First, they confirm a well-known fact about private label production. The large brands have an inherent advantage when producing private labels. They can leverage economies of scale to produce those private label goods at low costs. Moreover, manufacturing the private label goods, and further taking advantage of scale economies, can lower their costs of producing their branded products.
Second, they find that manufacturers may be supplying private label products in hopes of strengthening their relationships with key retailers. In so doing, they hope to gain more shelf space for their branded products. The scholars confirm that retailers do carry more of a manufacturer's branded products if that company supplies private label goods to their stores. If a manufacturer exits the private label business, they tend to lose shelf space for their branded goods.
However, interestingly, they find that the national brands do not gain market share in their categories simply because they have more shelf space and more availability of their product in the stores. In the end, the consumer drives the success of the brands. More shelf space doesn't mean more sales, and ultimately, a retailer may take shelf space away if products don't sell.
One thing that they do not examine is why some branded manufacturers are more successful at private label production than others. I suspect that some branded goods companies simply do not have the efficiencies and cost structure required to offer private label goods at competitive prices. Moreover, attempts to become more efficient might harm the quality of the branded goods the firm supplies.