Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

Efficiency Analysis with Stochastic Frontier Models Using Popular Statistical Softwares

  • Chapter
  • First Online:
Advances in Economic Measurement

Abstract

This chapter provides a brief introduction to the stochastic frontier paradigm—one of the most powerful techniques for performance analysis developed over the last few decades to address various research questions for many contexts with empirical applications in a wide variety of economic sectors such as banking, healthcare, agriculture and so on. The chapter also documents the estimation routines used to implement the classical models as well as the recent developments in this research area for practitioners, especially those who are willing to use Stata, but also with tips on sources for R and Matlab users.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Notes

  1. 1.

    Another powerful technique for performance analysis is data envelopment analysis—the technique based on the mathematical linear programming method proposed by Farrell (1957) and popularised by Charnes et al. (1978).

  2. 2.

    On this aspect, our chapter complements earlier surveys on empirical frontier application and productivity and efficiency analysis software, e.g., Daraio et al. (2019, 2020). Besides, the chapter also complements the previous contributions of Belotti et al. (2013) and Kumbhakar et al. (2015), who focused only on stochastic frontier analysis using Stata, by providing the sources on analogous implementations in Matlab and R. Moreover, we also include the discussion about the semi-parametric stochastic frontier models with ready-to-use Stata codes to implement the model proposed by Simar et al. (2017), which to the best of our knowledge have not been documented elsewhere before.

  3. 3.

    In the panel data context, which we will discuss in the next sections, the composed error can include four components.

  4. 4.

    In this chapter, our discussion will follow the traditional exposition based on the production function. A similar exposition (with some adaptations) applies to other characterisations of the production side, such as cost function and revenue function. Meanwhile, more elaboration is needed if one is interested in measuring profit efficiency (see Färe et al., 2019; Sickles & Zelenyuk, 2019 Chap. 2) and references therein.

  5. 5.

    The formulation here is a convenient representation of a production relationship, where actual output is decomposed into the maximum output (with noise) and inefficiency, i.e., \(y_{i}=f\left( x_{i}|\beta \right) \exp \left( \varepsilon _{i}\right) =f\left( x_{i}|\beta \right) \exp \left( v_{i}\right) \exp \left( -u_{i}\right)\). After log-transformation, we have a linear relationship as shown in Eq. (3.1).

  6. 6.

    Multiple outputs also can be considered. For example, this can be done by employing a distance function instead of the production function or by looking at the estimation of the cost frontier or by converting outputs into polar coordinates (e.g., see Simar & Zelenyuk, 2011). One can also use dimension reduction techniques to reduce the dimension outputs or inputs into smaller dimensions, e.g., via Principle Component Analysis, or using economic or price-based aggregation (e.g., see related discussion in Zelenyuk (2020) and an application in Nguyen and Zelenyuk [2021]). The latter approach can be especially useful in the case of very large dimensions (sometimes called ‘big wide data’ cases), e.g., as is done for measuring the total output of countries (e.g., GDP), industries or firms (total revenue) or for some inputs (e.g., capital). Due to space limitation, we will focus here on the single output case, as was also considered in ALS and many other studies.

  7. 7.

    Other distributional assumptions such as exponential, truncated normal, gamma, and so on, can be used for the inefficiency term (e.g., see Almanidis & Sickles, 2012; Almanidis et al., 2014; Greene, 1980a, 1980b, 1990; Meeusen & van den Broeck, 1977; Stevenson, 1980).

  8. 8.

    The exact expression of the expected level of efficiency is given by \(E\left[ \exp \left( -u_{i}\right) \right] =2\Phi \left( -\sigma _{u}\right) \exp \left( \dfrac{\sigma _{u}^{2}}{2}\right)\).

  9. 9.

    It is worth noting here that although this estimator is unbiased, it is an inconsistent estimator of individual inefficiency (see more discussion in Jondrow et al., 1982).

  10. 10.

    One also can estimate the efficiency of a production unit by using the relationship \(E\left[\exp \left( -u_{i}\right) |\varepsilon _{i}\right]\approx 1-E\left[u_{i}|\varepsilon _{i}\right]\) or utilising the exact expression \(E\left[\exp \left( -u_{i}\right) |\varepsilon _{i}\right]=\exp \left( -\mu _{*i}+\frac{1}{2}\sigma _{*}^{2}\right) \frac{\Phi \left( \frac{\mu _{*i}}{\sigma _{*}}-\sigma _{*}\right) }{\Phi \left( \frac{\mu _{*i}}{\sigma _{*}}\right) }\) (Battese & Coelli, 1988).

  11. 11.

    The sfcross command (and the sfpanel command that we will discuss later for the panel data context) can be installed by executing the following command lines in Stata: ssc install sfcross and ssc install sfpanel.

  12. 12.

    The sfmodel and other user-written commands provided in the handbook of Kumbhakar et al. (2015) can be installed in Stata by executing the following command lines: net install sfbook_install, from (https://sites.google.com/site/sfbook2014/home/install/) replace and sfbook_install (see more details in Kumbhakar et al. 2015 and its website, https://sites.google.com/site/sfbook2014/).

  13. 13.

    The package frontier uses the Fortran source codes of Frontier 4.1 originally developed by Tim Coelli (see more details in the manual of the package available at https://cran.r-project.org/web/packages/frontier/frontier.pdf).

  14. 14.

    The website can be found at https://sites.google.com/site/productivityefficiency/home.

  15. 15.

    The Matlab codes accompanying Sickles and Zelenyuk (2019) are also converted to R codes by Sickles et al. (2020), which can be accessed via the link provided on the book website or directly via https://sites.google.com/site/productivityinr.

  16. 16.

    Cornwell et al. (1990) outlined estimators for a general model in which any set of regressors could be drivers of efficiency change, if efficiency was interpreted as firm-specific heterogeneity. These regressors could be time varying. Thus, the Cornwell et al. (1990) model was the first study about which we are aware to address the issue of environmental variables influencing efficiency levels.

  17. 17.

    Greene (2005a) also utilised the simulated maximum likelihood approach to estimate the model in the random effects framework.

  18. 18.

    The sftfe command can be installed by executing the following command line in Stata: net install sftfe.pkg.

  19. 19.

    This model specification was cast in the panel data context and popularised by Battese and Coelli (1995).

  20. 20.

    It is worth mentioning here that although being popularised by Wang and Schmidt (2002), Simar et al. (1994) appear to be the first who analysed the scaling property in detail.

  21. 21.

    Software instructions and downloadable codes are accessible at https://www.jstatsoft.org/article/view/v059i06.

  22. 22.

    The distributional assumptions on \(u_{i}\) and \(v_{i}\) allow obtaining a generalised version of JLMS-type estimates, although more interesting in the semi/non-parametric context are the estimates of \(E(u_{i}|x_{i}=x,z_{i}=z)\), which can be done for any values of interest for (x, z). The elasticities of \(E(u_{i}|x_{i}=x,z_{i}=z)\) can also be obtained, which can be done without any parametric assumptions on distributions, just by assuming that \(u_{i}\) comes from a one-parameter scale family (see Sect. 4 in Simar et al. 2017 for more details ).

  23. 23.

    For the results to some extent to be comparable, we deliberately do not include in this empirical illustration the stochastic frontier models with determinants of inefficiency.

  24. 24.

    Also, due to the computational difficulty in optimising the likelihood function, the result from Kumbhakar (1990) is not available for the dataset used in this empirical illustration.

  25. 25.

    Downloaded from http://www.uq.edu.au/economics/cepa/crob2005/software/CROB2005.zip.

  26. 26.

    For an illustration with this data with various DEA models see, e.g., Simar and Zelenyuk (2020).

  27. 27.

    To estimate the cross-sectional models, e.g., Aigner et al. (1977) and Simar et al. (2017) models, we pool the data across years.

  28. 28.

    The estimated distribution of estimated inefficiency from the Simar et al. (2017) model is showing some mass at zero (i.e., the phenomenon referred to as “wrong skewness” in stochastic frontier analysis) because 79 out 344 observations have \(\widehat{\sigma }_{u}^{3}\left( x_{i},z_{i}\right) <0\) and their inefficiency is set to equal to 0.

  29. 29.

    It is important to clarify here that for all the models, the means we refer to are averages of the estimates of individual inefficiencies.

  30. 30.

    For example, see Van den Broeck et al. (1994), Griffin and Steel (2004, 2007), and Liu et al. (2017).

  31. 31.

    For example, see Battese et al. (2004), O’Donnell et al. (2008), and Huang et al. (2014).

  32. 32.

    For example, see Glass et al. (2016), Orea and Álvarez (2019).

  33. 33.

    For example, see Amsler et al. (2016), Kutlu (2010), Karakaplan and Kutlu (2015, 2017), and Karakaplan (2017).

References

  • Adams, R. M., Berger, A. N., & Sickles, R. C. (1997). Computation and inference in semiparametric efficient estimation. In H. Amman, B. Rustem, & A. Whinston (Eds.), Computational Approaches to Economic Problems (pp. 57–70). Springer.

    Google Scholar 

  • Adams, R. M., Berger, A. N., & Sickles, R. C. (1999). Semiparametric approaches to stochastic panel frontiers with applications in the banking industry. Journal of Business & Economic Statistics, 17(3), 349–358.

    Google Scholar 

  • Adams, R. M., & Sickles, R. C. (2007). Semiparametric efficient distribution free estimation of panel models. Communications in Statistics-Theory and Methods, 36(13), 2425–2442.

    Google Scholar 

  • Ahn, S. C., Lee, Y. H., & Schmidt, P. (2007). Stochastic frontier models with multiple time-varying individual effects. Journal of Productivity Analysis, 27(1), 1–12.

    Google Scholar 

  • Ahn, S. C., Lee, Y. H., & Schmidt, P. (2013). Panel data models with multiple time-varying individual effects. Journal of Econometrics, 174(1), 1–14.

    Google Scholar 

  • Aigner, D., Lovell, C. A. K., & Schmidt, P. (1977). Formulation and estimation of stochastic frontier production function models. Journal of Econometrics, 64(6), 1263–1297.

    Google Scholar 

  • Almanidis, P., Qian, J., & Sickles, R. C. (2014). Stochastic frontier models with bounded inefficiency. In R. C. Sickles & W. C. Horrace (Eds.), Festschrift in honor of Peter Schmidt: Econometric methods and applications (pp. 47–81). Springer.

    Google Scholar 

  • Almanidis, P., & Sickles, R. C. (2012). The skewness problem in stochastic frontier models: Fact or fiction? In I. V. Keilegom & P. W. Wilson (Eds.), Exploring research frontiers in contemporary statistics and econometrics: A Festschrift in honor of Léopold Simar (pp. 201–227). Springer.

    Google Scholar 

  • Alvarez, A., Amsler, C., Orea, L., & Schmidt, P. (2006). Interpreting and testing the scaling property in models where inefficiency depends on firm characteristics. Journal of Productivity Analysis, 25(3), 201–212.

    Google Scholar 

  • Álvarez, I. C., Barbero, J., & Zofío, J. L. (2017). A panel data toolbox for matlab. Journal of Statistical Software, 76(6), 1–27.

    Google Scholar 

  • Amsler, C., Prokhorov, A., & Schmidt, P. (2016). Endogeneity in stochastic frontier models. Journal of Econometrics, 190(2), 280–288.

    Google Scholar 

  • Bada, O., & Liebl, D. (2014). phtt: Panel data analysis with heterogeneous time trends in R. Journal of Statistical Software, 59(6), 1–33.

    Google Scholar 

  • Badunenko, O., Sickles, R. C., & Zelenyuk, V. (2021). Productivity and efficiency analysis in Stata, monograph in progress. Rice University.

    Google Scholar 

  • Banker, R. D., & Maindiratta, A. (1992). Maximum likelihood estimation of monotone and concave production frontiers. Journal of Productivity Analysis, 3(4), 401–415.

    Google Scholar 

  • Battese, G. E., & Broca, S. S. (1997). Functional forms of stochastic frontier production functions and models for technical inefficiency effects: A comparative study for wheat farmers in Pakistan. Journal of Productivity Analysis, 8(4), 395–414.

    Google Scholar 

  • Battese, G. E., & Coelli, T. J. (1988). Prediction of firm-level technical efficiencies with a generalized frontier production function and panel data. Journal of Econometrics, 38(3), 387–399.

    Google Scholar 

  • Battese, G. E., & Coelli, T. J. (1992). Frontier production functions, technical efficiency and panel data: With application to paddy farmers in India. Journal of Productivity Analysis, 3(1–2), 153–169.

    Google Scholar 

  • Battese, G. E., & Coelli, T. J. (1995). A model for technical inefficiency effects in a stochastic frontier production function for panel data. Empirical Economics, 20(2), 325–332.

    Google Scholar 

  • Battese, G. E., Rao, D. S. P., & O’Donnell, C. J. (2004). A metafrontier production function for estimation of technical efficiencies and technology gaps for firms operating under different technologies. Journal of Productivity Analysis, 21(1), 91–103.

    Google Scholar 

  • Belotti, F., Daidone, S., Ilardi, G., & Atella, V. (2013). Stochastic frontier analysis using Stata. The Stata Journal, 13(4), 719–758.

    Google Scholar 

  • Belotti, F., & Ilardi, G. (2018). Consistent inference in fixed-effects stochastic frontier models. Journal of Econometrics, 202(2), 161–177.

    Google Scholar 

  • Bogetoft, P., & Otto, L. (2019). Benchmarking: Benchmark and frontier analysis using DEA and SFA (R package version 0.28).

    Google Scholar 

  • Caudill, S. B., Ford, J. M., & Gropper, D. M. (1995). Frontier estimation and firm-specific inefficiency measures in the presence of heteroscedasticity. Journal of Business & Economic Statistics, 13(1), 105–111.

    Google Scholar 

  • Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European Journal of Operational Research, 2(6), 429–444.

    Google Scholar 

  • Chen, Y.-Y., Schmidt, P., & Wang, H.-J. (2014). Consistent estimation of the fixed effects stochastic frontier model. Journal of Econometrics, 181(2), 65–76.

    Google Scholar 

  • Coelli, T. J., & Henningsen, A. (2020). Package ‘frontier’ (R package version 1.1-8).

    Google Scholar 

  • Coelli, T. J., Rao, D. S. P., O’Donnell, C. J., & Battese, G. E. (2005). An introduction to efficiency and productivity analysis. Springer.

    Google Scholar 

  • Colombi, R., Kumbhakar, S. C., Martini, G., & Vittadini, G. (2014). Closed-skew normality in stochastic frontiers with individual effects and long/short-run efficiency. Journal of Productivity Analysis, 42(2), 123–136.

    Google Scholar 

  • Comans, T., Nguyen, K.-H., Zelenyuk, V., Gray, L., Tran, A., Nguyen, B. H., Wang, Z., & Moretto, N. (2020). The cost of residential aged care (Technical Report Research Paper 9). The Royal Commission into Aged Care Quality and Safety.

    Google Scholar 

  • Cornwell, C., Schmidt, P., & Sickles, R. C. (1990). Production frontiers with cross-sectional and time-series variation in efficiency levels. Journal of Econometrics, 46(1–2), 185–200.

    Google Scholar 

  • Daraio, C., Kerstens, K. H., Nepomuceno, T. C. C., & Sickles, R. C. (2019). Productivity and efficiency analysis software: An exploratory bibliographical survey of the options. Journal of Economic Surveys, 33(1), 85–100.

    Google Scholar 

  • Daraio, C., Kerstens, K. H., Nepomuceno, T. C. C., & Sickles, R. C. (2020). Empirical surveys of frontier applications: A meta-review. International Transactions in Operational Research, 27(2), 709–738.

    Google Scholar 

  • Duygun, M., Hao, J., Isaksson, A., & Sickles, R. C. (2017). World productivity growth: A model averaging approach. Pacific Economic Review, 22(4), 587–619.

    Google Scholar 

  • Fan, Y., Li, Q., & Weersink, A. (1996). Semiparametric estimation of stochastic production frontier models. Journal of Business & Economic Statistics, 14(4), 460–468.

    Google Scholar 

  • Färe, R., He, X., Li, S., & Zelenyuk, V. (2019). A unifying framework for Farrell profit efficiency measurement. Operations Research, 67(1), 183–197.

    Google Scholar 

  • Farrell, M. J. (1957). The measurement of productive efficiency. Series A (General): Journal of the Royal Statistical Society, 120(3), 253–290.

    Google Scholar 

  • Fenochietto, R., & Pessino, C. (2013). Understanding countries’ tax effort (IMF Working Paper).

    Google Scholar 

  • Ferrier, G. D., & Lovell, C. K. (1990). Measuring cost efficiency in banking: Econometric and linear programming evidence. Journal of Econometrics, 46(1–2), 229–245.

    Google Scholar 

  • Glass, A., Kenjegalieva, K., & Sickles, R. C. (2016). A spatial autoregressive stochastic frontier model for panel data with asymmetric efficiency spillovers. Journal of Econometrics, 190(2), 289–300.

    Google Scholar 

  • Greene, W. H. (1980a). Maximum likelihood estimation of econometric frontier functions. Journal of Econometrics, 13(1), 27–56.

    Google Scholar 

  • Greene, W. H. (1980b). On the estimation of a flexible frontier production model. Journal of Econometrics, 13(1), 101–115.

    Google Scholar 

  • Greene, W. H. (1990). A gamma-distributed stochastic frontier model. Journal of Econometrics, 46(1), 141–163.

    Google Scholar 

  • Greene, W. H. (2004). Distinguishing between heterogeneity and inefficiency: Stochastic frontier analysis of the World Health Organization’s panel data on national health care systems. Health Economics, 13(10), 959–980.

    Google Scholar 

  • Greene, W. H. (2005a). Fixed and random effects in stochastic frontier models. Journal of Productivity Analysis, 23(1), 7–32.

    Google Scholar 

  • Greene, W. H. (2005b). Reconsidering heterogeneity in panel data estimators of the stochastic frontier model. Journal of Econometrics, 126(2), 269–303.

    Google Scholar 

  • Griffin, J. E., & Steel, M. F. (2004). Semiparametric Bayesian inference for stochastic frontier models. Journal of Econometrics, 123(1), 121–152.

    Google Scholar 

  • Griffin, J. E., & Steel, M. F. (2007). Bayesian stochastic frontier analysis using winbugs. Journal of Productivity Analysis, 27(3), 163–176.

    Google Scholar 

  • Huang, C. J., Huang, T.-H., & Liu, N.-H. (2014). A new approach to estimating the metafrontier production function based on a stochastic frontier framework. Journal of Productivity Analysis, 42(3), 241–254.

    Google Scholar 

  • Isaksson, A., Shang, C., & Sickles, R. C. (2021). Nonstructural analysis of productivity growth for the industrialized countries: A jackknife model averaging approach. Econometric Reviews, 40(4), 321–358.

    Google Scholar 

  • Jondrow, J., Lovell, C. K., Materov, I. S., & Schmidt, P. (1982). On the estimation of technical inefficiency in the stochastic frontier production function model. Journal of Econometrics, 19(2–3), 233–238.

    Google Scholar 

  • Karakaplan, M. U. (2017). Fitting endogenous stochastic frontier models in Stata. The Stata Journal, 17(1), 39–55.

    Google Scholar 

  • Karakaplan, M. U., & Kutlu, L. (2015). Handling endogeneity in stochastic frontier analysis. Available at SSRN 2607276.

    Google Scholar 

  • Karakaplan, M. U., & Kutlu, L. (2017). Endogeneity in panel stochastic frontier models: An application to the Japanese cotton spinning industry. Applied Economics, 49(59), 5935–5939.

    Google Scholar 

  • Kneip, A., & Sickles, R. C. (2011). Panel data, factor models, and the Solow residual. In I. Van Keilegom & P. W. Wilson (Eds.), Exploring research frontiers in contemporary statistics and econometrics: A Festschrift for Léopold Simar (pp. 83–114). Physica.

    Google Scholar 

  • Kneip, A., Sickles, R. C., & Song, W. (2004). Functional data analysis and mixed effect models. In J. Antoch (Ed.), COMPSTAT 2004—Proceedings in Computational Statistics (pp. 315–326). Physica.

    Google Scholar 

  • Kneip, A., Sickles, R. C., & Song, W. (2012). A new panel data treatment for heterogeneity in time trends. Econometric Theory, 28(3), 590–628.

    Google Scholar 

  • Kneip, A., & Simar, L. (1996). A general framework for frontier estimation with panel data. Journal of Productivity Analysis, 7(2), 187–212.

    Google Scholar 

  • Kneip, A., Simar, L., & Van Keilegom, I. (2015). Frontier estimation in the presence of measurement error with unknown variance. Journal of Econometrics, 184(2), 379–393.

    Google Scholar 

  • Kumbhakar, S. C. (1987). The specification of technical and allocative inefficiency in stochastic production and profit frontiers. Journal of Econometrics, 34(3), 335–348.

    Google Scholar 

  • Kumbhakar, S. C. (1990). Production frontiers, panel data, and time-varying technical inefficiency. Journal of Econometrics, 46(1–2), 201–211.

    Google Scholar 

  • Kumbhakar, S. C., Ghosh, S., & McGuckin, J. T. (1991). A generalized production frontier approach for estimating determinants of inefficiency in U.S. dairy farms. Journal of Business & Economic Statistics, 9(3), 279–286.

    Google Scholar 

  • Kumbhakar, S. C., Lien, G., & Hardaker, J. B. (2014). Technical efficiency in competing panel data models: A study of Norwegian grain farming. Journal of Productivity Analysis, 41(2), 321–337.

    Google Scholar 

  • Kumbhakar, S. C., Park, B. U., Simar, L., & Tsionas, E. G. (2007). Nonparametric stochastic frontiers: A local maximum likelihood approach. Journal of Econometrics, 137(1), 1–27.

    Google Scholar 

  • Kumbhakar, S. C., Parmeter, C. F., & Zelenyuk, V. (2021a). Stochastic frontier analysis: Foundations and advances I. In S. C. Ray, R. Chambers, & S. C. Kumbhakar (Eds.), Handbook of production economics (pp. 1–40). Springer Singapore.

    Google Scholar 

  • Kumbhakar, S. C., Parmeter, C. F., & Zelenyuk, V. (2021b). Stochastic frontier analysis: Foundations and advances II. In S. C. Ray, R. Chambers, & S. C. Kumbhakar (Eds.), Handbook of production economics (pp. 1–38). Springer Singapore.

    Google Scholar 

  • Kumbhakar, S. C., & Tsionas, E. G. (2005). Measuring technical and allocative inefficiency in the translog cost system: A Bayesian approach. Journal of Econometrics, 126(2), 355–384.

    Google Scholar 

  • Kumbhakar, S. C., & Tsionas, E. G. (2008). Estimation of input-oriented technical efficiency using a nonhomogeneous stochastic production frontier model. Agricultural Economics, 38(1), 99–108.

    Google Scholar 

  • Kumbhakar, S. C., Wang, H., & Horncastle, A. P. (2015). A practitioner’s guide to stochastic frontier analysis using Stata. Cambridge University Press.

    Google Scholar 

  • Kutlu, L. (2010). Battese-Coelli estimator with endogenous regressors. Economics Letters, 109(2), 79–81.

    Google Scholar 

  • Lee, Y. H., & Schmidt, P. (1993). A production frontier model with flexible temporal variation in technical efficiency. In H. O. Fried, S. S. Schmidt, & C. K. Lovell (Eds.), The measurement of productive efficiency: Techniques and applications (pp. 237–255). Oxford University Press.

    Google Scholar 

  • Liu, J., Sickles, R. C., & Tsionas, E. G. (2017). Bayesian treatments for panel data stochastic frontier models with time varying heterogeneity. Econometrics, 5(3), 1–21.

    Google Scholar 

  • Malikov, E., Kumbhakar, S. C., & Tsionas, M. G. (2016). A cost system approach to the stochastic directional technology distance function with undesirable outputs: The case of US banks in 2001–2010. Journal of Applied Econometrics, 31(7), 1407–1429.

    Google Scholar 

  • Meeusen, W., & van den Broeck, J. (1977). Efficiency estimation from Cobb-Douglas production functions with composed error. International Economic Review, 18(2), 435–444.

    Google Scholar 

  • Mutter, R. L., Greene, W. H., Spector, W., Rosko, M. D., & Mukamel, D. B. (2013). Investigating the impact of endogeneity on inefficiency estimates in the application of stochastic frontier analysis to nursing homes. Journal of Productivity Analysis, 39(2), 101–110.

    Google Scholar 

  • Nguyen, B. H., & Zelenyuk, V. (2021), Aggregation of outputs and inputs for DEA analysis of hospital efficiency: Economics, operations research and data science perspectives. In J. Zhu & V. Charles (Eds.), Data-enabled analytics: DEA for big data (pp. 123–158). Springer.

    Google Scholar 

  • O’Donnell, C. J., Rao, D. S. P., & Battese, G. E. (2008). Metafrontier frameworks for the study of firm-level efficiencies and technology ratios. Empirical Economics, 34(2), 231–255.

    Google Scholar 

  • Orea, L., & Álvarez, I. C. (2019). A new stochastic frontier model with cross-sectional effects in both noise and inefficiency terms. Journal of Econometrics, 213(2), 556–577.

    Google Scholar 

  • Park, B. U., Sickles, R. C., & Simar, L. (1998). Stochastic panel frontiers: A semiparametric approach. Journal of Econometrics, 84(2), 273–301.

    Google Scholar 

  • Park, B. U., Sickles, R. C., & Simar, L. (2003). Semiparametric-efficient estimation of AR(1) panel data models. Journal of Econometrics, 117(2), 279–309.

    Google Scholar 

  • Park, B. U., Sickles, R. C., & Simar, L. (2007). Semiparametric efficient estimation of dynamic panel data models. Journal of Econometrics, 136(1), 281–301.

    Google Scholar 

  • Park, B. U., Simar, L., & Zelenyuk, V. (2015). Categorical data in local maximum likelihood: Theory and applications to productivity analysis. Journal of Productivity Analysis, 43(2), 199–214.

    Google Scholar 

  • Parmeter, C. F., & Zelenyuk, V. (2019). Combining the virtues of stochastic frontier and data envelopment analysis. Operations Research, 67(6), 1628–1658.

    Google Scholar 

  • Pitt, M. M., & Lee, L.-F. (1981). The measurement and sources of technical inefficiency in the Indonesian weaving industry. Journal of Development Economics, 9(1), 43–64.

    Google Scholar 

  • Rosko, M. D. (2001). Cost efficiency of US hospitals: A stochastic frontier approach. Health Economics, 10(6), 539–551.

    Google Scholar 

  • Schmidt, P., & Sickles, R. C. (1984). Production frontiers and panel data. Journal of Business & Economic Statistics, 2(4), 367–374.

    Google Scholar 

  • Sickles, R. C. (2005). Panel estimators and the identification of firm-specific efficiency levels in parametric, semiparametric and nonparametric settings. Journal of Econometrics, 126(2), 305–334.

    Google Scholar 

  • Sickles, R. C., Song, W., & Zelenyuk, V. (2020). Econometric analysis of productivity: Theory and implementation in R. Handbook of Statistics. In H. D. Vinod & C. R. Rao (Eds.), Financial, macro and micro econometrics using R (Vol. 42, pp. 267–297). Elsevier.

    Google Scholar 

  • Sickles, R. C., & Zelenyuk, V. (2019). Measurement of productivity and efficiency. Cambridge University Press.

    Google Scholar 

  • Simar, L., Lovell, C. K., & van den Eeckaut, P. (1994). Stochastic frontiers incorporating exogenous influences on efficiency (STAT Discussion Papers).

    Google Scholar 

  • Simar, L., Van Keilegom, I., & Zelenyuk, V. (2017). Nonparametric least squares methods for stochastic frontier models. Journal of Productivity Analysis, 47(3), 189–204.

    Google Scholar 

  • Simar, L., & Zelenyuk, V. (2011). Stochastic FDH/DEA estimators for frontier analysis. Journal of Productivity Analysis, 36(1), 1–20.

    Google Scholar 

  • Simar, L., & Zelenyuk, V. (2020). Improving finite sample approximation by central limit theorems for estimates from data envelopment analysis. European Journal of Operational Research, 284(3), 1002–1015.

    Google Scholar 

  • Stevenson, R. E. (1980). Likelihood functions for generalized stochastic frontier estimation. Journal of Econometrics, 13(1), 57–66.

    Google Scholar 

  • Van den Broeck, J., Koop, G., Osiewalski, J., & Steel, M. F. (1994). Stochastic frontier models: A Bayesian perspective. Journal of Econometrics, 61(2), 273–303.

    Google Scholar 

  • Wang, H. J. (2002). Heteroscedasticity and non-monotonic efficiency effects of a stochastic frontier model. Journal of Productivity Analysis, 18(3), 241–253.

    Google Scholar 

  • Wang, H. J., & Schmidt, P. (2002). One-step and two-step estimation of the effects of exogenous variables on technical efficiency levels. Journal of Productivity Analysis, 157, 286–296.

    Google Scholar 

  • Zelenyuk, V. (2020). Aggregation of inputs and outputs prior to data envelopment analysis under big data. European Journal of Operational Research, 282(1), 172–187.

    Google Scholar 

  • Zuckerman, S., Hadley, J., & Lezzoni, L. (1994). Measuring hospital efficiency with frontier cost functions. Journal of Health Economics, 13(3), 255–280.

    Google Scholar 

Download references

Acknowledgements

We thank the Editor and two anonymous referees for fruitful comments. Bao Hoang Nguyen and Valentin Zelenyuk acknowledge the support from the University of Queensland and the financial support from the Australian Research Council (FT170100401). We also thank Hong Ngoc Nguyen, Zhichao Wang, Evelyn Smart, Anne-Claire Bouton, and Travis Alan Smith for their valuable feedback. These individuals and organisations are not responsible for the views expressed in this paper.

Author information

Authors and Affiliations

  1. School of Economics, The University of Queensland, Brisbane, QLD, Australia

    Bao Hoang Nguyen

  2. Economics Department, Rice University, Houston, TX, USA

    Robin C. Sickles

  3. School of Economics and Centre for Efficiency and Productivity Analysis, The University of Queensland, Brisbane, QLD, Australia

    Valentin Zelenyuk

Authors
  1. Bao Hoang Nguyen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Robin C. Sickles
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Valentin Zelenyuk
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Valentin Zelenyuk .

Editor information

Editors and Affiliations

  1. Caulfield, VIC, VIC, Australia

    Duangkamon Chotikapanich

  2. St Lucia, QLD, Australia

    Alicia N. Rambaldi

  3. Southport, QLD, Australia

    Nicholas Rohde

Appendix

Appendix

Box A.1: Stata codes for the empirical illustration

figure a
figure b
figure c
figure d
figure e

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Nguyen, B.H., Sickles, R.C., Zelenyuk, V. (2022). Efficiency Analysis with Stochastic Frontier Models Using Popular Statistical Softwares. In: Chotikapanich, D., Rambaldi, A.N., Rohde, N. (eds) Advances in Economic Measurement. Palgrave Macmillan, Singapore. https://doi.org/10.1007/978-981-19-2023-3_3

Download citation

  • DOI: https://doi.org/10.1007/978-981-19-2023-3_3

  • Published:

  • Publisher Name: Palgrave Macmillan, Singapore

  • Print ISBN: 978-981-19-2022-6

  • Online ISBN: 978-981-19-2023-3

  • eBook Packages: Economics and FinanceEconomics and Finance (R0)

Publish with us

Policies and ethics

Search

Navigation