This study analyzes the sensitivity of trade flows to trade barriers from gravity equations, using different econometric techniques recently highlighted in the literature. Specifically, we compare a benchmark OLS fixed effects specification a la Feenstra (2002) with three emerging estimation methods: the standard Heckman correction for selection bias, to account for zero trade flows; the Eaton and Tamura (1994) Tobit estimator, to solve limited-dependent variable issues; and, finally, the Poisson pseudo-maximum-likelihood (PPML) technique, to correct for the presence of heteroskedasticity. Our gravity model includes trade among 193 exporter and 99 importer countries, in 18 food industry sectors. The paper achieves two goals: First it provides estimates of the elasticity of substitution obtained using the four estimation techniques; Second, it gives a dimension to the trade reduction effect induced by existing border protection, by simulating the effect of a full trade liberalization scenario on 18 food sectors. The estimates reveal interesting variations in the elasticity of substitution across products and procedures. The simulation indicates that trade liberalization will strongly increase food exports, especially from emerging and developing countries.