IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2504.19832.html
   My bibliography  Save this paper

Identifying the Frontier Structural Function and Bounding Mean Deviations

Author

Listed:
  • Dan Ben-Moshe
  • David Genesove

Abstract

This paper analyzes a model in which an outcome variable equals a frontier function of inputs less a nonnegative unobserved deviation. If zero lies in the support of the deviation given inputs, then the frontier function is identified by the supremum outcome at those inputs. This obviates the need for instrumental variables. Implementation requires allowing for the distribution of deviations to depend on inputs, thus not ruling out endogeneity. Including random errors yields a stochastic frontier analysis model. We generalize this model to allow the joint distribution of deviations and errors to depend on inputs. We derive a lower bound for the mean deviation based only on variance and skewness, requiring no other distributional assumptions and remaining valid even when zero is not in the support of deviations or data are sparse near the frontier. We apply our results to a frontier production function, where deviations represent inefficiencies.

Suggested Citation

  • Dan Ben-Moshe & David Genesove, 2025. "Identifying the Frontier Structural Function and Bounding Mean Deviations," Papers 2504.19832, arXiv.org, revised May 2025.
  • Handle: RePEc:arx:papers:2504.19832
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2504.19832
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Richard Schmalensee, 2000. "Antitrust Issues in Schumpeterian Industries," American Economic Review, American Economic Association, vol. 90(2), pages 192-196, May.
    2. Jeffrey M. Perloff & Steven C. Salop, 1985. "Equilibrium with Product Differentiation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 52(1), pages 107-120.
    3. 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.
    4. Jean-Pierre Florens & Léopold Simar & Ingrid Van Keilegom, 2020. "Estimation of the Boundary of a Variable Observed With Symmetric Error," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(529), pages 425-441, January.
    5. Dan Ben-Moshe & David Genesove, 2022. "Regulation and Frontier Housing Supply," Papers 2208.01969, arXiv.org, revised Sep 2024.
    6. Subhash C. Ray & Robert G. Chambers & Subal C. Kumbhakar (ed.), 2022. "Handbook of Production Economics," Springer Books, Springer, number 978-981-10-3455-8, March.
    7. Léopold Simar & Ingrid Keilegom & Valentin Zelenyuk, 2017. "Nonparametric least squares methods for stochastic frontier models," Journal of Productivity Analysis, Springer, vol. 47(3), pages 189-204, June.
    8. Kutlu, Levent & Tran, Kien C. & Tsionas, Mike G., 2020. "A spatial stochastic frontier model with endogenous frontier and environmental variables," European Journal of Operational Research, Elsevier, vol. 286(1), pages 389-399.
    9. Christopher F. Parmeter & Valentin Zelenyuk, 2019. "Combining the Virtues of Stochastic Frontier and Data Envelopment Analysis," Operations Research, INFORMS, vol. 67(6), pages 1628-1658, November.
    10. Centorrino, Samuele & Pérez-Urdiales, María, 2023. "Maximum likelihood estimation of stochastic frontier models with endogeneity," Journal of Econometrics, Elsevier, vol. 234(1), pages 82-105.
    11. 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.
    12. 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.
    13. Aurélie Bertrand & Ingrid Van Keilegom & Catherine Legrand, 2019. "Flexible parametric approach to classical measurement error variance estimation without auxiliary data," Biometrics, The International Biometric Society, vol. 75(1), pages 297-307, March.
    14. Daniel A. Ackerberg & Kevin Caves & Garth Frazer, 2015. "Identification Properties of Recent Production Function Estimators," Econometrica, Econometric Society, vol. 83, pages 2411-2451, November.
    15. Aurore Delaigle & Peter Hall, 2016. "Methodology for non-parametric deconvolution when the error distribution is unknown," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(1), pages 231-252, January.
    16. 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.
    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. Amsler, Christine & Prokhorov, Artem & Schmidt, Peter, 2016. "Endogeneity in stochastic frontier models," Journal of Econometrics, Elsevier, vol. 190(2), pages 280-288.
    19. Emir Malikov & Shunan Zhao & Subal C. Kumbhakar, 2020. "Estimation of firm‐level productivity in the presence of exports: Evidence from China's manufacturing," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(4), pages 457-480, June.
    20. Sungho Park & Sachin Gupta, 2012. "Handling Endogenous Regressors by Joint Estimation Using Copulas," Marketing Science, INFORMS, vol. 31(4), pages 567-586, July.
    21. Goldenshluger, A. & Tsybakov, A., 2004. "Estimating the endpoint of a distribution in the presence of additive observation errors," Statistics & Probability Letters, Elsevier, vol. 68(1), pages 39-49, June.
    22. Reifschneider, David & Stevenson, Rodney, 1991. "Systematic Departures from the Frontier: A Framework for the Analysis of Firm Inefficiency," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 32(3), pages 715-723, August.
    23. Fan, Yanqin & Li, Qi & Weersink, Alfons, 1996. "Semiparametric Estimation of Stochastic Production Frontier Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(4), pages 460-468, October.
    24. Chad Syverson, 2004. "Market Structure and Productivity: A Concrete Example," Journal of Political Economy, University of Chicago Press, vol. 112(6), pages 1181-1222, December.
    25. Mustafa U. Karakaplan & Levent Kutlu, 2017. "Endogeneity in panel stochastic frontier models: an application to the Japanese cotton spinning industry," Applied Economics, Taylor & Francis Journals, vol. 49(59), pages 5935-5939, December.
    26. Luís Cabral, 2011. "Dynamic Price Competition with Network Effects," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 78(1), pages 83-111.
    27. 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.
    28. Hall, Robert E, 1988. "The Relation between Price and Marginal Cost in U.S. Industry," Journal of Political Economy, University of Chicago Press, vol. 96(5), pages 921-947, October.
    29. Kumbhakar, Subal C. & Park, Byeong U. & Simar, Leopold & Tsionas, Efthymios G., 2007. "Nonparametric stochastic frontiers: A local maximum likelihood approach," Journal of Econometrics, Elsevier, vol. 137(1), pages 1-27, March.
    30. Christopher F. Parmeter & Shirong Zhao, 2023. "An alternative corrected ordinary least squares estimator for the stochastic frontier model," Empirical Economics, Springer, vol. 64(6), pages 2831-2857, June.
    31. Glaeser, Edward L & Gyourko, Joseph & Saks, Raven, 2005. "Why Is Manhattan So Expensive? Regulation and the Rise in Housing Prices," Journal of Law and Economics, University of Chicago Press, vol. 48(2), pages 331-369, October.
    32. Artem Prokhorov & Kien C. Tran & Mike G. Tsionas, 2021. "Estimation of semi- and nonparametric stochastic frontier models with endogenous regressors," Empirical Economics, Springer, vol. 60(6), pages 3043-3068, June.
    33. Olson, Jerome A. & Schmidt, Peter & Waldman, Donald M., 1980. "A Monte Carlo study of estimators of stochastic frontier production functions," Journal of Econometrics, Elsevier, vol. 13(1), pages 67-82, May.
    34. Fan, Jianqing & Yao, Qiwei, 1998. "Efficient estimation of conditional variance functions in stochastic regression," LSE Research Online Documents on Economics 6635, London School of Economics and Political Science, LSE Library.
    35. Christopher R. Knittel, 2002. "Alternative Regulatory Methods And Firm Efficiency: Stochastic Frontier Evidence From The U.S. Electricity Industry," The Review of Economics and Statistics, MIT Press, vol. 84(3), pages 530-540, August.
    36. Aigner, Dennis & Lovell, C. A. Knox & Schmidt, Peter, 1977. "Formulation and estimation of stochastic frontier production function models," Journal of Econometrics, Elsevier, vol. 6(1), pages 21-37, July.
    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. Mike Tsionas & Christopher F. Parmeter & Valentin Zelenyuk, 2021. "Bridging the Divide? Bayesian Artificial Neural Networks for Frontier Efficiency Analysis," CEPA Working Papers Series WP082021, School of Economics, University of Queensland, Australia.
    2. Simone Lenzu & Francesco Manaresi, 2019. "Sources and implications of resource misallocation: new evidence from firm-level marginal products and user costs," Questioni di Economia e Finanza (Occasional Papers) 485, Bank of Italy, Economic Research and International Relations Area.
    3. 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.
    4. Lenzu, Simone & Manaresi, Francesco, 2018. "Do Marginal Products Differ from User Costs? Micro-Level Evidence from Italian Firms," Working Papers 276, The University of Chicago Booth School of Business, George J. Stigler Center for the Study of the Economy and the State.
    5. David Van Dijcke, 2022. "On the Non-Identification of Revenue Production Functions," Papers 2212.04620, arXiv.org, revised May 2024.
    6. Miller, Nathan H., 2025. "Industrial organization and The Rise of Market Power," International Journal of Industrial Organization, Elsevier, vol. 98(C).
    7. 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.
    8. 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.
    9. 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.
    10. Florin Maican & Matilda Orth, 2017. "Productivity Dynamics and the Role of ‘Big-Box’ Entrants in Retailing," Journal of Industrial Economics, Wiley Blackwell, vol. 65(2), pages 397-438, June.
    11. Kritikos, Alexander S. & Schiersch, Alexander & Stiel, Caroline, 2021. "The Productivity Puzzle in Business Services," IZA Discussion Papers 14610, Institute of Labor Economics (IZA).
    12. R. Monin & M. Suarez Castillo, 2020. "Product switching, market power and distance to core competency," Documents de Travail de l'Insee - INSEE Working Papers g2020-06, Institut National de la Statistique et des Etudes Economiques.
    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. Kutlu, Levent & Tran, Kien C. & Tsionas, Mike G., 2019. "A time-varying true individual effects model with endogenous regressors," Journal of Econometrics, Elsevier, vol. 211(2), pages 539-559.
    15. Dibyendu Maiti & Chiranjib Neogi, 2024. "Endogeneity-corrected stochastic frontier with market imperfections," Empirical Economics, Springer, vol. 67(3), pages 1149-1183, September.
    16. Lauren Chenarides & Miguel I. Gómez & Timothy J. Richards & Koichi Yonezawa, 2024. "Retail Markups and Discount-Store Entry," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 64(1), pages 147-181, February.
    17. Puggioni Daniela, 2019. "Productivity, Markups, and Trade: Evidence from Mexican Manufacturing Industries," Working Papers 2019-14, Banco de México.
    18. Sheng, Yu & Xu, Xinpeng & Rozelle, Scott, 2024. "Market structure, resource allocation, and industry productivity growth: Firm-level evidence from China's steel industry," China Economic Review, Elsevier, vol. 83(C).
    19. Dario Tortarolo & Roman D. Zarate, 2020. "Imperfect competition in product and labour markets. A quantitative analysis," Discussion Papers 2020-05, Nottingham Interdisciplinary Centre for Economic and Political Research (NICEP).
    20. 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.

    More about this item

    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:arx:papers:2504.19832. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.