The next Economics Seminar of Paris-Saclay will take place on Thursday, January 27 from 12h15 to 13h15. The seminar will take place at RITM, in room GAUDEMET. Geoffrey Barrows (CREST) will present “Production Function Estimation with Multi-Market Firms” (co-authored with Hélène Ollivier and Ariell Reshef).
Production function estimation is a central component of many economic analyses. Estimation procedures usually require that researchers observe inputs and outputs denominated in physical units and/or that firms engage in perfect competition, but most firm-level datasets report inputs and outputs in value, and perfect competition is an unrealistic assumption for most industries beyond agriculture. Standard methods for controlling for unobserved firm-specific output prices implicitly rely on the assumption that all firms sell in the same unique output market, which is usually not the case. In this paper, we develop a procedure to consistently estimate structural elements of supply and demand when firms compete imperfectly on multiple destination markets and when output and inputs are denominated in value. We specify a partial equilibrium model in which firms endogenously select destination markets to serve, destination-specific quantities and prices, and variable inputs to hire. The model delivers an estimation equation that expresses revenues as a quasi-linear function of inputs and an endogenous firm-level demand shifter. We design an instrumental variables extension to the factor shares estimation approach of Gandhi at al (2020) to estimate structural parameters and test our procedure against leading alternatives in Monte Carlo exercises and with French manufacturing data. Existing estimation procedures yield unrealistic estimates of variable returns to scale, while our procedure yields plausible ranges for factor output elasticities and demand elasticities.