This thesis considers the problem of estimating limited dependent variable models when the latent residuals are heteroskedastic normally distributed random variables. Commonly
used estimators are generally inconsistent in such situations. Two estimation methods that allow consistent estimation of the parameters of interest are presented and shown to be consistent when the latent residuals are heteroskedastic of unknown form. Both estimators use recent advances in the econometric literature on nonparametric estimation
and deal with the unknown form of heteroskedasticity by approximating the variance using a Fourier series type approximation.
The first estimator is based on the method of maximum likelihood and involves maximising
the likelihood function by choice of the parameters of the variance function approximation
and the other parameters of interest. Consistency is shown to hold in the three most popular limited dependent variable models — the Probit, Tobit, and sample selection models — provided that the number of terms in the approximation increases with the sample size. The second estimator, which can be used to estimate the Tobit and sample selection models, is based on a two-step procedure, using Fourier series approximations
in both steps. Consistency and asymptotic normality are proven under restrictions on the rate of increase of the number of parameters in the approximating functions.
Finally, a small Monte Carlo experiment is conducted to examine the small sample properties of the estimators. The results show that the estimators perform quite well and in many cases reduce the bias, relative to the commonly used estimators, with little or no efficiency loss. / Arts, Faculty of / Vancouver School of Economics / Graduate
| Identifer | oai:union.ndltd.org:UBC/oai:circle.library.ubc.ca:2429/30691 |
| Date | January 1990 |
| Creators | Donald, Stephen Geoffrey |
| Publisher | University of British Columbia |
| Source Sets | University of British Columbia |
| Language | English |
| Detected Language | English |
| Type | Text, Thesis/Dissertation |
| Rights | For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. |
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