IDEAS home Printed from https://ideas.repec.org/p/rtv/ceisrp/462.html
   My bibliography  Save this paper

Imposing monotonicity in stochastic frontier models: an iterative nonlinear least squares procedure

Author

Listed:

Abstract

Despite its importance, the monotonicity condition is typically overlooked in stochastic frontier analysis. This article illustrates a straightforward and useful method for the estimation of semiparametric stochastic frontier models imposing such constraint and incorporating exogenous inefficiency effects exploiting the scaling property. An iterative estimation algorithm based on nonlinear least squares is developed and the behavior of the proposed procedure is investigated through a set of Monte Carlo experiments comparing its finite sample properties with those of available alternatives. The simulation results highlight very good performance of the new algorithm which outperforms the competitors in small samples and in presence of small signal-to-noise ratios. Our results also show that the fraction of observations for which monotonicity naturally holds is generally quite small if this condition is not imposed. An application based on FADN agricultural data illustrates the usefulness of the proposed algorithm.

Suggested Citation

  • Federico Belotti & Giancarlo Ferrara, 2019. "Imposing monotonicity in stochastic frontier models: an iterative nonlinear least squares procedure," CEIS Research Paper 462, Tor Vergata University, CEIS, revised 29 Jan 2021.
    • Handle: RePEc:rtv:ceisrp:462
    as

    Download full text from publisher

    File URL: https://ceistorvergata.it/RePEc/rpaper/RP462.pdf
    File Function: Main text
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Mugabe, Douglas & Etienne, Xiaoli L., 2016. "How Efficient Is Maize Production among Smallholder Farmers in Zimbabwe?," 2016 Annual Meeting, July 31-August 2, Boston, Massachusetts 235938, Agricultural and Applied Economics Association.
    2. Racine, Jeff & Li, Qi, 2004. "Nonparametric estimation of regression functions with both categorical and continuous data," Journal of Econometrics, Elsevier, vol. 119(1), pages 99-130, March.
    3. 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.
    4. Francesco Vidoli & Giancarlo Ferrara, 2015. "Analyzing Italian citrus sector by semi-nonparametric frontier efficiency models," Empirical Economics, Springer, vol. 49(2), pages 641-658, September.
    5. Jondrow, James & Knox Lovell, C. A. & Materov, Ivan S. & Schmidt, Peter, 1982. "On the estimation of technical inefficiency in the stochastic frontier production function model," Journal of Econometrics, Elsevier, vol. 19(2-3), pages 233-238, August.
    6. Arne Henningsen & Christian Henning, 2009. "Imposing regional monotonicity on translog stochastic production frontiers with a simple three-step procedure," Journal of Productivity Analysis, Springer, vol. 32(3), pages 217-229, December.
    7. Hung-jen Wang & Peter Schmidt, 2002. "One-Step and Two-Step Estimation of the Effects of Exogenous Variables on Technical Efficiency Levels," Journal of Productivity Analysis, Springer, vol. 18(2), pages 129-144, September.
    8. Hayfield, Tristen & Racine, Jeffrey S., 2008. "Nonparametric Econometrics: The np Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 27(i05).
    9. Meeusen, Wim & van den Broeck, Julien, 1977. "Efficiency Estimation from Cobb-Douglas Production Functions with Composed Error," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 18(2), pages 435-444, June.
    10. Ferrara, Giancarlo & Vidoli, Francesco, 2017. "Semiparametric stochastic frontier models: A generalized additive model approach," European Journal of Operational Research, Elsevier, vol. 258(2), pages 761-777.
    11. Xiaoli L. Etienne & Giancarlo Ferrara & Douglas Mugabe, 2019. "How efficient is maize production among smallholder farmers in Zimbabwe? A comparison of semiparametric and parametric frontier efficiency analyses," Applied Economics, Taylor & Francis Journals, vol. 51(26), pages 2855-2871, June.
    12. Muggeo, Vito M.R. & Ferrara, Giancarlo, 2008. "Fitting generalized linear models with unspecified link function: A P-spline approach," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2529-2537, January.
    13. 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.
    14. Kumbhakar, Subal C & Ghosh, Soumendra & McGuckin, J Thomas, 1991. "A Generalized Production Frontier Approach for Estimating Determinants of Inefficiency in U.S. Dairy Farms," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(3), pages 279-286, July.
    15. 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.
    16. Konstantinos Giannakas & Kien C. Tran & Vangelis Tzouvelekas, 2003. "On the choice of functional form in stochastic frontier modeling," Empirical Economics, Springer, vol. 28(1), pages 75-100, January.
    17. Battese, G E & Coelli, T J, 1995. "A Model for Technical Inefficiency Effects in a Stochastic Frontier Production Function for Panel Data," Empirical Economics, Springer, vol. 20(2), pages 325-332.
    18. 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.
    19. Parmeter, Christopher F. & Kumbhakar, Subal C., 2014. "Efficiency Analysis: A Primer on Recent Advances," Foundations and Trends(R) in Econometrics, now publishers, vol. 7(3-4), pages 191-385, December.
    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. Hou, Zheng & Roseta-Palma, Catarina & Ramalho, Joaquim J.S., 2024. "Can operational efficiency in the Portuguese electricity sector be improved? Yes, but..," Energy Policy, Elsevier, vol. 190(C).

    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. Christopher F. Parmeter & Hung-Jen Wang & Subal C. Kumbhakar, 2017. "Nonparametric estimation of the determinants of inefficiency," Journal of Productivity Analysis, Springer, vol. 47(3), pages 205-221, June.
    2. Tran, Kien C. & Tsionas, Efthymios G., 2009. "Estimation of nonparametric inefficiency effects stochastic frontier models with an application to British manufacturing," Economic Modelling, Elsevier, vol. 26(5), pages 904-909, September.
    3. Giovanni Forchini & Raoul Theler, 2023. "Semi-parametric modelling of inefficiencies in stochastic frontier analysis," Journal of Productivity Analysis, Springer, vol. 59(2), pages 135-152, April.
    4. Czekaj, Tomasz G., 2015. "Measuring the Technical Efficiency of Farms Producing Environmental Output: Semiparametric Estimation of Multi-output Stochastic Ray Production Frontiers," 2015 Conference, August 9-14, 2015, Milan, Italy 211555, International Association of Agricultural Economists.
    5. Valentin Zelenyuk & Zhichao Wang, 2023. "Random vs. Explained Inefficiency in Stochastic Frontier Analysis: The Case of Queensland Hospitals," CEPA Working Papers Series WP052023, School of Economics, University of Queensland, Australia.
    6. Ferrara, Giancarlo & Vidoli, Francesco, 2017. "Semiparametric stochastic frontier models: A generalized additive model approach," European Journal of Operational Research, Elsevier, vol. 258(2), pages 761-777.
    7. 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.
    8. Taining Wang & Jinjing Tian & Feng Yao, 2021. "Does high debt ratio influence Chinese firms’ performance? A semiparametric stochastic frontier approach with zero inefficiency," Empirical Economics, Springer, vol. 61(2), pages 587-636, August.
    9. Tomasz Gerard Czekaj, 2013. "Measuring the Technical Efficiency of Farms Producing Environmental Output: Parametric and Semiparametric Estimation of Multi-output Stochastic Ray Production Frontiers," IFRO Working Paper 2013/21, University of Copenhagen, Department of Food and Resource Economics.
    10. Antti Saastamoinen, 2015. "Heteroscedasticity Or Production Risk? A Synthetic View," Journal of Economic Surveys, Wiley Blackwell, vol. 29(3), pages 459-478, July.
    11. Subal C. Kumbhakar & Christopher F. Parmeter & Valentin Zelenyuk, 2022. "Stochastic Frontier Analysis: Foundations and Advances I," Springer Books, in: Subhash C. Ray & Robert G. Chambers & Subal C. Kumbhakar (ed.), Handbook of Production Economics, chapter 8, pages 331-370, Springer.
    12. ferrara, giancarlo & campagna, arianna & bucci, valeria & atella, vincenzo, 2021. "Presumptive taxation and firms’ efficiency: an integrated approach for tax compliance analysis," MPRA Paper 111516, University Library of Munich, Germany.
    13. Schmidt, Rouven & Kneib, Thomas, 2023. "Multivariate distributional stochastic frontier models," Computational Statistics & Data Analysis, Elsevier, vol. 187(C).
    14. Paul, Satya & Shankar, Sriram, 2018. "Modelling Efficiency Effects in a True Fixed Effects Stochastic Frontier," MPRA Paper 87437, University Library of Munich, Germany.
    15. Satya Paul & Sriram Shankar, 2020. "Estimating efficiency effects in a panel data stochastic frontier model," Journal of Productivity Analysis, Springer, vol. 53(2), pages 163-180, April.
    16. Bao Hoang Nguyen & Robin C. Sickles & Valentin Zelenyuk, 2021. "What do we know from the vast literature on efficiency and productivity in healthcare? A Systematic Review and Bibliometric Analysis," CEPA Working Papers Series WP092021, School of Economics, University of Queensland, Australia.
    17. Larson, Donald F. & Plessmann, Frank, 2009. "Do farmers choose to be inefficient? Evidence from Bicol," Journal of Development Economics, Elsevier, vol. 90(1), pages 24-32, September.
    18. Bao Hoang Nguyen & Robin C. Sickles & Valentin Zelenyuk, 2022. "Efficiency Analysis with Stochastic Frontier Models Using Popular Statistical Softwares," Springer Books, in: Duangkamon Chotikapanich & Alicia N. Rambaldi & Nicholas Rohde (ed.), Advances in Economic Measurement, chapter 0, pages 129-171, Springer.
    19. Martín Rossi, 2015. "The Econometrics Approach to the Measurement of Efficiency: A Survey," Working Papers 117, Universidad de San Andres, Departamento de Economia, revised Feb 2015.
    20. Giancarlo Ferrara & Arianna Campagna & Vincenzo Atella, 2019. "Disentangling tax evasion from inefficiency in firms tax declaration: an integrated approach," CEIS Research Paper 468, Tor Vergata University, CEIS, revised 06 Sep 2019.

    More about this item

    Keywords

    Efficiency; stochastic frontiers; monotonicity; nonlinear least squares; heteroskedasticity; simulation;
    All these keywords.

    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:rtv:ceisrp:462. 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: Barbara Piazzi (email available below). General contact details of provider: https://edirc.repec.org/data/csrotit.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.