While the current economic situation requires strong and persistent productivity growth to maintain economic prosperity, this growth is hampered by an increasingly uncertain international environment. The welfare cost associated with this uncertain international environment, however, remains unclear. Current quantitative trade models are not sufficiently general nor reliable to provide a clear picture of the impact of trade on technological change and subsequent economic prosperity. This project exactly aims to improve the understanding of the welfare impact of trade by improving the characterization and measurement of technological change using Finite Mixture Models (FMMs). While it is known that trade integration can accelerate aggregate productivity growth, more empirical work is still needed to establish the relative importance of the different channels that drive this growth. FMMs provides a flexible, semi-parametric approximation of the firm-level productivity growth process that allows both to match the productivity distribution for all firms and to identify those channels that mainly drive productivity growth. This knowledge culminates in a general quantitative trade model that allows quantifying the dynamic impact of trade shocks on economic welfare. The obtained model will allow policy-makers to quantify and evaluate the full impact of trade policy on the productivity growth of all firms and will guide them in choosing among alternative trade policy options.