IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/87437.html
   My bibliography  Save this paper

Modelling Efficiency Effects in a True Fixed Effects Stochastic Frontier

Author

Listed:
  • Paul, Satya
  • Shankar, Sriram

Abstract

This paper proposes a stochastic frontier panel data model which includes time-invariant unobserved heterogeneity along with the efficiency effects. Following Paul and Shankar (2018), the efficiency effects are specified by a standard normal cumulative distribution function of exogenous variables which ensures the efficiency scores to lie in a unit interval. This specification eschews one-sided error term present in almost all the existing inefficiency effects models. The model parameters can be estimated by non-linear least squares after removing the individual effects by the usual within transformation or using non-linear least squares dummy variables (NLLSDV) estimator. The efficiency scores are directly calculated once the model is estimated. An empirical illustration based on widely used panel data on Indian farmers is presented.

Suggested Citation

  • Paul, Satya & Shankar, Sriram, 2018. "Modelling Efficiency Effects in a True Fixed Effects Stochastic Frontier," MPRA Paper 87437, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:87437
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/87437/1/MPRA_paper_87437.pdf
    File Function: original version
    Download Restriction: no
    File URL: https://mpra.ub.uni-muenchen.de/89235/1/MPRA_paper_87437.pdf
    File Function: revised version
    Download Restriction: no
    File URL: https://mpra.ub.uni-muenchen.de/89236/9/MPRA_paper_89236.pdf
    File Function: revised version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Roberto Colombi & Subal Kumbhakar & Gianmaria Martini & Giorgio Vittadini, 2014. "Closed-skew normality in stochastic frontiers with individual effects and long/short-run efficiency," Journal of Productivity Analysis, Springer, vol. 42(2), pages 123-136, October.
    2. Wikström, Daniel, 2015. "Consistent method of moments estimation of the true fixed effects model," Economics Letters, Elsevier, vol. 137(C), pages 62-69.
    3. Barrett, Christopher B., 1996. "On price risk and the inverse farm size-productivity relationship," Journal of Development Economics, Elsevier, vol. 51(2), pages 193-215, December.
    4. Massimo Filippini & William Greene, 2016. "Persistent and transient productive inefficiency: a maximum simulated likelihood approach," Journal of Productivity Analysis, Springer, vol. 45(2), pages 187-196, April.
    5. Coelli, Tim J. & Battese, George E., 1996. "Identification Of Factors Which Influence The Technical Inefficiency Of Indian Farmers," Australian Journal of Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 40(2), pages 1-26, August.
    6. Helfand, Steven M. & Levine, Edward S., 2004. "Farm size and the determinants of productive efficiency in the Brazilian Center-West," Agricultural Economics, Blackwell, vol. 31(2-3), pages 241-249, December.
    7. Caudill, Steven B. & Ford, Jon M., 1993. "Biases in frontier estimation due to heteroscedasticity," Economics Letters, Elsevier, vol. 41(1), pages 17-20.
    8. Hadri, Kaddour, 1999. "Estimation of a Doubly Heteroscedastic Stochastic Frontier Cost Function," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(3), pages 359-363, July.
    9. Justin Kagin & J. Edward Taylor & Antonio Yúnez-Naude, 2016. "Inverse Productivity or Inverse Efficiency? Evidence from Mexico," Journal of Development Studies, Taylor & Francis Journals, vol. 52(3), pages 396-411, March.
    10. Wang, Hung-Jen & Ho, Chia-Wen, 2010. "Estimating fixed-effect panel stochastic frontier models by model transformation," Journal of Econometrics, Elsevier, vol. 157(2), pages 286-296, August.
    11. 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.
    12. Dominique Deprins & Léopold Simar, 1989. "Estimation de frontières déterministes avec facteurs exogénes d'inefficacité," Annals of Economics and Statistics, GENES, issue 14, pages 117-150.
    13. 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.
    14. Belotti, Federico & Ilardi, Giuseppe, 2018. "Consistent inference in fixed-effects stochastic frontier models," Journal of Econometrics, Elsevier, vol. 202(2), pages 161-177.
    15. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    16. Schmidt, Peter & Sickles, Robin C, 1984. "Production Frontiers and Panel Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(4), pages 367-374, October.
    17. Bhalla, Surjit S & Roy, Prannoy L, 1988. "Mis-specification in Farm Productivity Analysis: The Role of Land Quality," Oxford Economic Papers, Oxford University Press, vol. 40(1), pages 55-73, March.
    18. 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.
    19. Chen, Yi-Yi & Schmidt, Peter & Wang, Hung-Jen, 2014. "Consistent estimation of the fixed effects stochastic frontier model," Journal of Econometrics, Elsevier, vol. 181(2), pages 65-76.
    20. 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.
    21. repec:adr:anecst:y:1989:i:14:p:06 is not listed on IDEAS
    22. K. Kalirajan, 1981. "An Econometric Analysis of Yield Variability in Paddy Production," Canadian Journal of Agricultural Economics/Revue canadienne d'agroeconomie, Canadian Agricultural Economics Society/Societe canadienne d'agroeconomie, vol. 29(3), pages 283-294, November.
    23. Antonio Alvarez & Christine Amsler & Luis Orea & Peter Schmidt, 2006. "Interpreting and Testing the Scaling Property in Models where Inefficiency Depends on Firm Characteristics," Journal of Productivity Analysis, Springer, vol. 25(3), pages 201-212, June.
    24. Carter, Michael R, 1984. "Identification of the Inverse Relationship between Farm Size and Productivity: An Empirical Analysis of Peasant Agricultural Production," Oxford Economic Papers, Oxford University Press, vol. 36(1), pages 131-145, March.
    25. 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.
    26. Greene, William, 2005. "Reconsidering heterogeneity in panel data estimators of the stochastic frontier model," Journal of Econometrics, Elsevier, vol. 126(2), pages 269-303, June.
    27. Dominique DEPRINS & Léopold SIMAR, 1989. "Estimating Technical Inefficiencies With Correction For Environmental Conditions," Annals of Public and Cooperative Economics, Wiley Blackwell, vol. 60(1), pages 81-102, January.
    28. Hung-Jen Wang, 2002. "Heteroscedasticity and Non-Monotonic Efficiency Effects of a Stochastic Frontier Model," Journal of Productivity Analysis, Springer, vol. 18(3), pages 241-253, November.
    29. Battese, George E. & Coelli, Tim J. & Colby, T.C., 1989. "Estimation of Frontier Production Functions and the Efficiencies of Indian Farms Using Panel Data from ICRISAT's Village Level Studies," 1989 Conference (33rd), February 7-9, 1989, Christchurch, New Zealand 144383, Australian Agricultural and Resource Economics Society.
    30. Kumbhakar, Subal C., 1991. "Estimation of technical inefficiency in panel data models with firm- and time-specific effects," Economics Letters, Elsevier, vol. 36(1), pages 43-48, May.
    31. Amartya K. Sen, 1966. "Peasants and Dualism with or without Surplus Labor," Journal of Political Economy, University of Chicago Press, vol. 74, pages 425-425.
    32. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    33. Subal C. Kumbhakar & Almas Heshmati, 1995. "Efficiency Measurement in Swedish Dairy Farms: An Application of Rotating Panel Data, 1976–88," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 77(3), pages 660-674.
    34. Eswaran, Mukesh & Kotwal, Ashok, 1986. "Access to Capital and Agrarian Production Organisation," Economic Journal, Royal Economic Society, vol. 96(382), pages 482-498, June.
    35. Benjamin, Dwayne, 1995. "Can unobserved land quality explain the inverse productivity relationship?," Journal of Development Economics, Elsevier, vol. 46(1), pages 51-84, February.
    36. Paul, Satya & Shankar, Sriram, 2018. "On estimating efficiency effects in a stochastic frontier model," European Journal of Operational Research, Elsevier, vol. 271(2), pages 769-774.
    37. 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.
    38. Kumbhakar, Subal C., 1990. "Production frontiers, panel data, and time-varying technical inefficiency," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 201-211.
    39. Simar, Leopold & Wilson, Paul W., 2007. "Estimation and inference in two-stage, semi-parametric models of production processes," Journal of Econometrics, Elsevier, vol. 136(1), pages 31-64, January.
    40. Kumbhakar, Subal C & Hjalmarsson, Lennart, 1995. "Labour-Use Efficiency in Swedish Social Insurance Offices," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(1), pages 33-47, Jan.-Marc.
    41. Lancaster, Tony, 2000. "The incidental parameter problem since 1948," Journal of Econometrics, Elsevier, vol. 95(2), pages 391-413, April.
    42. Battese, George E. & Coelli, Tim J., 1988. "Prediction of firm-level technical efficiencies with a generalized frontier production function and panel data," Journal of Econometrics, Elsevier, vol. 38(3), pages 387-399, July.
    43. Pitt, Mark M. & Lee, Lung-Fei, 1981. "The measurement and sources of technical inefficiency in the Indonesian weaving industry," Journal of Development Economics, Elsevier, vol. 9(1), pages 43-64, August.
    44. Caudill, Steven B & Ford, Jon M & Gropper, Daniel M, 1995. "Frontier Estimation and Firm-Specific Inefficiency Measures in the Presence of Heteroscedasticity," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(1), pages 105-111, January.
    45. Heltberg, Rasmus, 1998. "Rural market imperfections and the farm size-- productivity relationship: Evidence from Pakistan," World Development, Elsevier, vol. 26(10), pages 1807-1826, October.
    46. 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.
    47. 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)

    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. 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.
    2. Paul, Satya & Shankar, Sriram, 2018. "On estimating efficiency effects in a stochastic frontier model," European Journal of Operational Research, Elsevier, vol. 271(2), pages 769-774.
    3. 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.
    4. Ali M. Oumer & Amin Mugera & Michael Burton & Atakelty Hailu, 2022. "Technical efficiency and firm heterogeneity in stochastic frontier models: application to smallholder maize farms in Ethiopia," Journal of Productivity Analysis, Springer, vol. 57(2), pages 213-241, April.
    5. Subal Kumbhakar & Gudbrand Lien & J. Hardaker, 2014. "Technical efficiency in competing panel data models: a study of Norwegian grain farming," Journal of Productivity Analysis, Springer, vol. 41(2), pages 321-337, April.
    6. Orea, Luis, 2019. "The Econometric Measurement of Firms’ Efficiency," Efficiency Series Papers 2019/02, University of Oviedo, Department of Economics, Oviedo Efficiency Group (OEG).
    7. Gralka, Sabine, 2018. "Stochastic frontier analysis in higher education: A systematic review," CEPIE Working Papers 05/18, Technische Universität Dresden, Center of Public and International Economics (CEPIE).
    8. Martini, Gianmaria & Scotti, Davide & Viola, Domenico & Vittadini, Giorgio, 2020. "Persistent and temporary inefficiency in airport cost function: An application to Italy," Transportation Research Part A: Policy and Practice, Elsevier, vol. 132(C), pages 999-1019.
    9. Belotti, Federico & Ilardi, Giuseppe, 2018. "Consistent inference in fixed-effects stochastic frontier models," Journal of Econometrics, Elsevier, vol. 202(2), pages 161-177.
    10. Lien, Gudbrand & Kumbhakar, Subal C. & Alem, Habtamu, 2018. "Endogeneity, heterogeneity, and determinants of inefficiency in Norwegian crop-producing farms," International Journal of Production Economics, Elsevier, vol. 201(C), pages 53-61.
    11. 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.
    12. Idaira Cabrera‐Suárez & Jorge V. Pérez‐Rodríguez, 2021. "Bank branch performance and cost efficiency: A stochastic frontier panel data approach," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(4), pages 5850-5863, October.
    13. Roberto Colombi & Gianmaria Martini & Giorgio Vittadini, 2017. "Determinants of transient and persistent hospital efficiency: The case of Italy," Health Economics, John Wiley & Sons, Ltd., vol. 26(S2), pages 5-22, September.
    14. Badunenko, Oleg & D’Inverno, Giovanna & De Witte, Kristof, 2023. "On distinguishing the direct causal effect of an intervention from its efficiency-enhancing effects," European Journal of Operational Research, Elsevier, vol. 310(1), pages 432-447.
    15. Antti Saastamoinen, 2015. "Heteroscedasticity Or Production Risk? A Synthetic View," Journal of Economic Surveys, Wiley Blackwell, vol. 29(3), pages 459-478, July.
    16. Anbes Tenaye, 2020. "Technical Efficiency of Smallholder Agriculture in Developing Countries: The Case of Ethiopia," Economies, MDPI, vol. 8(2), pages 1-27, April.
    17. Émilie Caldeira & Ali Compaore & Alou Adessé Dama & Mario Mansour & Grégoire Rota-Graziosi, 2019. "Effort fiscal en Afrique subsaharienne : les résultats d’une nouvelle base de données," Revue d’économie du développement, De Boeck Université, vol. 27(4), pages 5-51.
    18. 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.
    19. 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.
    20. Ajayi, Victor & Weyman-Jones, Tom, 2021. "State-level electricity generation efficiency: Do restructuring and regulatory institutions matter in the US?," Energy Economics, Elsevier, vol. 104(C).

    More about this item

    Keywords

    Fixed effects; Stochastic frontier; Technical efficiency; Standard normal cumulative distribution function; Non-linear least squares.;
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity
    • Q12 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Agriculture - - - Micro Analysis of Farm Firms, Farm Households, and Farm Input Markets

    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:pra:mprapa:87437. 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: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.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.