Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-27T18:25:51.760Z Has data issue: false hasContentIssue false
  • English
  • Français

Asymptotic Distribution of the Maximum Likelihood Estimator for a Stochastic Frontier Function Model with a Singular Information Matrix

Published online by Cambridge University Press:  11 February 2009

Lung-Fei Lee
Lung-Fei Lee
Affiliation:
University of Michigan
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper investigates the asymptotic distribution of the maximum likelihood estimator in a stochastic frontier function when the firms are all technically efficient. For such a situation the true parameter vector is on the boundary of the parameter space, and the scores are linearly dependent. The asymptotic distribution of the maximum likelihood estimator is shown to be a mixture of certain truncated distributions. The maximum likelihood estimates for different parameters may have different rates of stochastic convergence. The model can be reparameterized into one with a regular likelihood function. The likelihood ratio test statistic has the usual mixture of chi-square distributions as in the regular case.

Type
Articles
Information
Econometric Theory , Volume 9 , Issue 3 , June 1993 , pp. 413 - 430
Copyright
Copyright © Cambridge University Press 1993

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Aigner, D.J., Lovell, C.A.K. & Schmidt, P.. Formulation and estimation of stochastic frontier production function models. Journal of Econometrics 6 (1977): 21–37.CrossRefGoogle Scholar
2.Chant, D.On asymptotic tests of composite hypotheses. Biometrika 61 (1974): 291–298.CrossRefGoogle Scholar
3.Chernoff, H.On the distribution of the likelihood ratio. Annals of Mathematical Statistics 25 (1954): 573–578.CrossRefGoogle Scholar
4.Forsund, F.R., Lovell, C.A.K. & Schmidt, P.. A survey of frontier production functions and of their relationship to efficiency measurement. Journal of Econometrics 13 (1980): 5–25.CrossRefGoogle Scholar
5.Gourieroux, C., Holly, A. & Monfort, A.. Likelihood ratio test, Wald test, and Kuhn-Tucker test in linear models with inequality constraints on the regression parameters. Econometrica 50 (1982): 63–80.CrossRefGoogle Scholar
6.Kodde, D.A. & Palm, F.C.. Wald criterion for jointly testing equality and inequality restrictions. Econometrica 54 (1986): 1243–1248.Google Scholar
7.Lee, L.F. & Chesher, A.. Specification testing when score test statistics are identically zero. Journal of Econometrics 31 (1986): 121–149.CrossRefGoogle Scholar
8.Lewin, A.Y. & Lovell, C.A. Knox. Frontier analysis: Parametric and nonparametric approaches, Annals, Journal of Econometrics, Vol. 46, No. 1/2. Amsterdam: North-Holland, 1990.Google Scholar
9.Moran, P.A.P.Maximum-likelihood estimation in non-standard conditions. Proceeding of Cambridge Philos. Society 70 (1971): 441–450.CrossRefGoogle Scholar
10.Olson, J.A., Schmidt, P. & Waldman, D.M.. A Monte Carlo study of estimators of stochastic frontier production functions. Journal of Econometrics 13 (1980): 67–82.Google Scholar
11.Rao, C.R.Linear Statistical Inference and its Applications, 2nd ed.New York: Wiley, 1973.CrossRefGoogle Scholar
12.Rothenberg, T.J.Identification in parametric models. Econometrica 39 (1971): 577–591.Google Scholar
13.Sargan, J.D.Identification and lack of identification. Econometrica 51 (1983): 1605–1633.CrossRefGoogle Scholar
14.Schmidt, P.Frontier production functions. Econometric Reviews 4 (1985): 289–328.CrossRefGoogle Scholar
15.Schmidt, P. & Lin, T.-F.. Simple tests of alternative specification in stochastic frontier models. Journal of Econometrics 24 (1984): 349–361.CrossRefGoogle Scholar
16.Silvey, S.D.Statistical Inference. London: Chapman and Hall, 1975.Google Scholar
17.Waldman, D.M.A stationary point for the stochastic frontier likelihood. Journal of Econometrics 18 (1982): 275–279.Google Scholar
18.Wolak, F.A.Local and global testing of linear and nonlinear inequality constraints in nonlinear econometric models. Econometric Theory 5 (1989): 1–35.CrossRefGoogle Scholar
19.Wolak, F.A.Testing inequality constraints in linear econometric models. Journal of Econometrics 41 (1989): 205–235.Google Scholar
20.Wolak, F.A.The local natUre of hypothesis tests involving inequality constraints in nonlinear models. Econometrica 59 (1991): 981–995.Google Scholar
21.Yancy, T.A., Judge, G.G. & Bock, M.E.. Testing multiple equality and inequality hypothesis in economics. Economic Letters 4 (1981): 249–255.Google Scholar