In this paper, we study the competition between national brands and private labels (or store brands) by analyzing the impacts of their presence on strategies, sales, and profits in a vertical channel structure. We use a differential game, where the channel members control price and non--price marketing variables, and investigate two scenarios. The first is used as a benchmark. It considers an exclusive retailer that distributes only a national brand provided by a manufacturer, who invests in national advertising to build its brand's goodwill. In the second scenario, the retailer owns a private label that competes with the national brand. By computing the results under both scenarios, we provide answers to the following research questions: (i) What should the price and the non--price marketing strategies be, with and without the private label? (ii) How do they compare? (iii) Is the presence of a private label always profitable for the retailer and harmful to the manufacturer, as the literature suggests? One of our main results indicates that the manufacturer is not necessarily always hurt by the private label. More specifically, we find that, when the local advertising competition between both brands is lower than the price competition, the national brand's manufacturer could charge a higher transfer price to a retailer carrying a private label. This result brings into question an oft-cited explanation given in the literature, namely, that retailers choose to sell private labels as a counter-strategy to overcome double marginalization and to gain market power against the manufacturer.