Productivity and Quality of Multi-product Firms

This paper introduces a method for estimating productivity and quality at the firm-product level using a transformation function framework. We use firm optimization conditions to establish a one-to-one mapping between observed data and unobserved productivity and quality. We do not need to impute firm-product input shares and can avoid imposing productivity evolution processes. The method is scalable to numerous products and can address the bias caused by unobserved heterogeneous intermediate input prices. We apply the method to a set of Mexican manufacturing industries and examine the roles of across-firm and within-firm technological spillovers, accounting for the trade-off between productivity and quality. Our quantitative analysis shows that an exogenous, product-specific technological improvement generates substantial gains in welfare, amplified by both within-firm and across-firm spillovers by approximately 17 percent and 5 percent, respectively. Moreover, within-firm resource reallocation toward the most productive products accounts for 60 percent of the resulting firm-level productivity gains.