We develop and structurally estimate a model of heterogeneous multiproduct firms that can be used to decompose the firm-size distribution into the contributions of costs, "appeal" (quality or taste), markups, and product scope. Using Nielsen bar-code data on prices and sales, we find that variation in firm appeal and product scope explains at least four fifths of the variation in firm sales. We show that the imperfect substitutability of products within firms, and the fact that larger firms supply more products than smaller firms, implies that standard productivity measures are highly dependent on implicit demand system assumptions and probably dramatically understate the relative productivity of the largest firms. Although most firms are well approximated by the monopolistic competition benchmark of constant markups, we find that the largest firms that account for most of aggregate sales depart substantially from this benchmark, and exhibit both variable markups and substantial cannibalization effects.

We develop and structurally estimate a model of heterogeneous multiproduct firms that can be used to decompose the firm-size distribution into the contributions of costs, “appeal” (quality or taste), markups, and product scope. Using Nielsen barcode data on prices and sales, we find that variation in firm appeal and product scope explains at least four fifths of the variation in firm sales. We show that the imperfect substitutability of products within firms, and the fact that larger firms supply more products than smaller firms, implies that standard productivity measures are highly dependent on implicit demand system assumptions and probably dramatically understate the relative productivity of the largest firms. Although most firms are well approximated by the monopolistic competition benchmark of constant markups, we find that the largest firms that account for most of aggregate sales depart substantially from this benchmark, and exhibit both variable markups and substantial cannibalization effects.

Using supplier-level trade data, we estimate the effect on consumer welfare from changes in U.S. imports both in the aggregate and for different household income groups from 1998 to 2014. To do this, we use consumer preferences which feature non-homotheticity both within sectors and across sectors. After structurally estimating the parameters of the model, using the universe of U.S. goods imports, we construct import price indexes in which a variety is defined as a foreign establishment producing an HS10 product that is exported to the United States. We find that lower income households experienced the most import price inflation, while higher income households experienced the least import price inflation during our time period. Thus, we do not find evidence that the consumption channel has mitigated the distributional effects of trade that have occurred through the nominal income channel in the United States over the past two decades.

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