We present a theory for growth accounting in open economies with distortions. In addition to domestic distortions, we include distortions from imported intermediate inputs and from exports. We show that trade can influence aggregate TFP growththrough three channels:, the distortion of exports, the production network propagation of import distortions and through how imports are accounted for in national accounts. We quantify these forces by using administrative firm-to-firm and tax data for the universe of formal firms from Chile between 2005 and 2021. Observed TFP growth is explained by allocative efficiency rather than technological change. International trade accounts for 48% of aggregate TFP growth, with all three channels being quantitatively important.