This paper compares the solution methods and baseline calibration of three different quantitative trade models (QTMs): computable general equilibrium (CGE) models, structural gravity (SG) models and models employing exact hat algebra (EHA). The different solution methods generate identical results on counterfactual experiments if baseline trade shares or baseline trade costs are identical. SG models, calibrating the baseline to gravity-predicted shares, potentially suffer from bias in the predicted welfare effects as a result of misspecification of the gravity equation, whereas the other methods, calibrating to actual shares, potentially suffer from bias as a result of random variation and measurement error of trade flows. Simulations show that predicted shares calibration can generate large biases in predicted welfare effects if the gravity equation does not contain pairwise fixed effects or is estimated without domestic trade flows. Calibration to actual shares and to fitted shares based on gravity estimation including pairwise fixed effects display similar performance in terms of robustness to the different sources of bias.