Productivity and Quality of Multi-product Firms

This paper proposes a novel method to estimate productivity and quality at the firm-product level, together with transformation function and demand parameters. The method relies on firm optimization conditions to obtain a one-to-one mapping between observed data and unobserved productivity and quality. It has the advantage of allowing for heterogeneous unobserved intermediate input prices and scalability to handle a large number of products, without imputing firm-product input shares or relying on productivity evolution. We apply this method to a set of Mexican manufacturing industries. We find that multi-product firms’ better performing products have both higher productivity and higher quality, with the former emerging as a stronger predictor of within-firm performance. However, firms face a trade-off between quality and productivity, which we refer to as the cost of quality. The cost of quality is higher for more differentiated products and declines with product age. In a counterfactual exercise, we show that a reduction in the cost of quality can lead to substantial firm-level productivity gains and that, on average, about 26.5 percent of these gains are due to the within-firm reallocation of production. Importantly, a larger product scope allows more room for intra-firm resource reallocation, leading to higher productivity gains. This reveals a new mechanism for enhancing the performance of multi-product firms.