Abstract
The paper takes up inference in the stochastic frontier model with gamma distributed inefficiency terms, without restricting the gamma distribution to known integer values of its shape parameter (the Erlang form). The paper shows that Gibbs sampling with data augmentation can be used in a computationally efficient way to explore the posterior distribution of the model and conduct inference regarding parameters as well as functions of interest related to technical inefficiency.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aigner, D., C.A. Knox-Lovell, and P. Schmidt. (1977). “Formulation and Estimation of Stochastic Frontier Production Function Models.” Journal of Econometrics 6, 21-37.
Bauer, P.W. (1990). “Recent Developments in the Econometric Estimation of Frontiers.” Journal of Econometrics 46, 39-56.
Brooks, S.P., P. Dellaportas and G.O. Roberts. (1997). “A Total Variation Method for Diagnosing Convergence of MCMC Algorithms.” Journal of Computational and Graphical Statistics, forthcoming
van der Broeck, J., G. Koop, J. Osiewalski, and M.F.J. Steel. (1994). “Stochastic Frontier Models: A Bayesian Perspective.” Journal of Econometrics 61, 273-303.
Fernandez, C., J. Osiewalski, and M.F.J. Steel. (1997). “On the Use of Panel Data in Stochastic Frontier Models.” Journal of Econometrics 79, 169-193.
Gelfand, A.E., and A.F.M. Smith. (1989). “Sampling Based Approaches to Calculating Marginal Densities.” Journal of the American Statistical Association 85, 398-409.
Gelman, A., and D. Rubin. (1992). “Inference from Iterative Simulation Using Multiple Sequences.” Statistical Science 7, 457-511.
Geweke, J. (1992). “Evaluating the Accuracy of Sampling-Based Approaches to the Calculation of Posterior Moments.” In J.M. Bernardo, A.F.M. Smith, A.P. Dawid, and J.O. Berger (eds.), Bayesian Statistics, vol. 4, pp. 169-193. New York: Oxford University Press.
Geweke, J.F. (1993). “Bayesian Treatment of the Independent Student-t Linear Model.” Journal of Applied Econometrics 8, S19-S40.
Greene, W.H. (1990). “A Gamma-Distributed Stochastic Frontier Model.” Journal of Econometrics 46, 141-163.
Greene, W.H. (1993). “The Econometric Approach to Efficiency Analysis.” In H.O. Fried, C.A.K. Lovell, and S.S. Schmidt (eds.), The Measurement of Productive Efficiency: Techniques and Applications. Oxford: Oxford University Press.
Koop, G., M.F.J. Steel, and J. Osiewalski. (1995). “Posterior Analysis of Stochastic Frontier Models Using Gibbs Sampling.” Computational Statistics 10, 353-373.
Meeusen, W., and J. van der Broeck. (1977). “Efficiency Estimation from Cobb-Douglas Production Functions with Composed Error.” International Economic Review 18, 435-444.
Osiewalski, J., and M.F.J. Steel. (1998). “Numerical Tools for the Bayesian Analysis of Stochastic Frontier Models.” Journal of Productivity Analysis 10, 103-117
Ripley, W. (1988). Stochastic Simulation. New York: Wiley.
Ritter, C. (1993). “The Normal-Gamma Frontier Model under a Common Vague Prior Does Not Produce a Proper Posterior.” Mimeo, Universite Catholique de Louvain, Louvain-la-Neuve.
Ritter, C., and L. Simar. (1993). “Two Notes on the Normal-Gamma Stochastic Frontier Model: A Simple Analysis of the American Utility Data and Corrections to the Results in Greene (1990).” Mimeo, University of Louvain, Louvain-la-Neuve.
Ritter, C., and L. Simar. (1997). “Pitfalls of Normal-Gamma Stochastic Frontier Models.” Journal of Productivity Analysis 8, 167-182.
Roberts, C.O., and A.F.M. Smith. (1994). “Simple Conditions for the Convergence of the Gibbs Sampler and Hastings-Metropolis Algorithms.” Stochastic Processes and their Applications 49, 207-216.
Smith, A.F.M., and C.O. Roberts. (1993). “Bayesian Computation via the Gibbs Sampler and Related Markov Chain Monte Carlo Methods.” Journal of the Royal Statistical Society B55, 3-23.
Stevenson, R.E. (1980). “Likelihood Functions for Generalized Stochastic Frontier Estimation.” Journal of Econometrics 13, 57-66.
Tanner, M.A., and W.H. Wong. (1987). “The Calculation of Posterior Distributions by Data Augmentation (with Discussion).” Journal of the American Statistical Association 82, 528-550.
Tierney, L. (1994). “Markov Chains for Exploring Posterior Distributions (with Discussion).” Annals of Statistics 22, 1701-1762.
Tsionas, E.G. (1999a). “Monte Carlo Inference in Econometric Models with Symmetric Stable Disturbances.” Journal of Econometrics 88, 365-401.
Tsionas, E.G. (1999b). “Bayesian Analysis of the Multivariate Poisson Distribution.” Communications in Statistics (Theory and Methods) 28, 431-451.
Yu, B., and P. Mykland. (1997). “Looking at Markov Sampler through CUSUM Path Plots: A Simple Diagnostic Idea.” Statistics and Computing, forthcoming.
Verdinelli, I., and L. Wasserman. (1995). “Computing Bayes Factors Using a Generalization of the Savage-Dickey Density Ratio.” Journal of the American Statistical Association 90, 614-618
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Tsionas, E.G. Full Likelihood Inference in Normal-Gamma Stochastic Frontier Models. Journal of Productivity Analysis 13, 183–205 (2000). https://doi.org/10.1023/A:1007845424552
Issue Date:
DOI: https://doi.org/10.1023/A:1007845424552