Quantifying the gains from multinational production has been a vital topic of economic research. Positive productivity gains are often attributed to knowledge spillover from multinational to domestic firms. An alternative, less stressed explanation is firm selection whereby competition from multinationals leads to market reallocation and survival of only the most productive domestic firms. We develop a model that incorporates both aspects and identify their relative importance in the gains from multinational production by exploring their distinct predictions on domestic productivity and revenue distributions. We show that knowledge spillover shifts both distributions rightward while selection and reallocation raise the left truncation of the distributions and shift revenue leftward. Using a rich firm-level panel dataset that spans 60 countries, our structural estimates suggest firm selection and market reallocation constitute an important source of productivity gains while its relative importance varies across nations. Ignoring the role of this source can lead to significant bias in understanding the nature of gains. We also perform counterfactual analysis and quantify both the aggregate and the decomposed welfare effects of multinational production.