DeFiPP research seminar by Ariell Reshef

Production Function Estimation with Multi-Destination Firms (with Geoffrey Barrows and Hélène Ollivier)

Abstract: We develop a procedure to consistently estimate production functions and productivity when firms endogenously select into multiple destination markets where they compete imperfectly, and when researchers only observe output denominated in value. We show that ignoring the multi-destination dimension (i.e., exporting) yields biased and inconsistent inference. 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 function of inputs and an endogenous firm-level demand shifter. We show how to proxy for this demand shifter using just the domestic revenue share. We estimate the model using a two-step procedure that extends Gandhi et al. (2020) to our setting. In Monte Carlo simulations we show that our estimator is consistent and has good small-sample properties, while estimators that do not take into account the multi-destination dimension are biased and inconsistent. Using French manufacturing data, we find that existing estimation procedures yield unrealistic estimates of returns to scale, demand elasticities and learning by exporting, while our procedure yields plausible ones.

Contact : Christian Kiedaisch - christian.kiedaisch@unamur.be
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