Stochastic frontier models with dependent error components. (English) Zbl 1135.91407
Summary: In the productivity modelling literature, the disturbances \(U\) (representing technical inefficiency) and \(V\) (representing noise) of the composite error \(W = V - U\) of the stochastic frontier model are assumed to be independent random variables. By employing the copula approach to statistical modelling, the joint behaviour of \(U\) and \(V\) can be parametrized thereby allowing the data the opportunity to determine the adequacy of the independence assumption. In this context, three examples of the copula approach are given: the first is algebraic (the logistic-exponential stochastic frontier model with margins bound by the Farlie-Gumbel-Morgenstern copula), the second uses a cross-section of cost data sampled from the US electrical power industry and the third constructs a model for panel data that is then used to conduct a Monte Carlo exercise in which estimator bias is examined when the dependence structure is incorrectly ignored.
MSC:
| 91B70 | Stochastic models in economics |
Software:
MathematicaReferences:
| [1] | DOI: 10.1016/0304-4076(88)90053-X · doi:10.1016/0304-4076(88)90053-X |
| [2] | DOI: 10.1007/BF00158774 · doi:10.1007/BF00158774 |
| [3] | Burns R., The Simulated Maximum Likelihood Estimation of Stochastic Frontier Models with Correlated Error Components (2004) |
| [4] | Carley H., Distributions With Given Marginals and Statistical Modelling pp 29– (2002) · doi:10.1007/978-94-017-0061-0_4 |
| [5] | Cherubini U., Copula Methods in Finance (2004) · Zbl 1163.62081 · doi:10.1002/9781118673331 |
| [6] | Coelli T., An Introduction to Efficiency and Productivity Analysis (1998) · Zbl 0935.62128 · doi:10.1007/978-1-4615-5493-6 |
| [7] | Dall’Aglio G., Advances in Probability Distributions with Given Marginals: Beyond the Copulas pp 13– (1991) · doi:10.1007/978-94-011-3466-8 |
| [8] | DOI: 10.1007/s003550000085 · Zbl 1069.91584 · doi:10.1007/s003550000085 |
| [9] | DOI: 10.1006/jmva.2001.2017 · Zbl 1002.62016 · doi:10.1006/jmva.2001.2017 |
| [10] | Fisher N. I., Encyclopedia of Statistical Sciences 1 pp 159– (1997) |
| [11] | Frechet M., Ann. Univ. Lyon, Section A, Series 3 14 pp 53– (1951) |
| [12] | Frees E. W., North American Actuarial Journal 2 pp 1– (1998) · Zbl 1081.62564 · doi:10.1080/10920277.1998.10595667 |
| [13] | DOI: 10.1016/0304-4076(90)90052-U · Zbl 0713.62110 · doi:10.1016/0304-4076(90)90052-U |
| [14] | DOI: 10.1023/A:1022853416499 · doi:10.1023/A:1022853416499 |
| [15] | Hoeffding W., Schriften des Mathematischen Instituts und des Instituts fur Angewandte Mathematik der Universitat Berlin 5 pp 181– (1940) |
| [16] | Joe H., Multivariate Models and Dependence Concepts (1997) · Zbl 0990.62517 · doi:10.1201/b13150 |
| [17] | DOI: 10.1016/0304-4076(90)90055-X · doi:10.1016/0304-4076(90)90055-X |
| [18] | Kumbhakar S. C., Stochastic Frontier Analysis (2000) · Zbl 0968.62080 · doi:10.1017/CBO9781139174411 |
| [19] | Luke Y. L., The Special Functions and their Approximations (1969) · Zbl 0193.01701 |
| [20] | DOI: 10.1016/S0304-4076(01)00123-3 · Zbl 1030.62001 · doi:10.1016/S0304-4076(01)00123-3 |
| [21] | Moore D. S., The Annals of Statistics 3 pp 599– (1975) |
| [22] | DOI: 10.1111/j.1467-6419.2004.00215.x · doi:10.1111/j.1467-6419.2004.00215.x |
| [23] | Nelsen R. B., Advances in Probability Distributions with Given Marginals: Beyond the Copulas pp 51– (1991) · doi:10.1007/978-94-011-3466-8_3 |
| [24] | Nelsen R. B., An Introduction to Copulas, 2. ed. (2006) · Zbl 1152.62030 |
| [25] | Pal M., Indian Economic Review 39 pp 7– (2004) |
| [26] | Pal M., Sankhya B 61 pp 337– (1999) |
| [27] | DOI: 10.1016/0304-4076(80)90044-5 · Zbl 0427.62091 · doi:10.1016/0304-4076(80)90044-5 |
| [28] | Schweizer B., Advances in Probability Distributions with Given Marginals: Beyond the Copulas pp 51– (1991) |
| [29] | Schweizer B., Probabilistic Metric Spaces (1983) · Zbl 0546.60010 |
| [30] | Sklar A., Publications de l’Institute de Statistique de l’Universite de Paris 8 pp 229– (1959) |
| [31] | Sklar A., Kybernetika 9 pp 449– (1973) |
| [32] | Sklar A., Distributions With Fixed Marginals And Related Topics, Volume 28 pp 1– (1996) · doi:10.1214/lnms/1215452606 |
| [33] | Slater L. J., Generalized Hypergeometric Functions (1966) · Zbl 0135.28101 |
| [34] | DOI: 10.1111/1368-423X.00101 · Zbl 1037.62047 · doi:10.1111/1368-423X.00101 |
| [35] | DOI: 10.1561/0800000005 · Zbl 1195.91130 · doi:10.1561/0800000005 |
| [36] | DOI: 10.1111/j.1468-0084.2006.00158.x · doi:10.1111/j.1468-0084.2006.00158.x |
| [37] | Wolfram S., The Mathematica Book, 4. ed. (1999) |
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