多产品企业的生产率和质量

Number 1430 January 2026 Productivity and Quality of Multi-product Firms Mauro Caselli, Arpita Chatterjee, and Shengyu Li Caselli, Mauro, Arpita Chatterjee, and Shengyu Li (2026).“Productivity and Quality ofMulti-product Firms,” International Finance Discussion Papers 1430. Washington: Boardof Governors of the Federal Reserve System, https://doi.org/10.17016/IFDP.2026.1430. NOTE: International Finance Discussion Papers (IFDPs) are preliminary materials circulated to stimu-late discussion and critical comment.The analysis and conclusions set forth are those of the authors anddo not indicate concurrence by other members of the research staff or the Board of Governors. Referencesin publications to the International Finance Discussion Papers Series (other than acknowledgement) should Productivity and Quality of Multi-product Firms Mauro Caselli†, University of TrentoArpita Chatterjee‡, Federal Reserve BoardShengyu Li§, University of New South WalesDecember 22, 2025 Abstract This paper introduces a method for estimating productivity and quality at thefirm-product level using a transformation function framework. We use firm optimizationconditions to establish a one-to-one mapping between observed data and unobservedproductivity and quality. We do not need to impute firm-product input shares and canavoid imposing productivity evolution processes. The method is scalable to numerousproducts and can address the bias caused by unobserved heterogeneous intermediateinput prices. We apply the method to a set of Mexican manufacturing industries and Keywords:multi-product firms, productivity, quality, spillover, within-firm reallo- JEL classification:D24, L11, L15, O33. 1Introduction The production landscape of many manufacturing industries is dominated by multi-productfirms, which operate across a diverse range of product lines. However, existing empiricalstudies that explore the determinants of firm performance have primarily focused on analyzingvariations across different firms, such as heterogeneity in productivity levels and demandcharacteristics (e.g., Foster et al., 2008; Pozzi and Schivardi, 2016; Kumar and Zhang, 2019). This paper introduces a method to estimate productivity and quality (product appeal)at the firm-product level, along with the transformation function and demand parameters.This method constructs a unique one-to-one mapping from observed data to unobservablevariables by using firm optimization conditions. This offers several advantages over recentmethods (e.g., Dhyne et al., 2022; Orr, 2022; Valmari, 2023). First, it eliminates the need forimputing within-firm input allocations. Second, it does not need to impose restrictions on productivity evolution, allowing for flexibility in exploring complex productivity dynamicsafter estimation.Third, it is scalable to handle a large number of products.Fourth, it In modeling the production side, our method is designed to address the challenges commonlyfaced in estimating multi-product production functions. Most production function estimationmethodologies implicitly assume that each firm produces a single product (e.g., Olley andPakes, 1996; Levinsohn and Petrin, 2003; Ackerberg et al., 2015; Gandhi et al., 2020). Inthis context, the input allocation is observable to researchers and each firm only has a single Moreover, researchers do not observe the within-firm division of inputs used to producedifferent products because firms usually only report total inputs at the firm level.2Finally, intermediate input prices, which vary significantly across firms and over time due to variousreasons such as bargaining power in the input market and transport costs, as documented by Atalay (2014), should be controlled for to avoid “input price bias” (Ornaghi, 2006; De Loecker To address these issues, we model the production technology using a transformationfunction, which is a mapping from a vector of inputs at the firm level to an aggregator ofproduct-specific outputs. This saves us from modeling how the inputs are divided for the production of each individual product. Each product is associated with a potentially differentlevel of physical productivity (i.e., quantity-based productivity, or TFPQ, as in Foster et al.,2008).3The productivity levels, together with a parameter in the transformation functionthat characterizes the technological substitutability of the products, govern the marginalrate of transformation between any two products.The firm observes these productivitylevels before making input and output decisions to maximize profits. In the spirit of Grieco Although the primary innovation of our method lies on the production side, it is flexibleenough to accommodate a variety of demand systems. Conditional on the availability ofvalid instrumental variables, the approach can be applied to widely used demand models such as Constant Elasticity of Substitution (CES) demand, discrete-choice demand (e.g.,Berry, 1994), and random-coefficients logit d