Some contributions to finite-sample analysis in three econometric models
Degree GrantorUniversity of Canterbury
Degree NameDoctor of Philosophy
In the standard classical regression model the most commonly used procedures for estimation are based on the Ordinary Least Squares Method, which is justified on the basis of well known finite-sample properties. However, this model consists of a number of assumptions, such as, for example, homoskedastic, serially independent and normally distributed disturbances and nonstochastic regressors. By changing these assumptions in one way or another, different estimating situations are created, in many of which the OLS estimator may have no statistical justification at all. Further, alternative estimation methods have often been justified only on the basis of their asymptotic properties, although in practice economists frequently have to base their statistical analysis on a relatively small number of observations. This suggests that the particular estimator to use in any situation should be chosen on the basis of finite-sample considerations. The analysis of finite-sample properties of commonly used estimators in three well known Econometric models is the focus of this thesis. In particular the three models considered are: the limited-information simultaneous equations model, the nonnormal linear regression model and the nonnormal limited-information simultaneous equation model. The techniques used include the derivation of the estimators' exact distribution and when this is analytically intractable Monte Carlo methods are employed. The limited-information simultaneous equation model is analyzed in two stages. First, a useful method of numerically evaluating many of the commonly used estimators, including the two-stage least squares estimator, is presented. Secondly this method is then used, and combined with Monte Carlo analysis, to compare the distributions of the limited-information maximum likelihood and two-stage least squares estimators in misspecified simultaneous equations models. The result of this comparison indicates the superior performance of the limited-information maximum likelihood estimator over the two-stage least squares estimator in both correctly specified and misspecified simultaneous equations models. Recently, models with possibly nonnormal distributed disturbances have attracted more attention. For such models, independence and uncorrelatedness of the disturbance terms are not equivalent. Using the nonnormal regression model the statistical consequences of distinguishing between independence and uncorrelatedness are considered when the disturbances are Student-t distributed. The results obtained demonstrate that the distinction between the two assumptions is an important one and the consequences of making the wrong assumption can be serious. Consequently, specification tests are also presented which test for uncorrelatedness versus independence in the elliptically symmetric family. The nonnormal limited-information simultaneous equation model provides a relatively new area of analysis as there are few published results available on the effects of nonnormal disturbances in the limited-information simultaneous equation model. The objective here is to combine the themes pursued separately in the other two models previously considered. However, to narrow the range of possible models that can be examined, attention is focussed only on the exactly-identified simultaneous equation model. This model has a number of interesting features when the reduced-form disturbances are normally distributed. These features are illustrated and then comparisons are made with the same model when the distribution of the disturbances is widened to include the Student-t family. In this case, as for the nonnormal linear regression model, a distinction needs to be made between independently distributed and jointly distributed disturbances. The consequences of these different assumptions are shown to be important; specification tests relating to this distinction are therefore also presented.