Aggregating Distortions in Networks with Multi-Product Firms

Abstract

We propose a theory of aggregating product-level distortions in a network economy and assess its implications for total factor productivity (TFP) growth. To this end, we provide a theoretical framework for growth accounting in inefficient economies with production networks and firms that engage in joint production. Using sufficient statistics summarizing inefficiencies arising from firm’s product portfolio choices between products sold in different supply chains, we unpack between and within firm resource misallocation. This sufficient statistic is constructed as the covariance between the price change of a firm’s product and a measure of the distortions accumulated in the downstream supply chain faced by that product. We apply the framework using a product transaction database (including granular prices and quantities) for the universe of formal Chilean firms. We find that within-firm allocative efficiency explains much of Chile’s TFP growth after COVID-19 and in the subsequent high-inflation period.