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Theory for Extending Single-Product Production Function Estimation to Multi-Product Settings

Author

Listed:
  • Emmanuel Dhyne
  • Amil Petrin
  • Valerie Smeets
  • Frederic Warzynski

Abstract

We introduce a new methodology for estimating multi-product production functions. It embeds the seminal contributions of Diewert (1973) and Lau (1976) in our extended version of the semi-parametric econometric framework of Olley and Pakes (1996), where we address the simultaneity of inputs and outputs by allowing for the possibility of a possible vector of unobserved ”productivities,” all of which may be freely correlated with inputs and outputs. We show how to use the multi-product production function to recover estimates of firm-product marginal costs using the input and output elasticities by extending Hall’s (1988) single-product result to our multi-product setting using McFadden (1978). We focus on six 6-digit Belgian ”industries” that produce two products, finding all but five of the forty-eight input coefficients are positive and thirty eight are strongly significant. We find outputs are substitutes as the coefficients on ”other good output” is always negative and highly significant. 100% of marginal cost estimates are positive and close to 80% of markups are estimated to be greater than 1. We find very similar results when we move to 4-digit industries, when we use similar multi-product data from France, and when we use the trans-log approximation.

Suggested Citation

  • Emmanuel Dhyne & Amil Petrin & Valerie Smeets & Frederic Warzynski, 2022. "Theory for Extending Single-Product Production Function Estimation to Multi-Product Settings," NBER Working Papers 30784, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:30784
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    Cited by:

    1. Emmanuel Dhyne & Amil Petrin & Valerie Smeets & Frederic Warzynski, 2024. "Multiproduct Firms, Import Competition and Productivity," CESifo Working Paper Series 11155, CESifo.
    2. Mauro Caselli & Arpita Chatterjee & Shengyu Li, 2023. "Productivity and Quality of Multi-product Firms," Discussion Papers 2023-10, School of Economics, The University of New South Wales.

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    JEL classification:

    • L0 - Industrial Organization - - General

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