Abstract
The distinguishing feature of the Bayesian approach in performance evaluation is that parameter uncertainty of the various models is formally taken into account along with model uncertainty as well. The usual sampling-theory approach proceeds conditionally on the parameter estimates that have been obtained. Of course, the bootstrap can be used but the justification of the bootstrap itself is only asymptotic. We do not intend here to compare and contrast, in detail, the Bayesian versus the sampling-theory approach. We should mention, however, that the Bayesian approach is equipped with numerical techniques that can handle complicated models of performance, where the sampling-theory approach is quite difficult to implement.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
- 2.
All random effects are mutually independent and independent of the regressors for all DMUs and at all time periods.
- 3.
We assume for simplicity that we have only one output and that technical inefficiency and allocative distortion parameters \(\xi\) are time-invariant.
- 4.
These can be identified even if there are firm and time effects in the production function.
- 5.
See Table F4.4 in http://pages.stern.nyu.edu/~wgreene/Text/Edition7/tablelist8new.htm which contains data sets for W. Greene, Econometric Analysis, 8th edition, Pearson, 2018.
References
Assaf, A.G., H. Oh, and M.G. Tsionas. 2017. Bayesian approach for the measurement of tourism performance: A case of stochastic frontier models. Journal of Travel Research 56 (2): 172–186.
Atkinson, S.C., and M.G. Tsionas. 2016. Directional distance functions: Optimal endogenous directions. Journal of Econometrics 190: 301–314.
Chib, S. 1995. Marginal likelihood from the Gibbs output. Journal of the American Statistical Association 90: 1313–1321.
Cornwell, C., P. Schmidt, and R. Sickles. 1990. Production Frontiers with cross sectional and time series variation in efficiency levels. Journal of Econometrics 46: 185–200.
DiCiccio, T.J., R.E. Kass, A. Raftery, and L. Wasserman. 1997. Computing Bayes factors using simulation and asymptotic approximations. Journal of the American Statistical Association 92: 903–915.
Fernandez, C., G. Koop, and M.F.J. Steel. 2002. Multiple-output production with undesirable outputs. Journal of the American Statistical Association 97: 432–442.
Fernandez, C., J. Osiewalski, and M.F.J. Steel. 1997. On the use of panel data in stochastic frontier models with improper priors. Journal of Econometrics 79: 169–193.
Fried, H.O., C.A.K. Lovell, and S.S. Schmidt. 1993. The measurement of productive efficiency and productivity growth. Oxford: Oxford University Press.
Gandhi, A., S. Navarro, and D. Rivers. 2013. On the identification of production functions: How heterogeneous is productivity? Working Paper.
Geweke, J. 1989. Bayesian inference in econometric models using Monte Carlo integration. Econometrica 57: 1317–1339.
Geweke, J. 1991. Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments. In Bayesian statistics 4, ed. J.M. Bernardo, J.O. Berger, A.P. Dawid, and A.F.M. Smith. Oxford: Oxford Press.
Geweke, J. 1999. Using simulation methods for Bayesian econometric models: Inference, development, and communication. Econometric Reviews 18 (1): 1–73.
Greene, W. 1990. A gamma-distributed stochastic frontier model. Journal of Econometrics 46: 141–163.
Greene, W. 2005. Reconsidering heterogeneity in panel data estimators of the stochastic frontier model. Journal of Econometrics 126 (2): 269–303.
Griffin, J. 2011. Bayesian clustering of distributions in stochastic frontier analysis. Journal of Productivity Analysis 36: 275–283.
Griffin, J.E., and M.F.J. Steel. 2004. Semiparametric Bayesian inference for stochastic frontier models. Journal of Econometrics 123: 121–152.
Koop, G., J. Osiewalski, and M.F.J. Steel. 1997. Bayesian efficiency analysis through individual effects. Journal of Econometrics 76: 7–105.
Koop, G., M.F.J. Steel, and J. Osiewalski. 1995. Posterior analysis of stochastic frontiers models using Gibbs sampling. Computational Statistics 10: 353–373.
Kumbhakar, S.C. 1997. Modeling allocative inefficiency in a translog cost function and cost share equations: An exact relationship. Journal of Econometrics 76: 351–356.
Kumbhakar, S.C., and E.G. Tsionas. 2005a. Measuring technical and allocative inefficiency in the translog cost system: A Bayesian approach. Journal of Econometrics 126 (2): 355–384.
Kumbhakar, S.C., and E.G. Tsionas. 2005b. The Joint Measurement of Technical and Allocative Inefficiencies: An application of Bayesian inference in nonlinear random-effects models. Journal of the American Statistical Association 100: 736–747.
Kumbhakar, S.C., B.U. Park, L. Simar, and M.G. Tsionas. 2007. Nonparametric stochastic frontiers: A local maximum likelihood approach. Journal of Econometrics 137 (1): 1–27.
Kutlu, L. 2010. Battese-Coelli estimator with endogenous regressors. Economics Letters 109 (2): 79–81.
Levinsohn, J., and A. Petrin. 2003. Estimating production functions using inputs to control for unobservables. Review of Economic Studies 70 (2): 317–341.
Marschak, J., and W.H. Andrews. 1944. Random simultaneous equations and the theory of production. Econometrica 12 (3/4): 143–205.
Olley, G.S., and A. Pakes. 1996. The dynamics of productivity in the telecommunications equipment industry. Econometrica 64 (6): 1263–1297.
Simar, L., and W.P. Wilson. 1998. Sensitivity analysis of efficiency scores: How to bootstrap in nonparametric frontier models. Management Science 44 (1): 49–61.
Simar, L., and W.P. Wilson. 2000. Statistical inference in nonparametric frontier models: The state of the art. Journal of Productivity Analysis 13: 49–78.
Simar, L., and W.P. Wilson. 2004. Performance of the bootstrap for DEA estimators and iterating the principle. In Handbook on Data Envelopment Analysis, ed. W.W. Cooper, M.L. Seiford, and J. Zhu, 265–298. Dordrecht, The Netherlands: Kluwer Academic Publishers.
Tanner, M.A., and W.H. Wong. 1987. The calculation of posterior distributions by data augmentation. Journal of the American Statistical Association 82: 528–540.
Tran, K., and M.G. Tsionas. 2013. GMM estimation of stochastic frontier model with endogenous regressors. Economics Letters 108 (1): 233–236.
Tran, K., and M.G. Tsionas. 2015. One the estimation of zero-inefficiency stochastic frontier models with endogenous regressors. Economics Letters 147: 19–22.
Tran, K., and M.G. Tsionas. 2016. Endogeneity in stochastic frontier models: Copula approach without external instruments. Economics Letters 133: 85–88.
Tsionas, E.G. 2000. Full likelihood inference in normal-gamma stochastic frontier models. Journal of Productivity Analysis 13 (3): 183–205.
Tsionas, E.G. 2006. Inference in dynamic stochastic frontier models. Journal of Applied Econometrics 21 (5): 669–676.
Tsionas, E.G. 2012. Maximum likelihood estimation of stochastic frontier models by the Fourier transform. Journal of Econometrics 170: 234–248.
Tsionas, M.G. 2017. “When, where and how” of efficiency estimation: Improved procedures for stochastic frontier models. Journal of the American Statistical Association 112 (519): 948–965.
Tsionas, E.G., and S.C. Kumbhakar. 2012. Firm heterogeneity, persistent and transient technical inefficiency: A generalized true random-effects model. Journal of Applied Econometrics 29: 110–132.
van den Broeck, J., G. Koop, J. Osiewalski, and M.F.J. Steel. 1994. Stochastic frontier models: A Bayesian perspective. Journal of Econometrics 61: 273–303.
Acknowledgements
The author is indebted to an anonymous reviewer for comments on an earlier version of this chapter. Dedicated to John Geweke, Bill Greene, and Subal Kumbhakar for all that they taught me throughout the years.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 The Author(s)
About this chapter
Cite this chapter
Tsionas, M.G. (2019). Bayesian Performance Evaluation. In: ten Raa, T., Greene, W. (eds) The Palgrave Handbook of Economic Performance Analysis. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-030-23727-1_11
Download citation
DOI: https://doi.org/10.1007/978-3-030-23727-1_11
Published:
Publisher Name: Palgrave Macmillan, Cham
Print ISBN: 978-3-030-23726-4
Online ISBN: 978-3-030-23727-1
eBook Packages: Economics and FinanceEconomics and Finance (R0)