilateral trade between these two countries, but notwith third countries, researchers have attempted to incorporate as many relevant dummy variables as possible in the model to represent these bilateral ties so as to obtain an unbiased estimation. However, as so many unobservable dyadic factors remain, the choice of specific country-pair fixed variables is always an intractable problem in empirical studies. One effective alternative to solve the problem is to generate a full range of country-pair dummy variables to capture bilateral factors that are specific to country pairs but constant over time, so that all sources of time-invariant country-pair variability in exports can be included in the model. Finally, we estimate the model in its original multiplicative form to tackle the problems of zero trade and hete in the error term. As mentioned in Section 3, we follow the most recent developments in the gravity model literature and estimate a multinomial PML as described in Head and Mayer (forthcoming) and as explained in Section 3 above. To select between procedures we have used a MaMu test, the results of which are presented in Table A.3 in the Appendix and support the use of the structure.