Aspects of econometric modelling

Abstract

This thesis is concerned with some of the problems of econometric modelling with especial emphasis on the use of linear approximations, nonlinear estimation and specification tests. The motivation for this approach is given in the introductory chapter. In Chapter 2, the validity of linear approximations and their effects on estimation and hypothesis testing are discussed and a test for linearity is suggested. In respect of estimation, a new algorithm (based on variable linearisation) for estimating non-linear single equation functions is developed in Chapter 3, and the technique is subsequently extended to non-linear simultaneous equation systems in Chapter 9. With regard to model specification tests, emphasis is placed on the use of the Lagrange multiplier (LM) principle. In Chapter 4, a comparative study of different forms of the LM test statistic is conducted and some of its properties are discussed. Applications of the LM test are made in Chapters 5, 6 and 10. In Chapter 5, several tests for univariate normality are proposed, and one of the tests is generalized to the multivariate case in Chapter 10. Since most of the available model specification tests are one-directional and are not valid in the presence of more than one misspecification, a simultaneous approach to testing model specification is considered in Chapter 6. Tests developed for classical regression model are not applicable to limited dependent variable (LDV) models, so that specification tests for LDV models are discussed separately in Chapter 7. The test procedures mentioned above are suitable for testing nested hypotheses. In Chapter 8, test procedures for non-nested models are discussed and an attempt is made to test nested and non-nested hypotheses jointly. In the last chapter of the thesis suggestions are made to unify model estimation and testing by using robust estimates to calculate test statistics in order to increase their efficiency. Show more