This article analyzes the role of credit frictions in a trade model where producers differ in their capabilities to conduct process and quality innovations and require external finance for investments. Accounting for cost-based and quality-based sorting of firms in a unified framework allows us to demonstrate that the reactions of prices and commonly used productivity measures do not necessarily reflect welfare implications. Credit frictions lead to distortions through aggravated access to finance and endogenous price adjustments so that the responses of quantity-based and revenue-based productivity differ substantially. In counterfactual scenarios, we show that these differential effects are quantitatively important.