IDEAS home Printed from https://ideas.repec.org/p/boe/boeewp/1015.html
   My bibliography  Save this paper

On the non-identification of revenue production functions

Author

Listed:
  • van Dijcke, David

    (University of Michigan)

Abstract

It is well‑known that production functions are potentially misspecified when revenue is used as a proxy for output. In this paper, I formalise and strengthen this common knowledge by showing that neither the production function nor Hicks‑neutral productivity can be identified when revenue is used as a proxy for physical output. This result holds under the standard assumptions used in the literature for a large class of production functions, including all commonly used parametric forms. Among the prevalent approaches to address this issue, I show that only those which impose assumptions on the underlying demand system can possibly identify the production function.

Suggested Citation

  • van Dijcke, David, 2023. "On the non-identification of revenue production functions," Bank of England working papers 1015, Bank of England.
    • Handle: RePEc:boe:boeewp:1015
    as

    Download full text from publisher

    File URL: https://www.bankofengland.co.uk/-/media/boe/files/working-paper/2023/on-the-non-identification-of-revenue-production-functions.pdf
    File Function: Full text
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Wolfgang Keller & Stephen R. Yeaple, 2009. "Multinational Enterprises, International Trade, and Productivity Growth: Firm-Level Evidence from the United States," The Review of Economics and Statistics, MIT Press, vol. 91(4), pages 821-831, November.
    2. Mary Amiti & Jozef Konings, 2007. "Trade Liberalization, Intermediate Inputs, and Productivity: Evidence from Indonesia," American Economic Review, American Economic Association, vol. 97(5), pages 1611-1638, December.
    3. Nicholas Bloom & Mirko Draca & John Van Reenen, 2016. "Trade Induced Technical Change? The Impact of Chinese Imports on Innovation, IT and Productivity," Review of Economic Studies, Oxford University Press, vol. 83(1), pages 87-117.
    4. Tor Jakob Klette, 1999. "Market Power, Scale Economies and Productivity: Estimates from a Panel of Establishment Data," Journal of Industrial Economics, Wiley Blackwell, vol. 47(4), pages 451-476, December.
    5. Jan De Loecker & Pinelopi K. Goldberg & Amit K. Khandelwal & Nina Pavcnik, 2016. "Prices, Markups, and Trade Reform," Econometrica, Econometric Society, vol. 84, pages 445-510, March.
    6. Hunt Allcott & Allan Collard-Wexler & Stephen D. O'Connell, 2016. "How Do Electricity Shortages Affect Industry? Evidence from India," American Economic Review, American Economic Association, vol. 106(3), pages 587-624, March.
    7. Jan De Loecker & Jan Eeckhout & Gabriel Unger, 2020. "The Rise of Market Power and the Macroeconomic Implications [“Econometric Tools for Analyzing Market Outcomes”]," The Quarterly Journal of Economics, Oxford University Press, vol. 135(2), pages 561-644.
    8. Jan De Loecker & Frederic Warzynski, 2012. "Markups and Firm-Level Export Status," American Economic Review, American Economic Association, vol. 102(6), pages 2437-2471, October.
    9. Loren Brandt & Johannes Van Biesebroeck & Luhang Wang & Yifan Zhang, 2017. "WTO Accession and Performance of Chinese Manufacturing Firms," American Economic Review, American Economic Association, vol. 107(9), pages 2784-2820, September.
    10. Maarten De Ridder & Basile Grassi & Giovanni Morzenti, 2021. "The Hitchhiker’s Guide to Markup Estimation," Working Papers 677, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    11. Jan De Loecker, 2011. "Product Differentiation, Multiproduct Firms, and Estimating the Impact of Trade Liberalization on Productivity," Econometrica, Econometric Society, vol. 79(5), pages 1407-1451, September.
    12. James Levinsohn & Amil Petrin, 2003. "Estimating Production Functions Using Inputs to Control for Unobservables," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 70(2), pages 317-341.
    13. Allan Collard-Wexler & Jan De Loecker, 2015. "Reallocation and Technology: Evidence from the US Steel Industry," American Economic Review, American Economic Association, vol. 105(1), pages 131-171, January.
    14. Thomas A Abbott III, 1992. "Price Dispersion In U.S. Manufacturing: Implications For The Aggregation Of Products And Firms," Working Papers 92-3, Center for Economic Studies, U.S. Census Bureau.
    15. Jacques Mairesse & Jordi Jaumandreu, 2005. "Panel‐data Estimates of the Production Function and the Revenue Function: What Difference Does It Make?," Scandinavian Journal of Economics, Wiley Blackwell, vol. 107(4), pages 651-672, December.
    16. Basu, Susanto & Fernald, John G, 1997. "Returns to Scale in U.S. Production: Estimates and Implications," Journal of Political Economy, University of Chicago Press, vol. 105(2), pages 249-283, April.
    17. Chambers,Robert G., 1988. "Applied Production Analysis," Cambridge Books, Cambridge University Press, number 9780521314275.
    18. Chang-Tai Hsieh & Peter J. Klenow, 2009. "Misallocation and Manufacturing TFP in China and India," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 124(4), pages 1403-1448.
    19. Enghin Atalay, 2014. "Materials Prices And Productivity," Journal of the European Economic Association, European Economic Association, vol. 12(3), pages 575-611, June.
    20. Ornaghi, Carmine, 2008. "Price deflators and the estimation of the production function," Economics Letters, Elsevier, vol. 99(1), pages 168-171, April.
    21. Olley, G Steven & Pakes, Ariel, 1996. "The Dynamics of Productivity in the Telecommunications Equipment Industry," Econometrica, Econometric Society, vol. 64(6), pages 1263-1297, November.
    22. Daniel A. Ackerberg & Kevin Caves & Garth Frazer, 2015. "Identification Properties of Recent Production Function Estimators," Econometrica, Econometric Society, vol. 83, pages 2411-2451, November.
    23. Lucia Foster & John Haltiwanger & Chad Syverson, 2008. "Reallocation, Firm Turnover, and Efficiency: Selection on Productivity or Profitability?," American Economic Review, American Economic Association, vol. 98(1), pages 394-425, March.
    24. Steven T. Berry, 1994. "Estimating Discrete-Choice Models of Product Differentiation," RAND Journal of Economics, The RAND Corporation, vol. 25(2), pages 242-262, Summer.
    25. Smeets, Valerie & Warzynski, Frederic, 2013. "Estimating productivity with multi-product firms, pricing heterogeneity and the role of international trade," Journal of International Economics, Elsevier, vol. 90(2), pages 237-244.
    26. Scott Orr, 2022. "Within-Firm Productivity Dispersion: Estimates and Implications," Journal of Political Economy, University of Chicago Press, vol. 130(11), pages 2771-2828.
    27. Richard Blundell & Stephen Bond, 2000. "GMM Estimation with persistent panel data: an application to production functions," Econometric Reviews, Taylor & Francis Journals, vol. 19(3), pages 321-340.
    28. Amit Gandhi & Salvador Navarro & David A. Rivers, 2020. "On the Identification of Gross Output Production Functions," Journal of Political Economy, University of Chicago Press, vol. 128(8), pages 2973-3016.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jamil, Nida & Chaudhry, Theresa Thompson & Chaudhry, Azam, 2022. "Trading textiles along the new silk route: The impact on Pakistani firms of gaining market access to China," Journal of Development Economics, Elsevier, vol. 158(C).
    2. Geoffrey Barrows & Hélène Ollivier & Ariell Reshef, 2023. "Production Function Estimation with Multi-Destination Firms," CESifo Working Paper Series 10716, CESifo.
    3. De Loecker, Jan, 2021. "Comment on (Un)pleasant ... by Bond et al (2020)," Journal of Monetary Economics, Elsevier, vol. 121(C), pages 15-18.
    4. Bruno Merlevede & Angelos Theodorakopoulos, 2018. "Productivity Effects of Internationalisation Through the Domestic Supply Chain: Evidence from Europe," Working Papers of VIVES - Research Centre for Regional Economics 627689, KU Leuven, Faculty of Economics and Business (FEB), VIVES - Research Centre for Regional Economics.
    5. Jaumandreu, Jordi & Doraszelski, Ulrich, 2019. "Using Cost Minimization to Estimate Markups," CEPR Discussion Papers 14114, C.E.P.R. Discussion Papers.
    6. Pham, Hoang, 2023. "Trade reform, oligopsony, and labor market distortion: Theory and evidence," Journal of International Economics, Elsevier, vol. 144(C).
    7. Dobbelaere, Sabien & Kiyota, Kozo & Mairesse, Jacques, 2015. "Product and labor market imperfections and scale economies: Micro-evidence on France, Japan and the Netherlands," Journal of Comparative Economics, Elsevier, vol. 43(2), pages 290-322.
    8. Chen Yeh & Claudia Macaluso & Brad Hershbein, 2022. "Monopsony in the US Labor Market," American Economic Review, American Economic Association, vol. 112(7), pages 2099-2138, July.
    9. Fiorini, Matteo & Sanfilippo, Marco & Sundaram, Asha, 2021. "Trade liberalization, roads and firm productivity," Journal of Development Economics, Elsevier, vol. 153(C).
    10. Kritikos, Alexander S. & Schiersch, Alexander & Stiel, Caroline, 2021. "The Productivity Puzzle in Business Services," IZA Discussion Papers 14610, Institute of Labor Economics (IZA).
    11. Richard Bräuer & Matthias Mertens & Viktor Slavtchev, 2023. "Import competition and firm productivity: Evidence from German manufacturing," The World Economy, Wiley Blackwell, vol. 46(8), pages 2285-2305, August.
    12. Alvaro Garcia-Marin & Nico Voigtländer, 2019. "Exporting and Plant-Level Efficiency Gains: It's in the Measure," Journal of Political Economy, University of Chicago Press, vol. 127(4), pages 1777-1825.
    13. Alexander S. Kritikos & Alexander Schiersch & Caroline Stiel, 2022. "The productivity shock in business services," Small Business Economics, Springer, vol. 59(3), pages 1273-1299, October.
    14. Chad Syverson, 2011. "What Determines Productivity?," Journal of Economic Literature, American Economic Association, vol. 49(2), pages 326-365, June.
    15. Paul L. E. Grieco & Shengyu Li & Hongsong Zhang, 2022. "Input prices, productivity, and trade dynamics: long‐run effects of liberalization on Chinese paint manufacturers," RAND Journal of Economics, RAND Corporation, vol. 53(3), pages 516-560, September.
    16. Michael Rubens, 2023. "Market Structure, Oligopsony Power, and Productivity," American Economic Review, American Economic Association, vol. 113(9), pages 2382-2410, September.
    17. Jan De Loecker & Jan Eeckhout & Gabriel Unger, 2020. "The Rise of Market Power and the Macroeconomic Implications [“Econometric Tools for Analyzing Market Outcomes”]," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 135(2), pages 561-644.
    18. Emir Malikov & Shunan Zhao & Jingfang Zhang, 2024. "A System Approach to Structural Identification of Production Functions with Multi-Dimensional Productivity," Advances in Econometrics, in: Essays in Honor of Subal Kumbhakar, volume 46, pages 211-263, Emerald Group Publishing Limited.
    19. Dai, Xiaoyong & Sun, Zao & Liu, Hang, 2018. "Disentangling the effects of endogenous export and innovation on the performance of Chinese manufacturing firms," China Economic Review, Elsevier, vol. 50(C), pages 42-58.
    20. Umut Kılınç, 2018. "Assessing Productivity Gains from International Trade in a Small Open Economy," Open Economies Review, Springer, vol. 29(5), pages 953-980, November.

    More about this item

    Keywords

    Production function estimation; revenue production functions; productivity; market power; identification;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • D02 - Microeconomics - - General - - - Institutions: Design, Formation, Operations, and Impact
    • D04 - Microeconomics - - General - - - Microeconomic Policy: Formulation; Implementation; Evaluation
    • E02 - Macroeconomics and Monetary Economics - - General - - - Institutions and the Macroeconomy
    • L10 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - General

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:boe:boeewp:1015. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Digital Media Team (email available below). General contact details of provider: https://edirc.repec.org/data/boegvuk.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.