Productivity and Quality of Multi-product Firms

Abstract: This paper introduces a method for estimating productivity and quality at the firm-product level using a transformation function framework. Using firms’ optimization conditions, we obtain a one-to-one mapping from observed data to unobserved productivity and quality without imputing inputs. The method scales to many products, avoids specifying productivity dynamics, corrects bias from unobserved heterogeneous input prices, and accommodates productivity–quality trade-off. Applying it to Mexican manufacturing industries, we show that an exogenous, product-specific technological improvement raises firm-level productivity mainly through within-firm reallocation and delivers substantial industry-level welfare gains, further amplified by across-firm and within-firm spillovers.