Recent theoretical work on international trade emphasizes the importance of trade elasticity as the fundamental statistic needed to conduct welfare analysis. Eaton and Kortum (2002) proposed a two-step method to estimate this parameter, where exporter fixed effects are regressed on proxies for technology and wages. Within the same Ricardian model of trade, the trade share provides an alternative source of identification for the elasticity of trade. Following Santos Silva and Tenreyro (2006) both trade share and EK models are estimated using OLS and Poisson PML to test for the presence of heteroskedasticity-type-of-bias. The evidence from both specifications suggests that the bias in the OLS estimates significantly impacts the magnitude of trade cost elasticity. The welfare analysis reveals that the resulting extreme variability of the trade cost elasticity and the imposition of a common manufacturing share parameter for all countries generate substantial distortions in the calculation of benefits from trade.