IDEAS home Printed from https://ideas.repec.org/p/nbr/nberwo/25293.html

The Microeconomic Foundations of Aggregate Production Functions

Author

Listed:
  • David Baqaee
  • Emmanuel Farhi

Abstract

Aggregate production functions are reduced-form relationships that emerge endogenously from input-output interactions between heterogeneous producers and factors in general equilibrium. We provide a general methodology for analyzing such aggregate production functions by deriving their first- and second-order properties. Our aggregation formulas provide non-parameteric characterizations of the macro elasticities of substitution between factors and of the macro bias of technical change in terms of micro sufficient statistics. They allow us to generalize existing aggregation theorems and to derive new ones. We relate our results to the famous Cambridge-Cambridge controversy.

Suggested Citation

  • David Baqaee & Emmanuel Farhi, 2018. "The Microeconomic Foundations of Aggregate Production Functions," NBER Working Papers 25293, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:25293
    Note: EFG ITI ME PE
    as

    Download full text from publisher

    File URL: http://www.nber.org/papers/w25293.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Avi J. Cohen, 2003. "Retrospectives: Whatever Happened to the Cambridge Capital Theory Controversies?," Journal of Economic Perspectives, American Economic Association, vol. 17(1), pages 199-214, Winter.
    2. Charles Hulten & Leonard Nakamura, 2017. "Accounting for Growth in the Age of the Internet: The Importance of Output-Saving Technical Change," NBER Working Papers 23315, National Bureau of Economic Research, Inc.
    3. Charles R. Hulten, 1978. "Growth Accounting with Intermediate Inputs," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 45(3), pages 511-518.
    4. Enghin Atalay, 2017. "How Important Are Sectoral Shocks?," American Economic Journal: Macroeconomics, American Economic Association, vol. 9(4), pages 254-280, October.
    5. Christoph E. Boehm & Aaron Flaaen & Nitya Pandalai-Nayar, 2019. "Input Linkages and the Transmission of Shocks: Firm-Level Evidence from the 2011 Tōhoku Earthquake," The Review of Economics and Statistics, MIT Press, vol. 101(1), pages 60-75, March.
    6. Sato, Kazuo, 1969. "Micro and macro constant-elasticity-of-substitution production functions in a multifirm industry," Journal of Economic Theory, Elsevier, vol. 1(4), pages 438-453, December.
    7. Sattinger, Michael, 1993. "Assignment Models of the Distribution of Earnings," Journal of Economic Literature, American Economic Association, vol. 31(2), pages 831-880, June.
    8. Robert M. Solow, 1956. "A Contribution to the Theory of Economic Growth," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 70(1), pages 65-94.
    9. Ajay Agrawal & Joshua Gans & Avi Goldfarb, 2019. "The Economics of Artificial Intelligence: An Agenda," NBER Books, National Bureau of Economic Research, Inc, number agra-1, January-J.
    10. Stern, David I., 2010. "Derivation of the Hicks, or direct, elasticity of substitution using the input distance function," Economics Letters, Elsevier, vol. 108(3), pages 349-351, September.
    11. Daron Acemoglu & Pascual Restrepo, 2018. "Artificial Intelligence, Automation, and Work," NBER Chapters, in: The Economics of Artificial Intelligence: An Agenda, pages 197-236, National Bureau of Economic Research, Inc.
    12. S. Rao Aiyagari, 1994. "Uninsured Idiosyncratic Risk and Aggregate Saving," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 109(3), pages 659-684.
    13. George E. Johnson, 1997. "Changes in Earnings Inequality: The Role of Demand Shifts," Journal of Economic Perspectives, American Economic Association, vol. 11(2), pages 41-54, Spring.
    14. Ezra Oberfield & Devesh Raval, 2021. "Micro Data and Macro Technology," Econometrica, Econometric Society, vol. 89(2), pages 703-732, March.
    15. H. S. Houthakker, 1955. "The Pareto Distribution and the Cobb-Douglas Production Function in Activity Analysis," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 23(1), pages 27-31.
    16. Agrawal, Ajay & Gans, Joshua & Goldfarb, Avi (ed.), 2019. "The Economics of Artificial Intelligence," National Bureau of Economic Research Books, University of Chicago Press, number 9780226613338.
    17. Berthold Herrendorf & Richard Rogerson & ?kos Valentinyi, 2013. "Two Perspectives on Preferences and Structural Transformation," American Economic Review, American Economic Association, vol. 103(7), pages 2752-2789, December.
    18. Paul A. Samuelson, 1966. "A Summing Up," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 80(4), pages 568-583.
    19. Franklin M. Fisher, 1983. "On the Simultaneous Existence of Full and Partial Capital Aggregates," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(1), pages 197-208.
    20. Blackorby, Charles & Russell, R Robert, 1989. "Will the Real Elasticity of Substitution Please Stand Up? (A Comparison of the Allen/Uzawa and Morishima Elasticities)," American Economic Review, American Economic Association, vol. 79(4), pages 882-888, September.
    21. repec:bla:econom:v:45:y:1978:i:179:p:235-50 is not listed on IDEAS
    22. Franklin M. Fisher, 1982. "Aggregate Production Functions Revisited: The Mobility of Capital and the Rigidity of Thought," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 49(4), pages 615-626.
    23. Joan Robinson, 1953. "The Production Function and the Theory of Capital," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 21(2), pages 81-106.
    24. Per Krusell & Anthony A. Smith & Jr., 1998. "Income and Wealth Heterogeneity in the Macroeconomy," Journal of Political Economy, University of Chicago Press, vol. 106(5), pages 867-896, October.
    25. Baqaee, David Rezza & Farhi, Emmanuel, 2018. "Macroeconomics with Heterogeneous Agents and Input-Output Networks," CEPR Discussion Papers 13006, C.E.P.R. Discussion Papers.
    26. Jesus Felipe & Franklin M. Fisher, 2003. "Aggregation in Production Functions: What Applied Economists should Know," Metroeconomica, Wiley Blackwell, vol. 54(2‐3), pages 208-262, May.
    27. Daniel McFadden, 1963. "Constant Elasticity of Substitution Production Functions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 30(2), pages 73-83.
    28. Daron Acemoglu & Pascual Restrepo, 2018. "Artificial Intelligence, Automation and Work," Boston University - Department of Economics - Working Papers Series dp-298, Boston University - Department of Economics.
    29. Rosen, Sherwin, 1981. "The Economics of Superstars," American Economic Review, American Economic Association, vol. 71(5), pages 845-858, December.
    30. Per Krusell & Lee E. Ohanian & JosÈ-Victor RÌos-Rull & Giovanni L. Violante, 2000. "Capital-Skill Complementarity and Inequality: A Macroeconomic Analysis," Econometrica, Econometric Society, vol. 68(5), pages 1029-1054, September.
    31. Franklin M. Fisher, 1965. "Embodied Technical Change and the Existence of an Aggregate Capital Stock," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 32(4), pages 263-288.
    32. Huggett, Mark, 1993. "The risk-free rate in heterogeneous-agent incomplete-insurance economies," Journal of Economic Dynamics and Control, Elsevier, vol. 17(5-6), pages 953-969.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Andrew T. Foerster & Andreas Hornstein & Pierre-Daniel G. Sarte & Mark W. Watson, 2022. "Aggregate Implications of Changing Sectoral Trends," Journal of Political Economy, University of Chicago Press, vol. 130(12), pages 3286-3333.
    2. François Geerolf, 2022. "The “Baqaee-Farhi approach” and a russian gas embargo," Revue de l'OFCE, Presses de Sciences-Po, vol. 0(4), pages 143-165.
    3. Eric J. Bartelsman, 2019. "From New Technology to Productivity," European Economy - Discussion Papers 113, Directorate General Economic and Financial Affairs (DG ECFIN), European Commission.
    4. Bouakez, Hafedh & Rachedi, Omar & Santoro, Emiliano, 2025. "The sectoral origins of heterogeneous spending multipliers," Journal of Public Economics, Elsevier, vol. 248(C).
    5. Philippe Aghion & Céline Antonin & Simon Bunel & Xavier Jaravel, 2022. "Modern manufacturing capital, labor demand, and product market dynamics: Evidence from France," Sciences Po Economics Publications (main) hal-03943312, HAL.
    6. 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.
    7. Juan E. Jacobo, 2022. "Back to the Surplus: An Unorthodox Neoclassical Model of Growth, Distribution and Unemployment with Technical Change," Papers 2211.14978, arXiv.org.
    8. Carlo Milana, 2024. "Refuting Samuelson’s capitulation on the re-switching of techniques in the Cambridge capital controversy," The Review of Austrian Economics, Springer;Society for the Development of Austrian Economics, vol. 37(2), pages 179-197, June.
    9. Martina Kirchberger & Keelan Beirne, 2021. "Concrete Thinking About Development," Trinity Economics Papers tep0621, Trinity College Dublin, Department of Economics.

    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. David Rezza Baqaee & Emmanuel Farhi, 2018. "Macroeconomics with Heterogeneous Agents and Input-Output Networks," NBER Working Papers 24684, National Bureau of Economic Research, Inc.
    2. David Rezza Baqaee & Emmanuel Farhi, 2019. "The Macroeconomic Impact of Microeconomic Shocks: Beyond Hulten's Theorem," Econometrica, Econometric Society, vol. 87(4), pages 1155-1203, July.
    3. Gregory Casey & Ryo Horii, 2019. "A Multi-factor Uzawa Growth Theorem and Endogenous Capital-Augmenting Technological Change," ISER Discussion Paper 1051, Institute of Social and Economic Research, The University of Osaka.
    4. DeCanio, Stephen J., 2016. "Robots and humans – complements or substitutes?," Journal of Macroeconomics, Elsevier, vol. 49(C), pages 280-291.
    5. Paul E. Brockway & Matthew K. Heun & João Santos & John R. Barrett, 2017. "Energy-Extended CES Aggregate Production: Current Aspects of Their Specification and Econometric Estimation," Energies, MDPI, vol. 10(2), pages 1-23, February.
    6. Feld, Lars P. & Schmidt, Christoph M. & Schnabel, Isabel & Truger, Achim & Wieland, Volker, 2019. "Den Strukturwandel meistern. Jahresgutachten 2019/20 [Dealing with Structural Change. Annual Report 2019/20]," Annual Economic Reports / Jahresgutachten, German Council of Economic Experts / Sachverständigenrat zur Begutachtung der gesamtwirtschaftlichen Entwicklung, volume 127, number 201920.
    7. David Rezza Baqaee & Emmanuel Farhi, 2024. "Networks, Barriers, and Trade," Econometrica, Econometric Society, vol. 92(2), pages 505-541, March.
    8. Blair Fix, 2019. "The Aggregation Problem: Implications for Ecological and Biophysical Economics," Biophysical Economics and Resource Quality, Springer, vol. 4(1), pages 1-15, March.
    9. Nadia Garbellini, 2018. "Inequality in the 21st Century:A Critical Analysis of Piketty`s Work," Working Papers Series 69, Institute for New Economic Thinking.
    10. J. Barkley Rosser, 2020. "Austrian themes and the Cambridge capital theory controversies," The Review of Austrian Economics, Springer;Society for the Development of Austrian Economics, vol. 33(4), pages 415-431, December.
    11. Mandal, Biswajit & Roy Chakraborty, Labani & Sanyal, Alapan, 2023. "A Hybrid Mode of Production, Transaction, and Economic Growth: Implication of Digitalization," MPRA Paper 116960, University Library of Munich, Germany.
    12. Biswajit MANDAL & Labani Roy CHAKRABORTY & Alapan SANYAL, 2024. "A simple model of online marketing, production, profit and growth," Theoretical and Applied Economics, Asociatia Generala a Economistilor din Romania / Editura Economica, vol. 0(4(641), W), pages 53-66, Winter.
    13. Barbieri, Laura & Mussida, Chiara & Piva, Mariacristina & Vivarelli, Marco, 2019. "Testing the employment and skill impact of new technologies: A survey and some methodological issues," GLO Discussion Paper Series 397, Global Labor Organization (GLO).
    14. Avi J. Cohen & Geoffrey C. Harcourt, 2010. "Reswitching and Reversing in Capital Theory," Chapters, in: Mark Blaug & Peter Lloyd (ed.), Famous Figures and Diagrams in Economics, chapter 24, Edward Elgar Publishing.
    15. Fujiy,Brian C. & Ghose,Devaki & Khanna,Gaurav, 2024. "Production Networks and Firm-level Elasticities of Substitution," Policy Research Working Paper Series 10782, The World Bank.
    16. Jesus Felipe & Franklin M. Fisher, 2003. "Aggregation in Production Functions: What Applied Economists should Know," Metroeconomica, Wiley Blackwell, vol. 54(2‐3), pages 208-262, May.
    17. Jesus Felipe & John McCombie, 2024. "The Aggregate Production Function and Solow's "Three Denials"," Economics Working Paper Archive wp_1046, Levy Economics Institute.
    18. Fossen, Frank M. & Sorgner, Alina, 2022. "New digital technologies and heterogeneous wage and employment dynamics in the United States: Evidence from individual-level data," Technological Forecasting and Social Change, Elsevier, vol. 175(C).
    19. Laura Barbieri & Chiara Mussida & Mariacristina Piva & Marco Vivarelli, 2019. "Testing the employment impact of automation, robots and AI: A survey and some methodological issues," DISCE - Working Papers del Dipartimento di Politica Economica dipe0006, Università Cattolica del Sacro Cuore, Dipartimenti e Istituti di Scienze Economiche (DISCE).
    20. Sasaki, Hiroaki & Hagiwara, Takefumi & Pham, Huong & Fukatani, Noriki & Ogawa, Shogo & Okahara, Naoto, 2021. "How Does Automation Affect Economic Growth and Income Distribution in a Two-Class Economy?," MPRA Paper 106481, University Library of Munich, Germany.

    More about this item

    JEL classification:

    • E0 - Macroeconomics and Monetary Economics - - General
    • E1 - Macroeconomics and Monetary Economics - - General Aggregative Models
    • E25 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Aggregate Factor Income Distribution

    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:nbr:nberwo:25293. 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: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/nberrus.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.